aim of calorimetry experiment

5.2 Calorimetry

Learning objectives.

By the end of this section, you will be able to:

• Explain the technique of calorimetry
• Calculate and interpret heat and related properties using typical calorimetry data

One technique we can use to measure the amount of heat involved in a chemical or physical process is known as calorimetry . Calorimetry is used to measure amounts of heat transferred to or from a substance. To do so, the heat is exchanged with a calibrated object (calorimeter). The temperature change measured by the calorimeter is used to derive the amount of heat transferred by the process under study. The measurement of heat transfer using this approach requires the definition of a system (the substance or substances undergoing the chemical or physical change) and its surroundings (all other matter, including components of the measurement apparatus, that serve to either provide heat to the system or absorb heat from the system).

A calorimeter is a device used to measure the amount of heat involved in a chemical or physical process. For example, when an exothermic reaction occurs in solution in a calorimeter, the heat produced by the reaction is absorbed by the solution, which increases its temperature. When an endothermic reaction occurs, the heat required is absorbed from the thermal energy of the solution, which decreases its temperature ( Figure 5.11 ). The temperature change, along with the specific heat and mass of the solution, can then be used to calculate the amount of heat involved in either case.

Calorimetry measurements are important in understanding the heat transferred in reactions involving everything from microscopic proteins to massive machines. During her time at the National Bureau of Standards, research chemist Reatha Clark King performed calorimetric experiments to understand the precise heats of various fluorine compounds. Her work was important to NASA in their quest for better rocket fuels.

Scientists use well-insulated calorimeters that all but prevent the transfer of heat between the calorimeter and its environment, which effectively limits the “surroundings” to the nonsystem components with the calorimeter (and the calorimeter itself). This enables the accurate determination of the heat involved in chemical processes, the energy content of foods, and so on. General chemistry students often use simple calorimeters constructed from polystyrene cups ( Figure 5.12 ). These easy-to-use “coffee cup” calorimeters allow more heat exchange with the outside environment, and therefore produce less accurate energy values.

Commercial solution calorimeters are also available. Relatively inexpensive calorimeters often consist of two thin-walled cups that are nested in a way that minimizes thermal contact during use, along with an insulated cover, handheld stirrer, and simple thermometer. More expensive calorimeters used for industry and research typically have a well-insulated, fully enclosed reaction vessel, motorized stirring mechanism, and a more accurate temperature sensor ( Figure 5.13 ).

Before discussing the calorimetry of chemical reactions, consider a simpler example that illustrates the core idea behind calorimetry. Suppose we initially have a high-temperature substance, such as a hot piece of metal (M), and a low-temperature substance, such as cool water (W). If we place the metal in the water, heat will flow from M to W. The temperature of M will decrease, and the temperature of W will increase, until the two substances have the same temperature—that is, when they reach thermal equilibrium ( Figure 5.14 ). If this occurs in a calorimeter, ideally all of this heat transfer occurs between the two substances, with no heat gained or lost by either its external environment. Under these ideal circumstances, the net heat change is zero:

This relationship can be rearranged to show that the heat gained by substance M is equal to the heat lost by substance W:

The magnitude of the heat (change) is therefore the same for both substances, and the negative sign merely shows that q substance M and q substance W are opposite in direction of heat flow (gain or loss) but does not indicate the arithmetic sign of either q value (that is determined by whether the matter in question gains or loses heat, per definition). In the specific situation described, q substance M is a negative value and q substance W is positive, since heat is transferred from M to W.

Example 5.3

Heat transfer between substances at different temperatures.

Since we know how heat is related to other measurable quantities, we have:

Letting f = final and i = initial, in expanded form, this becomes:

The density of water is 1.0 g/mL, so 425 mL of water = 425 g. Noting that the final temperature of both the rebar and water is 42.7 °C, substituting known values yields:

Solving this gives T i,rebar = 248 °C, so the initial temperature of the rebar was 248 °C.

Check Your Learning

The initial temperature of the copper was 335.6 °C.

The final temperature (reached by both copper and water) is 38.7 °C.

This method can also be used to determine other quantities, such as the specific heat of an unknown metal.

Example 5.4

Identifying a metal by measuring specific heat.

In expanded form, this is:

Noting that since the metal was submerged in boiling water, its initial temperature was 100.0 °C; and that for water, 60.0 mL = 60.0 g; we have:

Solving this:

Comparing this with values in Table 5.1 , our experimental specific heat is closest to the value for copper (0.39 J/g °C), so we identify the metal as copper.

c metal = 0.13 J/g °C

This specific heat is close to that of either gold or lead. It would be difficult to determine which metal this was based solely on the numerical values. However, the observation that the metal is silver/gray in addition to the value for the specific heat indicates that the metal is lead.

When we use calorimetry to determine the heat involved in a chemical reaction, the same principles we have been discussing apply. The amount of heat absorbed by the calorimeter is often small enough that we can neglect it (though not for highly accurate measurements, as discussed later), and the calorimeter minimizes energy exchange with the outside environment. Because energy is neither created nor destroyed during a chemical reaction, the heat produced or consumed in the reaction (the “system”), q reaction , plus the heat absorbed or lost by the solution (the “surroundings”), q solution , must add up to zero:

This means that the amount of heat produced or consumed in the reaction equals the amount of heat absorbed or lost by the solution:

This concept lies at the heart of all calorimetry problems and calculations.

Example 5.5

Heat produced by an exothermic reaction.

The heat given off by the reaction is equal to that taken in by the solution. Therefore:

(It is important to remember that this relationship only holds if the calorimeter does not absorb any heat from the reaction, and there is no heat exchange between the calorimeter and the outside environment.)

Next, we know that the heat absorbed by the solution depends on its specific heat, mass, and temperature change:

To proceed with this calculation, we need to make a few more reasonable assumptions or approximations. Since the solution is aqueous, we can proceed as if it were water in terms of its specific heat and mass values. The density of water is approximately 1.0 g/mL, so 100.0 mL has a mass of about 1.0 × × 10 2 g (two significant figures). The specific heat of water is approximately 4.184 J/g °C, so we use that for the specific heat of the solution. Substituting these values gives:

Finally, since we are trying to find the heat of the reaction, we have:

The negative sign indicates that the reaction is exothermic. It produces 2.9 kJ of heat.

1.34 × × 10 3 kJ; assume no heat is absorbed by the calorimeter, no heat is exchanged between the calorimeter and its surroundings, and that the specific heat and mass of the solution are the same as those for water

Chemistry in Everyday Life

Thermochemistry of hand warmers.

When working or playing outdoors on a cold day, you might use a hand warmer to warm your hands ( Figure 5.15 ). A common reusable hand warmer contains a supersaturated solution of NaC 2 H 3 O 2 (sodium acetate) and a metal disc. Bending the disk creates nucleation sites around which the metastable NaC 2 H 3 O 2 quickly crystallizes (a later chapter on solutions will investigate saturation and supersaturation in more detail).

The process NaC 2 H 3 O 2 ( a q ) ⟶ NaC 2 H 3 O 2 ( s ) NaC 2 H 3 O 2 ( a q ) ⟶ NaC 2 H 3 O 2 ( s ) is exothermic, and the heat produced by this process is absorbed by your hands, thereby warming them (at least for a while). If the hand warmer is reheated, the NaC 2 H 3 O 2 redissolves and can be reused.

Another common hand warmer produces heat when it is ripped open, exposing iron and water in the hand warmer to oxygen in the air. One simplified version of this exothermic reaction is 2 Fe ( s ) + 3 2 O 2 ( g ) ⟶ Fe 2 O 3 ( s ) . 2 Fe ( s ) + 3 2 O 2 ( g ) ⟶ Fe 2 O 3 ( s ) . Salt in the hand warmer catalyzes the reaction, so it produces heat more rapidly; cellulose, vermiculite, and activated carbon help distribute the heat evenly. Other types of hand warmers use lighter fluid (a platinum catalyst helps lighter fluid oxidize exothermically), charcoal (charcoal oxidizes in a special case), or electrical units that produce heat by passing an electrical current from a battery through resistive wires.

Link to Learning

This link shows the precipitation reaction that occurs when the disk in a chemical hand warmer is flexed.

Example 5.6

Heat flow in an instant ice pack.

Calculate the value of q for this reaction and explain the meaning of its arithmetic sign. State any assumptions that you made.

with “rxn” and “soln” used as shorthand for “reaction” and “solution,” respectively.

Assuming also that the specific heat of the solution is the same as that for water, we have:

The positive sign for q indicates that the dissolution is an endothermic process.

1.33 kJ; assume that the calorimeter prevents heat transfer between the solution and its external environment (including the calorimeter itself) and that the specific heat of the solution is the same as that for water

If the amount of heat absorbed by a calorimeter is too large to neglect or if we require more accurate results, then we must take into account the heat absorbed both by the solution and by the calorimeter.

The calorimeters described are designed to operate at constant (atmospheric) pressure and are convenient to measure heat flow accompanying processes that occur in solution. A different type of calorimeter that operates at constant volume, colloquially known as a bomb calorimeter , is used to measure the energy produced by reactions that yield large amounts of heat and gaseous products, such as combustion reactions. (The term “bomb” comes from the observation that these reactions can be vigorous enough to resemble explosions that would damage other calorimeters.) This type of calorimeter consists of a robust steel container (the “bomb”) that contains the reactants and is itself submerged in water ( Figure 5.17 ). The sample is placed in the bomb, which is then filled with oxygen at high pressure. A small electrical spark is used to ignite the sample. The energy produced by the reaction is absorbed by the steel bomb and the surrounding water. The temperature increase is measured and, along with the known heat capacity of the calorimeter, is used to calculate the energy produced by the reaction. Bomb calorimeters require calibration to determine the heat capacity of the calorimeter and ensure accurate results. The calibration is accomplished using a reaction with a known q , such as a measured quantity of benzoic acid ignited by a spark from a nickel fuse wire that is weighed before and after the reaction. The temperature change produced by the known reaction is used to determine the heat capacity of the calorimeter. The calibration is generally performed each time before the calorimeter is used to gather research data.

Click on this link to view how a bomb calorimeter is prepared for action.

This site shows calorimetric calculations using sample data.

Example 5.7

Bomb calorimetry.

The heat produced by the reaction is absorbed by the water and the bomb:

This reaction released 48.7 kJ of heat when 3.12 g of glucose was burned.

q rx = –39.0 kJ (the reaction produced 39.0 kJ of heat)

Since the first one was constructed in 1899, 35 calorimeters have been built to measure the heat produced by a living person. 2 These whole-body calorimeters of various designs are large enough to hold an individual human being. More recently, whole-room calorimeters allow for relatively normal activities to be performed, and these calorimeters generate data that more closely reflect the real world. These calorimeters are used to measure the metabolism of individuals under different environmental conditions, different dietary regimes, and with different health conditions, such as diabetes.

For example Carla Prado's team at University of Alberta undertook whole-body calorimetry to understand the energy expenditures of women who had recently given birth. Studies like this help develop better recommendations and regimens for nutrition, exercise, and general wellbeing during this period of significant physiological change. In humans, metabolism is typically measured in Calories per day. A nutritional calorie (Calorie) is the energy unit used to quantify the amount of energy derived from the metabolism of foods; one Calorie is equal to 1000 calories (1 kcal), the amount of energy needed to heat 1 kg of water by 1 °C.

Measuring Nutritional Calories

In your day-to-day life, you may be more familiar with energy being given in Calories, or nutritional calories, which are used to quantify the amount of energy in foods. One calorie (cal) = exactly 4.184 joules, and one Calorie (note the capitalization) = 1000 cal, or 1 kcal. (This is approximately the amount of energy needed to heat 1 kg of water by 1 °C.)

The macronutrients in food are proteins, carbohydrates, and fats or oils. Proteins provide about 4 Calories per gram, carbohydrates also provide about 4 Calories per gram, and fats and oils provide about 9 Calories/g. Nutritional labels on food packages show the caloric content of one serving of the food, as well as the breakdown into Calories from each of the three macronutrients ( Figure 5.18 ).

For the example shown in (b), the total energy per 228-g portion is calculated by:

So, you can use food labels to count your Calories. But where do the values come from? And how accurate are they? The caloric content of foods can be determined by using bomb calorimetry; that is, by burning the food and measuring the energy it contains. A sample of food is weighed, mixed in a blender, freeze-dried, ground into powder, and formed into a pellet. The pellet is burned inside a bomb calorimeter, and the measured temperature change is converted into energy per gram of food.

Today, the caloric content on food labels is derived using a method called the Atwater system that uses the average caloric content of the different chemical constituents of food, protein, carbohydrate, and fats. The average amounts are those given in the equation and are derived from the various results given by bomb calorimetry of whole foods. The carbohydrate amount is discounted a certain amount for the fiber content, which is indigestible carbohydrate. To determine the energy content of a food, the quantities of carbohydrate, protein, and fat are each multiplied by the average Calories per gram for each and the products summed to obtain the total energy.

Click on this link to access the US Department of Agriculture (USDA) National Nutrient Database, containing nutritional information on over 8000 foods.

• 2 Francis D. Reardon et al. “The Snellen human calorimeter revisited, re-engineered and upgraded: Design and performance characteristics.” Medical and Biological Engineering and Computing 8 (2006)721–28, http://link.springer.com/article/10.1007/s11517-006-0086-5.

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Access for free at https://openstax.org/books/chemistry-2e/pages/1-introduction

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• Publisher/website: OpenStax
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• Publication date: Feb 14, 2019
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• Book URL: https://openstax.org/books/chemistry-2e/pages/1-introduction
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Thermochemistry

Calorimetry, learning objectives.

• Define calorimetry.
• Perform calculations involving calorimetry relationships.

How many calories are in your food?

At one time, calories in foods were measured with a bomb calorimeter (see figure above). A weighed amount of the food would be placed in the calorimeter and the system was then sealed and filled with oxygen. An electric spark ignited the food-oxygen mixture. The amount of heat released when the food burned would give an idea of the food calories present. Today calories are calculated from the protein, carbohydrate, and fat content of the food (all determined by chemical analysis). No more bombs needed.

Calorimetry is the measurement of the transfer of heat into or out of a system during a chemical reaction or physical process. A calorimeter is an insulated container that is used to measure heat changes. The majority of reactions that can be analyzed in a calorimetry experiment are either liquids or aqueous solutions. A frequently used and inexpensive calorimeter is a set of nested foam cups fitted with a lid to limit the heat exchange between the liquid in the cup and the air in the surroundings (see Figure below ). In a typical calorimetry experiment, specific volumes of the reactants are dispensed into separate containers and the temperature of each is measured. They are then mixed into the calorimeter, which starts the reaction. The reactant mixture is stirred until the reaction is complete, while the temperature of the reaction is continuously monitored.

Figure 17.6

A simple constant-pressure calorimeter.

The key to all calorimetry experiments is the assumption that there is no heat exchange between the insulated calorimeter and the room. Consider the case of a reaction taking place between aqueous reactants. The water in which the solids have been dissolved is the surroundings, while the dissolved substances are the system. The temperature change that is measured is the temperature change that is occurring in the surroundings. If the temperature of the water increases as the reaction occurs, the reaction is exothermic. Heat was released by the system into the surrounding water. An endothermic reaction absorbs heat from the surroundings, so the temperature of the water decreases as heat leaves the surroundings to enter the system.

Sample Problem: Calorimetry and Enthalpy Changes

Step 1: List the known quantities and plan the problem .

• Density = 1.00 g/mL

Step 2: Solve .

Step 3: Think about the result .

The enthalpy change is negative because the reaction releases heat to the surroundings, resulting in an increase in temperature of the water.

Key Takeaways

• The process of calorimetry is described.
• Calculations involving enthalpy changes are illustrated.

Work the problems at the link below:

http://misterguch.brinkster.net/PRA047.pdf

• What kinds of reactions are usually analyzed in a calorimeter?
• What is a constant-pressure calorimeter?
• Why are foam cups used in a calorimeter?
• calorimeter: An insulated container that is used to measure heat changes.
• calorimetry: The measurement of the transfer of heat into or out of a system during a chemical reaction or physical process.
• User:Lanzi/Wikimedia Commons. http://commons.wikimedia.org/wiki/File:Drawing-kalorimeter.svg .
• CK-12 Foundation – Christopher Auyeung.

In this article

• Calculations

Quantitative analysis

Qualitative analysis, calorimetry problems.

Resources Year 11 Chemistry

Year 11 Chemistry Practical Investigation | Calorimetry Experiment

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How to perform the calorimetry experiment in Year 11 Chemistry Practical

A popular Year 11 Chemistry practical investigation is the calorimetry experiment. Not only is this experiment commonly performed by students during their Year 11 Chemistry course but also in the HSC Chemistry course. In this article, you will find a complete Chemistry practical report on determining the enthalpy of combustion of fuels via calorimetry.

This Year 11 Chemistry practical report on the calorimetry experiment consists of:

• Safety information 
• Practice calorimetry problems

Calorimetry Experiment

To determine the enthalpy of combustion of fuels using a calorimeter.

The standard enthalpy of combustion \small (\Delta H_c^\circ) is the enthalpy change when one mole of a substance undergoes complete combustion with oxygen at standard states, under standard conditions.

The steps which can be used to determine the enthalpy changes of combustion are outlined below:

Step 1: Write a balanced chemical equation of the process.

\large \text{Fuel}_{(s)/(l)/(g)} + {O_2}_{(g)} \rarr {CO_2}_{(g)} + {H_2O}_{(l)}

Step 2: Calculate the heat gained by the substance (water).

\Large q_\text{ substance} =mc\Delta T

• \small q_\text{ substance} is the heat gained by water in joules \small \text{(J)}
• \small \text{m} is the mass of water in kilograms \small (\text{kg})
• \small \text{c} is the specific heat capacity of water (4.18 × 10 3 \small \text{J kg}^{-1}\text{K}^{-1}   or 4.18 \small \text{J g}^{-1}\text{K}^{-1} )
• \small \Delta \text{ T} is the change in temperature of water in kelvin \small \text{(K)}

Step 3: Calculate the heat released by the combustion process.

The quantity of heat exchanged between the process and the substance will be the same but opposite sign .

\Large q_\text{ combustion process} = -q_\text{ substance}

Step 4: Calculate the enthalpy change of the process.

To calculate the standard enthalpy of combustion from the results of a calorimetry experiment:

\Large \Delta H_c = \dfrac{q_\text{ combustion process}}{n_\text{ combustion process}}

Since the standard enthalpy of combustion of fuels (∆H c ) is always negative, we often use the term “heat of combustion”. The heat of combustion is the absolute value of the standard enthalpy of combustion, as the amount of heat released for a specified amount of the fuel.

The equation q=mc\Delta T and the value for the specific heat capacity of water can be found on the HSC Chemistry Formula and Data Sheet .

The fuels used during this experiment are alcohols which have a general formula:

\Large C_nH_{2n+1}OH .

For example,

• Methanol has the formula \small CH_3OH .
• Ethanol has the formula \small C_2H_5OH .
• Propanol has the formula \small C_3H_7OH .
• Retort stand and clamp
• Methanol spirit burner
• Ethanol spirit burner
• Propan-1-ol spirit burner
• 250 \small \text{mL} measuring cylinder
• Thermometer (0 – 100 \small \degree \text{C} accurate to 0.1 \small \degree \text{C} )
• Electronic balance

Safety Information

• Set up the equipment as shown below. The copper can should be clamped so that the tip of the flame just touches the can when lit.
• Add 200 \small \text{mL} of cold water to the can using a measuring cylinder to measure the volume of water.
• Record the initial temperature of the water using a thermometer.
• Weigh the spirit burner with its liquid contents as accurately as possible, and record the mass.
• Light the wick and stir the water gently with a glass rod. Monitor the temperature and observe the flame.
• When the temperature has risen by about 10 \small \degree \text{C} , extinguish the flame by replacing the cap.
• Accurately record the maximum temperature for the water.
• Reweigh the burner and record its final mass.
• Examine the bottom of the can for soot accumulation. Remove soot before using the next alcohol.

Table 1: Experimental measurements and observations

Calorimetry formulas

Calorimetry calculations.

An example of the calculation of the enthalpy of combustion of methanol \small (CH_3OH) is shown below.

{CH_3OH}_{(l)} + \frac{3}{2} {O_2}_{(g)} \rarr 2{H_2O}_{(l)} + {CO_2}_{(g)}

Step 2: Calculate the heat gained by the water.

\begin{aligned} q_\text{ substance} & = mc\Delta T \\ \\ & = 200 \text{ kg} \times (4.18 \times 10^{-3} \text{J kg}^{-1}\text{K}^{-1}) \times (35.0-25.0) \text{ K} \\ \\ &= 8360 \text{ J} \end{aligned}

\begin{aligned} q_\text{ combustion process} &= -q_\text{ substance} \\ \\ &=-8360 \text{ J} \\ \\ &=-8.360 \text{ kJ} \end{aligned}

\begin{aligned} n(CH_3OH) & = \dfrac{n}{MM} \\ \\ &=\dfrac{0.55}{12.01+4\times 1.008+16} \\ \\ &=0.01716 \dots \text{ mol} \end{aligned}

\begin{aligned} \Delta H_c&=\dfrac{q_\text{ combustion process}}{n_\text{ combustion process}} \\ \\ & = -\dfrac{8.36}{0.01716 \dots} \\ \\ & = - 490 \text{ kJ mol}^{-1} \text{(2 s.f.)} \end{aligned}

A summary of the calculations for the enthalpy of combustion of methanol, ethanol and propan-1-ol is displayed in the table below.

Table 2: Calculations

Students are often asked to answer the following quantitative and qualitative analysis questions after performing a chemistry practical on calorimetry.

1. The theoretical value for the enthalpy of combustion of each alcohol is given in the table below. 

Calculate the percentage error of the experimental result compared to the theoretical result for each alcohol. 

\% \text{ error} = \dfrac{| \text{theoretical value} - \text{experimental value}|}{\text{theoretical value}} \times 100

\begin{aligned} \% \text{ error}_\text{ methanol} &= \dfrac{|-726 -(-490)|}{726} \times 100 \\ \\ & = 32.5 \% \\ \\ \% \text{ error}_\text{ ethanol} &= \dfrac{|-1368 -(-850)|}{1368} \times 100 \\ \\ &=37.9\%\\ \\ \% \text{ error}_\text{ propan-1-ol} &= \dfrac{|-2021 -(-1200)|}{2021} \times 100 \\ \\ &=40.6 \% \end{aligned}

Let’s investigate the safety, errors, reliability and accuracy of this experiment.

1. Outline two safety risks in this experiment. Describe how the risks were minimised. 

2. Account for the differences between the experimental value and the theoretical values for the standard enthalpies of combustion. 

In the experiment, not all of the heat produced was used in heating the water. Some of the heat was lost to the surroundings (heating the copper can and the air around the flame) . Since this was not taken into account in the calculations, it caused the experimental value for the enthalpy of combustion to be significantly higher than the theoretical value.

3. Assess the validity of this experiment

Validity relates to the experimental method and how appropriate it is in addressing the aim of the experiment.

The aim of this experiment was to determine the enthalpy of combustion of fuels using a calorimeter. Therefore, the validity of the experiment can be assessed based on how suitable the method was in determining the enthalpy of combustion of each fuel. 

• The enthalpy of combustion of a fuel refers to the energy released in the complete combustion of one mole of fuel. Therefore the fuels should have undergone complete combustion. However, this is not true for ethanol and propan-1-ol as black soot was observed on the base of the copper can. Black soot which is C (s) is an indication of incomplete combustion. The blue-yellow and orange flame observed during the combustion of ethanol and propan-1-ol is also an indication of incomplete combustion.
• The calculation of enthalpy made in this experiment assumes that there is no heat loss. However, this assumption is not satisfied as considerable heat is lost to the surroundings. 

Since the experimental method contains assumptions that are not valid, the experiment is not valid.

4. Suggest techniques that could be used to improve the validity of the results.

The validity of an experiment can be improved by:

• Keeping the control variables constant and preventing them from affecting the dependent variable.
• Ensuring that any assumptions made are valid.

5. What can be done to ensure the reliability of the results?

Reliability is the extent to which the experiment yields the same result each time.

The reliability can be improved by conducting more trials for each fuel, excluding outliers and averaging concordant results. Using a greater volume of water and recording results over a larger change in temperature will also reduce the percentage error, minimise the effect of random errors and improve the reliability of the results.

6. What can be done to improve the accuracy of the results?

Accuracy is the extent to which the calculated value differs from the true, accepted value.

Eliminating systematic errors arising from the incorrect use of equipment or improper calibration of instruments such as zero setting error (where the instrument does not read zero when the quantity to be measured is zero) will improve accuracy.

Using more precise measuring devices will also improve accuracy. For example, use a 0–50 \small \degree \text{C} thermometer. It will be more accurate than a 0–100 \small \degree \text{C} one as the scale divisions are smaller. Alternatively, use a digital thermometer.

For more information on how to perform quantitative and qualitative data analysis on chemistry practical investigations, read the guide on How to study on data analysis task

A calorimetry experiment was conducted to determine the molar enthalpy of combustion of ethanol \small (C_2H_5OH) , molar mass = 46.07 \small \text{g mol}^{-1} ). The following data were collected:

Question 2 

One method for improving the experimental design is to take into account the energy absorbed by the calorimeter. This energy is then added to the energy absorbed by the water to calculate the enthalpy of combustion.

Use the measurements provided below to calculate the approximate enthalpy of combustion of butan-1-ol ( \small MM =74.12 \small \text{g mol}^{-1} ). (4 marks)

Solutions to calorimetry problems

Written by Varisara Laosuksri

Varisara is a 2019 St George Girls High School graduate who achieved Band 6 in her HSC Chemistry and Physics.

Learnable Education and www.learnable.education, 2019. Unauthorised use and/or duplications of this material without express and written permission from this site's author and/or owner is strictly prohibited. Excerpts and links may be used, provided that full and clear credit is given to Learnable Education and www.learnable.education with appropriate and specific direction to the original content.

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Coffee Cup Calorimetry

So how can such simple equipment be used to measure the quantity of heat gained or lost by a system? We have learned on the previous page , that water will change its temperature when it gains or loses energy. And in fact, the quantity of energy gained or lost is given by the equation

Q = m water •C water •ΔT water

where C water is 4.18 J/g/°C. So if the mass of water and the temperature change of the water in the coffee cup calorimeter can be measured, the quantity of energy gained or lost by the water can be calculated.

Q ice = - Q surroundings = -Q calorimeter

The role of the Styrofoam in a coffee cup calorimeter is that it reduces the amount of heat exchange between the water in the coffee cup and the surrounding air. The value of a lid on the coffee cup is that it also reduces the amount of heat exchange between the water and the surrounding air. The more that these other heat exchanges are reduced, the more true that the above mathematical equation will be. Any error analysis of a calorimetry experiment must take into consideration the flow of heat from system to calorimeter to other parts of the surroundings . And any design of a calorimeter experiment must give attention to reducing the exchanges of heat between the calorimeter contents and the surroundings .

Bomb Calorimetry

The coffee cup calorimeters used in high school science labs provides students with a worthwhile exercise in calorimetry. But at the professional level, a cheap Styrofoam cup and a thermometer isn't going to assist a commercial food manufacturer in determining the Calorie content of their products. For situations in which exactness and accuracy is at stake, a more expensive calorimeter is needed. Chemists often use a device known as a bomb calorimeter to measure the heat exchanges associated with chemical reactions, especially combustion reactions. Having little to nothing to do with bombs of the military variety, a bomb calorimeter includes a reaction chamber where the reaction (usually a combustion reaction) takes place. The reaction chamber is a strong vessel that can withstand the intense pressure of heated gases with exploding. The chamber is typically filled with mostly oxygen gas and the fuel . An electrical circuit is wired into the chamber in order to electrically ignite the contents in order to perform a study of the heat released upon combustion. The reaction chamber is surrounded by a jacket of water with a thermometer inserted. The heat released from the chamber warms the water-filled jacket, allowing a scientist to determine the quantity of energy released by the reaction.

Solving Calorimetry Problems

Now let's look at a few examples of how a coffee cup calorimeter can be used as a tool to answer some typical lab questions. The next three examples are all based on laboratory experiments involving calorimetry.

Example Problem 1: A physics class has been assigned the task of determining an experimental value for the heat of fusion of ice. Anna Litical and Noah Formula dry and mass out 25.8-gram of ice and place it into a coffee cup with 100.0 g of water at 35.4°C. They place a lid on the coffee cup and insert a thermometer. After several minutes, the ice has completely melted and the water temperature has lowered to 18.1°C. What is their experimental value for the specific heat of fusion of ice?

The basis for the solution to this problem is the recognition that the quantity of energy lost by the water when cooling is equal to the quantity of energy required to melt the ice. In equation form, this could be stated as

Q ice = -Q calorimeter

(The negative sign indicates that the ice is gaining energy and the water in the calorimeter is losing energy.) Here the calorimeter (as in the Q calorimeter term) is considered to be the water in the coffee cup. Since the mass of this water and its temperature change are known, the value of Q calorimeter can be determined.

Q calorimeter = m•C•ΔT Q calorimeter = (100.0 g)•(4.18 J/g/°C)•(18.1°C - 35.4°C) Q calorimeter = -7231.4 J

Q ice = m ice •ΔH fusion-ice +7231.4 J = (25.8 g)•ΔH fusion-ice ΔH fusion-ice = (+7231.4 J)/(25.8 g) ΔH fusion-ice = 280.28 J/g ΔH fusion-ice = 2.80x10 2 J/g (rounded to two significant figures)

Example Problem 2: A chemistry student dissolves 4.51 grams of sodium hydroxide in 100.0 mL of water at 19.5°C (in a calorimeter cup). As the sodium hydroxide dissolves, the temperature of the surrounding water increases to 31.7°C. Determine the heat of solution of the sodium hydroxide in J/g.

Once more, the solution to this problem is based on the recognition that the quantity of energy released when sodium hydroxide dissolves is equal to the quantity of energy absorbed by the water in the calorimeter. In equation form, this could be stated as

(The negative sign indicates that the NaOH is losing energy and the water in the calorimeter is gaining energy.) Since the mass and temperature change of the water have been measured, the energy gained by the water (calorimeter) can be determined.

Q calorimeter = m•C•ΔT Q calorimeter = (100.0 g)•(4.18 J/g/°C)•(31.7°C - 19.5°C) Q calorimeter = 5099.6 J

The assumption is that this energy gained by the water is equal to the quantity of energy released by the sodium hydroxide when dissolving. So Q NaOH-dissolving = -5099.6 J. (The negative sign indicates an energy lost.) This quantity is the amount of heat released when dissolving 4.51 grams of the sodium hydroxide. When the heat of solution is determined on a per gram basis, this 5099.6 J of energy must be divided by the mass of sodium hydroxide that is being dissolved.

ΔH solution = Q NaOH-dissolving / m NaOH ΔH solution = (-5099.6 J) / (4.51 g) ΔH solution = -1130.7 J/g ΔH solution = -1.13x10 3 J/g (rounded to three significant figures)

Example Problem 3: A large paraffin candle has a mass of 96.83 gram. A metal cup with 100.0 mL of water at 16.2°C absorbs the heat from the burning candle and increases its temperature to 35.7°C. Once the burning is ceased, the temperature of the water was 35.7°C and the paraffin had a mass of 96.14 gram. Determine the heat of combustion of paraffin in kJ/gram. GIVEN: density of water = 1.0 g/mL.

As is always the case, calorimetry is based on the assumption that all the heat lost by the system is gained by the surroundings . It is assumed that the surroundings is the water that undergoes the temperature change. In equation form, it could be stated that

Q paraffin = -Q water

Since the mass and temperature change of the water are known, the energy gained by the water in the calorimeter can be determined.

Q calorimeter = m•C•ΔT Q calorimeter = (100.0 g)•(4.18 J/g/°C)•(35.7°C - 16.2°C) Q calorimeter = 8151 J

The paraffin released 8151 J or 8.151 kJ of energy when burned. This is based on the burning of 0.69 gram (96.83 g - 96.14 g). To determine the heat of combustion on a per gram basis, the Q paraffin value (-8.151 kJ) must be divided by the mass of paraffin burned:

ΔH combustion - paraffin = (-8.151 kJ) / (0.69 g) ΔH combustion - paraffin = -11.813 kJ/g ΔH combustion - paraffin = -12 kJ/g (rounded to two significant digits)

Check Your Understanding

1. Consider Example Problem 3 above. Identify as many sources of error as you can. For each source indicate the direction of error that would have resulted. That is, identify whether the error would have caused the experimentally derived value to be less than or more than the accepted value.

Answers will vary. Three common choices include: A. Energy is transferred from the water to the surrounding air. This would cause the experimental value to be less than the accepted value since this energy is not contributing to the water's temperature change. B. Energy is being absorbed by the metal cup as the metal also encounters a temperature change. This would cause since this energy is not being accounted for in the calculations. C. Some of the energy released by the burning candle fails to warm either the cup or the water. This energy simply warms the surrounding air. Failure to account for this energy would cause the experimental value to be less than the accepted value.

2. A 2.15-gram cashew nut is burned. The heat released raises the temperature of a 100.0-gram sample of water from 18.2°C to 31.5°C. The mass of the nut after the experiment is 1.78 grams. Determine the calorie content of the nut in Calories/gram. Assume that the water is only able to absorb 25% of the heat released by the burning nut. Given 1.00 Calorie=4.18 kJ.

Answer: ~15 Cal/g

Q water = m water •C water •ΔT water Q water = (100.0 g)•(4.18J/g/°C)•(31.5°C - 18.2°C) = 5559.4 J = 5.5594 kJ Q water = 5.5594 kJ•(1.00 Calorie/4.18 kJ) = 1.3560 Calorie The energy absorbed by the water is one-fourth (25%) of the energy released by the nut. Q nut = -1.3560 Calorie/0.25 = -5.4238 Calorie This 5.4238 Calorie of energy was released by burning 0.37 grams of the Cashew. To determine the Calorie content on a per gram basis, the Calorie-to-gram ratio must be determined. Calorie Content = 5.4248 Calorie/0.37 gram = 14.6589 Cal/g Calorie content = 15 Calorie/gram (rounded to two significant figures)

Calorimetry experiments

In this post

The amount of heat energy released by a chemical reaction can be measured using a method known as calorimetry. Simple calorimetry experiments can be used to calculate the heat energy transferred during reactions such as combustion, displacement, dissolving and neutralisation. These experiments often involve measuring the temperature changes that occur in water or aqueous solutions during these reactions. The calorimetry experiments for these four types of reactions will now be described.

Combustion reactions are exothermic reactions. A fuel is a substance which releases heat energy when it is burned. Different fuels will release different amounts of heat energy. The heat energy released by the fuel is transferred to the surroundings.

To measure the heat energy released by a fuel, we burn a sample of the fuel with a known mass, below a glass or metal container full of water. The glass or metal container is known as a calorimeter.

The heat energy released from the combustion of the fuel is transferred to the water, causing the temperature of the water to increase. The method used to determine this temperature increase is described below:

• 50cm 3 of cold water is measured into a calorimeter.
• The initial temperature of the water is measured and recorded.
• A spirit burner containing the fuel is placed below the calorimeter and the wick is lit using a lit splint.
• The fuel is burned for a set amount of time (usually a couple of minutes).
• The highest temperature reached by the water is recorded.

During combustion reactions, the heat energy produced is transferred to the surroundings. This means that not all of the heat energy will be transferred directly into the water. Some will also be transferred to the container itself, as well as the air surrounding the container. The following steps should be taken to minimise this heat loss, and achieve measurements which are as accurate as possible:

• Use of shielding around the spirit burner to reduce heat loss to the air
• Use of a lid on the calorimeter to reduce heat loss through convection
• Use as small a distance as possible between the flame and container to reduce convection

When comparing the heat energy transferred by different fuels it is important that everything is kept the same in order to make it a fair test. The distance between the flame and calorimeter, the type of calorimeter used, the volume of water used and the amount of time the fuel is burned for should all be kept the same for each experiment completed.

Displacement reactions

A displacement reaction is one in which a more reactive metal replaces a less reactive metal in a compound. Displacement reactions are exothermic, so heat energy is released to the surroundings. If the metal added is in solid form and the metal compound is present as an aqueous solution, the amount of heat energy released can be calculated using the measured temperature increase of the solution of the metal compound.

The method used to determine the temperature increase is described below using the addition of zinc powder to copper sulphate solution as an example:

• Measure 50cm 3 of the copper sulphate solution into a polystyrene cup or glass beaker.
• Measure and record the initial temperature of the copper sulphate solution.
• Add a known mass of zinc powder to the copper sulphate solution and stir.
• Measure the temperature continually and record the highest temperature reached by the solution.

Dissolving occurs when a solid is added to a liquid and the bonds between the particles in the solid are broken, causing the solid particles to separate and spread out between the liquid particles.

One common type of dissolving experiment used is salts dissolving in water. Salts are ionic compounds. When they dissolve in water, the ions separate. Energy is required to overcome the forces of attraction between the ions in the solid form. This part of dissolving is endothermic.

When the ions have separated, they are able to spread out between the water particles. Forces of attraction are formed between the ions and the water molecules. This forming of the forces of attraction releases heat energy and is exothermic.

The dissolving of salts can be either an endothermic or exothermic change depending on how much energy is taken in to separate the ions in the solid compared to the energy released when the forces of attraction are formed between the ions and water molecules. The method for the calorimetry experiment is as follows:

• Place a polystyrene cup in a beaker.
• Measure and transfer 50cm 3 of water into the cup and measure the initial temperature.
• Add a known mass of the solid solute to the water in the cup and stir the solution to dissolve the solid.
• Once the solid has dissolved, measure and record the final temperature reached by the water.

Neutralisation

A neutralisation reaction is one in which an acid reacts with an alkali to produce water and a salt. For example, hydrochloric acid and sodium hydroxide solution react together, forming water and sodium chloride solution.

Neutralisation reactions are exothermic as the system releases heat energy to the surroundings. The system in a neutralisation reaction is the acid and alkali. The surroundings are the solution in which they are contained. When the acid and alkali react, they release heat energy into the surroundings, meaning that the temperature of the solution increases.

The temperature increase of the solution can be measured and used to calculate the amount of heat energy transferred during the reaction. The method for this experiment is describe below:

• Measure out 25cm 3 of the acid solution with a known concentration into a polystyrene cup. Place the cup into a glass beaker to prevent the cup being knocked over during the experiment.
• Measure and record the initial temperature of the acid.
• Measure out 25cm 3 of the alkali solution. This alkali solution should have the same concentration as the acid solution to make sure that the number of moles of acid and alkali used are equal.
• Add the 25cm 3 of alkali solution into the polystyrene cup and stir the solution.
• Measure and record the highest temperature reached by the solution.

Calculating the heat energy change

Once the temperature change has been measured from the calorimetry experiment, the amount of heat energy transferred can be calculated using the expression:

Energy transferred (Q) = mass of water (m) x specific heat capacity (c) x temperature change (△T)

= energy transferred (in J)

= mass of water or aqueous solution (in g)

= specific heat capacity of water (4.2J/g o C)

= temperature change (in o C)

The mass of water or aqueous solution used can be calculated using its volume and the density. The density of water is 1g/cm 3 . This means that 1cm 3 of water has a mass of 1g. 50cm 3 would therefore have a mass of 50g. Aqueous solutions are those made using water as a solvent. We therefore use the density of water to measure the mass of these solutions. For example, 50cm 3 of an aqueous solution would have a mass of 50g.

The specific heat capacity of a substance is the amount of energy needed to raise the temperature of 1g of the substance by 1 o C. The specific heat capacity of water is taken to be 4.2J/g. This means that it takes 4.2 Joules (J) of energy to raise the temperature of 1g of water by 1 o C.

The temperature change is the increase or decrease in temperature of the water or solution. This is calculated by subtracting the initial temperature from the final temperature. The heat energy change equation essentially tells us that the amount of heat energy transferred is equal to the mass of the water or solution that is heated, multiplied by the specific heat capacity of water (this is a constant and is equal to 4.2 joules for 1 gram of water) multiplied by the temperature change.

The heat energy change for any calorimetry experiment can be calculated using this equation. Worked example 1 on the next page shows how the equation can be applied and used in the example of a combustion reaction.

Ethanol in a spirit burner is burned below a calorimeter containing 50cm 3 of water. The initial temperature of the water was 21.5 o C and the highest temperature reached after heating was 82.5 o C. Calculate the heat energy change for the combustion of ethanol.

• Calculate the temperature change for the reaction.

The temperature of the water in the calorimeter before heating is 21.5. The temperature of this after heating is 82.5 To work out the temperature change we subtract the temperature before heating (21.5) from the temperature after heating (52.5).

82.5 – 21.5 = 61.0

• Substitute the values into the heat energy change equation:

Q = 50 x 4.2 x 31 = 12810J

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How do you measure the energy change of a reaction? It's not possible to do this directly. However, we can do it  indirectly. One way of doing this is by measuring the reaction's enthalpy change using a process called calorimetry . 

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Calorimetry is used to determine the enthalpy of neutralisation between acid A and base B. A figure of -134 kJ mol -1 is found experimentally. State whether the real value is likely to be larger or smaller in magnitude.

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Calorimetry is a method for measuring the enthalpy change of a reaction by measuring the temperature change the reaction causes.

Enthalpy change is the heat change of a reaction at constant pressure. We explore this topic in much more depth in the article Enthalpy Changes .

• This article is about calorimetry in physical chemistry .
• We'll start by looking at the different types of calorimetry.
• We'll then explore the equation you use in calorimetry to calculate enthalpy change.
• After that, we'll look at how you use calorimetry to calculate enthalpies of reaction, neutralisation, and combustion .
• Finally, we'll go over some of the limitations of calorimetry.

What is Calorimetry?

As we explored above, calorimetry is a method used to measure the enthalpy change of the reaction. In other words, it measures the heat change of a reaction. However, it is impossible to measure heat change directly. Instead, we have to measure the temperature change caused by heat.

Temperature and heat are different things. Heat is a form of energy. It is the total sum of all the energies of particles in a substance. Like all types of energy, it is measured in joules (J) or kilojoules (kJ). On the other hand, temperature is a measure of energy. It's to do with the average energy of particles in a substance and is measured in kelvin (K), degrees Celsius ( ° C), or degrees Fahrenheit ( ° F). You can also say that temperature is just a measure of how hot or cold something is.

One important thing to note is that heat is related to the number of particles in a substance , while temperature is not. If you have more particles in a substance, the total energy store increases, and so their heat increases. However, their average energy won't necessarily change, and so temperature can stay the same.

Heat energy always flows from a higher temperature to a lower temperature - in other words, from a hot substance to a cold substance. When you heat a substance, you transfer energy to it. This could cause an increase in temperature. However, it could also cause a change in state. But provided the substance stays in the same state, this means that change in temperature is a handy way of measuring change in heat. In other words, it is a way of measuring enthalpy change .

Types of Calorimetry

There are a few different types of calorimetry:

Direct calorimetry

Indirect calorimetry, differential scanning calorimetry.

For your exams, you only need to know about direct calorimetry . This is generally what people mean when they refer to calorimetry and unless we say otherwise, this is what we're talking about when we say calorimetry in the rest of this article. However, we've included the other types of calorimetry below as further examples of interest.

Direct calorimetry , as the name suggests, measures the heat change of a chemical reaction by directly measuring the temperature change it causes. It does this using a calorimeter .

A calorimeter is a tool used to measure the enthalpy change of a chemical reaction.

A simple calorimeter can be made with a polystyrene drinking cup, water, and a thermometer. The reaction we're interested in releases heat energy which warms the water up. The idea is that we minimise heat loss and measure the temperature change of the water, and then use this to calculate the enthalpy change of the reaction.

In biology, direct calorimetry generally refers to measuring the heat change of a living organism by placing it in a sealed chamber and measuring the temperature change of the surrounding air.

Indirect calorimetry is a term used in biology. It is a way of measuring the heat change of an organism by measuring either their intake of oxygen or their output of carbon dioxide or nitrogen .

Different substances all need different amounts of heat energy to raise their temperature. Differential scanning calorimetry is a technique used to measure the difference in the amount of energy needed to raise the temperatures of a sample and a reference substance by the same amount. It is often used in biology to find out the specific heat capacity of various proteins and other biological molecules, and investigate their response to heating.

Calorimetry Equation

As we explored above, the aim of calorimetry is to measure the enthalpy change of a reaction. We do this by measuring the temperature change of another substance that a reaction causes. Let's call this substance X. Temperature and enthalpy are related by the following equation:

q = mcΔT

In this equation:

• q is the enthalpy change of the reaction, measured in J.
• m is the mass of X, measured in g.
• c is the specific heat capacity of X, measured in J g -1 K -1 .
• ΔT is the temperature change of X, measured in K.

Specific heat capacity , c , is the energy needed to raise the temperature of one gram of a substance by one kelvin. It is measured in joules per gram per kelvin, J g - 1 K - 1 .

You can read more on specific heat capacity in our article Thermal Physics.

Don't worry - we'll practice using this equation in just a second. But for now, let's get on to the main focus of this article: carrying out calorimetry.

Calorimetry E xperiment

We've already explored one type of calorimeter. It consists of a polystyrene cup filled with water or another solution. The heat energy released by a reaction is used to heat the water and the water's temperature change is measured. We're now going to look in more detail at how you can use calorimetry to work out enthalpies of reaction , neutralisation, and combustion .

The enthalpy change of reaction is the enthalpy change when equation quantities of reactants react to make products, with all species in their standard states and under standard conditions.

The enthalpy change of neutralisation is the enthalpy change when an acid and an alkali react together to make one mole of water, under standard conditions.

The enthalpy change of combustion is the enthalpy change when one mole of a species fully combusts in oxygen, with all species in their standard states and under standard conditions.

Standard conditions involve a pressure of 100 kPa and 298 K. Standard states are the states a species is found in, under these conditions.

If this is your first time encountering enthalpies, we'd recommend heading over to Enthalpy Changes for a more detailed look.

Finding enthalpy of reaction

For reactions involving mixing two solutions or adding a solid to a solution, you can work out the enthalpy of reaction using calorimetry. You do this by either mixing the two solutions or adding the solid to the solution, and measuring the solution's temperature change. In this example, we'll add a solid to an aqueous solution. Here's the method:

• Rinse a polystyrene cup and a measuring cylinder in the solution you are going to use, then dry thoroughly.
• Measure out 50 cm 3 of the solution and pour into the polystyrene cup. Place the cup in a beaker and add a lid on top.
• Weigh out approximately 2.00g of your solid reactant into a weighing boat.
• Poke a thermometer through a hole in the lid. Measure the temperature of the solution every 30 seconds for three minutes.
• At the third minute, don't measure the temperature, but instead, add your solid reactant to your solution. Reweigh the weighing boat to see if any solid is left behind, and subtract this from the starting weight.
• Measure the temperature of the solution every 30 seconds for five minutes, or until the temperature remains constant.

If you want to mix two aqueous solutions together instead, measure out each solution into separate measuring cylinders, both rinsed in their respective solution. Pour the first solution into the polystyrene cup. Measure the temperatures of both solutions every 30 seconds. At the three-minute mark, add the second solution to the first and continue measuring its temperature every 30 seconds as for the above method.

Finding the enthalpy change

We now need to find the temperature change of the reaction, as we can use this to calculate the reaction's enthalpy change. However, we haven't got a temperature value for the exact moment when we added the solid and started the reaction. The point of addition is 3 minutes, whereas our first data point is at the 3 minute 30 second mark. To find the exact temperature rise of the reaction, we first need to plot a graph of the temperature of the solution against time and extrapolate the temperature back to the point of addition. Sound confusing? Here is how you do it.

2.00g of zinc is added to 50 cm 3 of 0.2 mol dm -3 copper sulphate solution and gives the following data. The zinc is added at 180 seconds.

Work out the enthalpy of reaction . You can assume that copper sulphate solution has a density of 1 g cm - 3 and a specific heat capacity of 4 . 18 J g - 1 K - 1 .

To calculate the enthalpy change of the reaction, we need to use the equation we discussed earlier: q = mcΔT . What values do we know?

Well, m refers to the mass of the solution being heated, in this case, copper sulphate solution. Copper sulphate has a density of 1 g cm - 3 and so our solution weighs 50g. c refers to the specific heat capacity of the copper sulphate solution, which is given in the question: 4 . 18 J g - 1 K - 1 . We just need to find ΔT , the total temperature change of the reaction. To do this, let's plot our points on a graph. Put temperature on the y-axis and time on the x-axis. You should end up with something like this:

We now need to draw two lines of best fit – one before we added the zinc at the 3-minute mark, and one after. Notice how there isn't a data point at the 3-minute mark itself. instead, we extrapolate our lines back to that point. You can see this below:

To find the temperature change of the reaction, we measure the difference between the two lines at the point of addition, which is the 3-minute mark.

You might have noticed that we've measured temperature in ℃, but the equation for enthalpy change needs temperature in K. However, we are only interested in temperature change. A change of 1 ℃ is the same as a change of 1 K, and so here the units are interchangeable.

We can now substitute all of these values into the equation:

q = mc ∆ T q = 50 x 4 . 18 x 27 = 5643 J

However, this isn't quite the final answer. We need to do two more things.

Firstly, we've simply calculated enthalpy change. The question has asked for the enthalpy of reaction, which is given in kJ per mole . We need to work out how many moles of zinc reacted and divide the enthalpy change we worked out by this number. Zinc has an atomic number of 65.4, and we have 2.00 grams of it in the question. We therefore have 2 ÷ 65 . 4 = 0 . 0306 mol . 5643 ÷ 0 . 0306 = 184 . 4 kJ mol - 1 .

Finally, this was an exothermic reaction. Overall, energy was released. Therefore, the final answer needs a negative sign in front of it: - 184 . 4 kJ mol - 1 .

Finding enthalpy of neutralisation

Finding the enthalpy of neutralisation works in exactly the same way as finding the enthalpy of reaction. You combine your two reactants, whether they be solutions or a solid and a solution, and record the temperature change over several minutes. You then plot a graph and extrapolate back to the point of addition in order to find a maximum temperature. You then work out the temperature change and calculate enthalpy change, as described above.

Finding enthalpy of combustion

For reactions involving combustion, we can calculate the enthalpy of combustion using calorimetry. We do this by burning a fuel below a beaker of water and measuring the temperature change of the water. Here's how you go about it:

• Measure a known mass of cold water into a copper can.
• Suspend the copper can above a fuel burner using a stand and clamp or a tripod.
• Measure the temperature of the water and the mass of the fuel burner.
• Light the fuel burner and let it burn until the temperature of the water has risen by approximately 25 ° C . Keep measuring the temperature as it could still increase after the fuel has been extinguished.
• Measure the mass of the fuel burner again and subtract this from its starting mass to find the fuel burner's change in mass.

Finding the enthalpy of combustion is easier than finding the enthalpy of reaction. You can easily find the change in temperature by subtracting the starting temperature of the water from the highest temperature it reaches. From there, you simply substitute your values into the equation we used before, q = mc ∆ T . Let's go through an example.

0.5g of propan-2-ol combusts completely, heating up 150g of water. The temperature of the water increases from 21 ℃ to 50 ℃. Calculate the enthalpy change of combustion for the reaction. The specific heat capacity of water is 4 . 18 J g - 1 K - 1 .

First, we need to calculate the enthalpy change of the reaction. Here, m = 150 and c = 4.18. To find ΔT, the change in temperature, we subtract the starting temperature from the end temperature. Here, ΔT = 50 - 21 = 29 ℃ . Putting all of these values into the equation for enthalpy gives us the following:

q = mc ∆ T q = 150 x 4 . 18 x 29 = 18183 J

However, the enthalpy of combustion is measured in kilojoules per mole. We now need to divide the enthalpy change by the number of moles of ethanol burnt. Ethanol has a relative formula mass of 46. We therefore have 0 . 5 ÷ 46 = 0 . 0109 moles of ethanol. Ethanol's enthalpy of combustion is therefore 18183 ÷ 0 . 0109 = 1668 . 2 kJ mol - 1 . But we're not quite finished - once again, this is an example of an exothermic reaction and so we need a negative sign in front of the answer. Our final answer is - 1668 . 2 kJ mol - 1 .

Limitations of Calorimetry

Calorimetry can be extremely frustrating. You may follow an identical method to your partner but obtain extremely different results. This is because there are many variables that come into play during calorimetry and it is impossible to accurately control all of them. For example:

• There could be energy transfer to or from the environment, usually in the form of heat loss.
• We always assume the solution used has the specific heat capacity and density of pure water, but this might not be the case.
• The reaction could be incomplete.
• Some of the heat energy released could heat up the apparatus instead of the solution itself.
• Some of the fuel might evaporate.

However, there are ways to minimise variation in results. These mostly involve minimising heat loss to the environment. Examples include:

• When measuring the enthalpy of reaction, you put the reacting solution inside of a polystyrene cup, which is in turn placed inside a beaker. This insulates the solution.
• When measuring the enthalpy of combustion, you might use a wind shield to protect the fuel burner from any drafts. You should also keep the beaker of water a fixed distance above the burner, to make your results more reproducible.
• In both cases, you could put a lid on top of the beaker or polystyrene cup, again to improve insulation and minimise any heat loss.

Calorimetry - Key takeaways

Calorimetry is a method of measuring the enthalpy change of a reaction by measuring the temperature change the reaction causes.

A simple calorimeter can be made with a polystyrene drinking cup, water, and a thermometer. We use the heat energy released by the reaction to heat the water up and use the water's temperature change to work out the reaction's enthalpy change.

Enthalpy change, mass, specific heat capacity, and temperature change are linked by the equation q = mc ∆ T .

You can use calorimetry to measure the enthalpy of reaction , enthalpy of neutralisation, and enthalpy of combustion .

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Frequently Asked Questions about Calorimetry

What is calorimetry?

Calorimetry is a method of measuring enthalpy change during a reaction. It most commonly does this by measuring how the reaction changes the temperature of a body of water.

How to find the mass in calorimetry?

Mass in calorimetry refers to the mass of the water or solution used in the experiment. You can find the mass by measuring the volume of the solution and multiplying its volume by its density. However, if you know the enthalpy change of the reaction, you can work backwards using the equation q = mcΔT. In this equation, q is the enthalpy change, m is the mass of the solution, c is the specific heat capacity of the solution, and ΔT is the solution's change in temperature.

What is calorimetry used for?

Calorimetry is used to measure the enthalpy changes during a reaction. It is often used to study the thermal properties of drugs and biological molecules, such as their denaturation temperature. It is also used to analyse polymers, helping us find out values such as their crystallisation temperature.

Where is calorimetry used in industry?

Widespread use of calorimetry is in food laboratories to find the calorie content of foods. Calorimetry is also used to analyse drugs, proteins and other biological molecules, to determine their thermal properties.

How do we find the final temperature in calorimetry?

We measure the temperature change over several minutes at regular intervals after the reaction has started. The final temperature  is the highest  temperature reached during the reaction. If you are finding the enthalpy of reaction, you might need to plot a graph of temperature against time and extrapolate back to the point where the reaction started, to find the true highest temperature. Don't worry - this article will show you how.

Test your knowledge with multiple choice flashcards

Calorimetry is used to determine the enthalpy of neutralisation between acid A and base B. A figure of -134 kJ mol-1 is found experimentally. State whether the real value is likely to be larger or smaller in magnitude.

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Calorimetry for the ePIC Experiment

The Electron-Ion Collider (EIC) will deliver collisions of electrons with protons and nuclei at a wide variety of energies and at luminosities up to 1000 times higher than HERA. Precise measurement of both the scattered electron and the hadronic final state is crucial for the physics of the EIC, necessitating unique designs for the electromagnetic and hadronic calorimeters in the backward (-4 < η 𝜂 \eta italic_η < -1.4), central (-1.4 < η 𝜂 \eta italic_η < 1.4), and forward (1.4 < η 𝜂 \eta italic_η < 4) regions. To ensure maximal containment of energy and acceptance for the required physics processes, the Electron-Proton/Ion Collider (ePIC) detector employs calorimetry over almost the entire polar angle. This proceedings will provide an overview of the current calorimeter designs being employed in ePIC.

1 Calorimetry at the EIC

The ePIC experiment is a general-purpose, hermetic collider detector with the goal of carrying out the broad EIC physics program  [ 1 ] . The EIC will collide electrons with protons and nuclei at center of mass energies ranging from s ≈ 30 𝑠 30 \sqrt{s}\approx 30 square-root start_ARG italic_s end_ARG ≈ 30 GeV to 140 140 140 140 GeV, at luminosities up to 10 34 ⁢  cm − 2 superscript 10 34 superscript  cm 2 10^{34}\text{ cm}^{-2} 10 start_POSTSUPERSCRIPT 34 end_POSTSUPERSCRIPT cm start_POSTSUPERSCRIPT - 2 end_POSTSUPERSCRIPT per second  [ 15 ] . The physics of the EIC imposes stringent requirements on tracking, particle identification, and calorimetry, with each region of the detector subject to unique challenges. A few of the challenges facing the calorimeter systems (shown in Fig.  1 ) are:

Identifying and precisely measuring the scattered electron.

Measuring single particles with momenta from tens of MeV to tens of GeV.

Containing jets with energies over 100 GeV and providing information to particle-flow reconstruction algorithms.

Separating single photons from the two photons arising in decays of neutral pions.

In addition to these physics requirements, the calorimeters must be able to handle streaming readout at up to 500 kHz of event rate and radiation loads of 5 ⋅ 10 9 ⋅ 5 superscript 10 9 5\cdot 10^{9} 5 ⋅ 10 start_POSTSUPERSCRIPT 9 end_POSTSUPERSCRIPT (in the backward and barrel regions) to 2 ⋅ 10 11 ⋅ 2 superscript 10 11 2\cdot 10^{11} 2 ⋅ 10 start_POSTSUPERSCRIPT 11 end_POSTSUPERSCRIPT (in the forward region) 1 MeV neutron equivalent dose per cm 2 per year.

2 ePIC Electromagnetic Calorimeters

2.1 backward electromagnetic calorimeter.

The design of the backward electromagnetic calorimeter is driven in large part by the requirement of excellent energy resolution for measuring the scattered electron kinematics and separating pion showers from electron showers via E/p. To reduce the large photoproduction background for DIS observables, the rate of pions being misidentified as electrons should be on the order of 1-in-10000 or better for the combined system of tracking, PID, and calorimetry. The energy resolution required for the calorimeter is on the order of σ E E ≈ 2 % E ⊕ 1 − 3 % subscript 𝜎 𝐸 𝐸 direct-sum percent 2 𝐸 1 percent 3 \frac{\sigma_{E}}{E}\approx\frac{2\%}{\sqrt{E}}\oplus 1-3\% divide start_ARG italic_σ start_POSTSUBSCRIPT italic_E end_POSTSUBSCRIPT end_ARG start_ARG italic_E end_ARG ≈ divide start_ARG 2 % end_ARG start_ARG square-root start_ARG italic_E end_ARG end_ARG ⊕ 1 - 3 % . Furthermore, the design should be radiation hard, have a small Molière radius, and enable detection of photons above 50 MeV. The only realistic option for meeting all of these requirements is a homogeneous calorimeter based on scintillating lead tungstate crystals. The backward ECal design, shown schematically in Fig.  2 , is similar to that of the Neutral Particle Spectrometer currently taking data in Hall C at Jefferson Lab  [ 13 , 12 ] . The crystals are rectangular with dimensions 2x2x20 cm 3 , resulting in around 22 X 0 subscript 𝑋 0 X_{0} italic_X start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT for particles at normal incidence. The PbWO 4 scintillation light from an individual crystal is measured by a 4x4 array of Hamamatsu S14160-3010PS SiPMs. To reduce the amount of dead material between the crystals, they are supported by two thin (0.5 mm) frames of carbon fiber located at the front and back of each crystal.

2.2 Barrel Electromagnetic Calorimeter

Similar to the backward direction, the barrel region of ePIC should deliver an electron-pion separation power of 1-in-10000. To achieve this level of separation, the ePIC barrel electromagnetic calorimeter, also known as the Barrel Imaging Calorimeter or BIC, incorporates a lead/scintillating fiber design with HV-MAPS AstroPix  [ 10 , 16 ] silicon pixel detectors designed for the AMEGO-X  [ 14 ] gamma-ray astronomy missions. The barrel calorimeter is around 4.5 meters long including services, is divided azimuthally into 48 sectors, and covers pseudorapidities between -1.7 and 1.3. The Pb/SciFi section emulates the design implemented successfully in GlueX  [ 9 ] and KLOE  [ 2 ] . The Pb/SciFi bulk section of the calorimeter utilizes 435 cm-long scintillating fibers readout on both sides by 1.2 cm x 1.2 cm Hamamatsu S14161 SiPM arrays of 50 micron pixel size, of which there are 60 per sector per side. The AstroPix sensors consist of 500 μ 𝜇 \mu italic_μ m x 500 μ 𝜇 \mu italic_μ m square pixels capable of measuring dE/dx via time-over-threshold. The low power consumption of AstroPix, on the order of a few mW/cm 2 , enables them to be inserted between the layers of Pb/SciFi without substantial cooling infrastructure. The high spatial granularity of the AstroPix sensors, combined with the excellent energy resolution of the SciFi portion, enables this detector to meet the strict electron-pion and π 0 / γ superscript 𝜋 0 𝛾 \pi^{0}/\gamma italic_π start_POSTSUPERSCRIPT 0 end_POSTSUPERSCRIPT / italic_γ separation requirements. The energy resolution is expected to be σ E E ≈ 5 % E ⊕ 1 % subscript 𝜎 𝐸 𝐸 direct-sum percent 5 𝐸 percent 1 \frac{\sigma_{E}}{E}\approx\frac{5\%}{\sqrt{E}}\oplus 1\% divide start_ARG italic_σ start_POSTSUBSCRIPT italic_E end_POSTSUBSCRIPT end_ARG start_ARG italic_E end_ARG ≈ divide start_ARG 5 % end_ARG start_ARG square-root start_ARG italic_E end_ARG end_ARG ⊕ 1 % .

2.3 Forward Electromagnetic Calorimeter

The ePIC forward electromagnetic calorimeter builds on the Tungsten/SciFi SpaCal design studied throughout the EIC R&D effort  [ 18 , 17 ] and applied in the sPHENIX experiment  [ 5 , 6 ] . The energy resolution requirements are modest, but the detector should have the granularity and density necessary to reduce the number of high-energy π 0 superscript 𝜋 0 \pi^{0} italic_π start_POSTSUPERSCRIPT 0 end_POSTSUPERSCRIPT decay photon pairs being misreconstructed as single photons. The scintillating fibers run in the z-direction and are embedded in a mixture of tungsten powder and epoxy, which provides an overall density of around 10 g/cm 2 . A block of W/SciFi is 5 x 5 x 17 cm and is subdivided into four towers. Each tower is instrumented with four 6x6 mm Hamamatsu S14160 series SiPMs. The light is guided from the face of the block to the SiPM by a 2 cm light guide. This design allows for separation of π 0 superscript 𝜋 0 \pi^{0} italic_π start_POSTSUPERSCRIPT 0 end_POSTSUPERSCRIPT and photon clusters up to around 40 GeV. The expected energy resolution of the forward EMCal is σ E E ≈ 10 % E ⊕ 1 − 3 % subscript 𝜎 𝐸 𝐸 direct-sum percent 10 𝐸 1 percent 3 \frac{\sigma_{E}}{E}\approx\frac{10\%}{\sqrt{E}}\oplus 1-3\% divide start_ARG italic_σ start_POSTSUBSCRIPT italic_E end_POSTSUBSCRIPT end_ARG start_ARG italic_E end_ARG ≈ divide start_ARG 10 % end_ARG start_ARG square-root start_ARG italic_E end_ARG end_ARG ⊕ 1 - 3 % .

3 ePIC Hadronic Calorimeters

3.1 backward hadronic calorimeter.

The hadronic final state at low- x 𝑥 x italic_x is typically scattered in the backward direction, necessitating the ability to distinguish the scattered electron from energy deposits created by the final state hadrons. This ambiguity limited the precision of HERA measurements at low- x 𝑥 x italic_x . Since the energies of hadrons in the backward direction are not very high, the backward hadronic calorimeter serves primarily as a tail-catcher for hadrons and a muon identification system for decays of vector mesons. The backward hadronic calorimeter subtends the region − 4.1 < η < − 1.2 4.1 𝜂 1.2 -4.1<\eta<-1.2 - 4.1 < italic_η < - 1.2 . The design consists of ten layers of 4 cm thick non-magnetic steel and 4 mm thick plastic scintillator, producing a total depth of around 2.4 λ 0 subscript 𝜆 0 \lambda_{0} italic_λ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT .

3.2 Barrel Hadronic Calorimeter

The ePIC barrel hadronic calorimeter is a refurbished version of the sPHENIX outer HCal, described in Refs.  [ 5 , 3 ] . The absorber consists of long magnetic steel plates tilted by 12 degrees in azimuth, as shown in the top left portion of Fig.  4 . Between the steel plates are 7 mm thick scintillating tiles, in which are embedded wavelength shifting fibers to collect the scintillation light and transport it to an SiPM on the outer radius of the detector. The 12 degree tilt ensures that a particle travelling radially will hit at least four scintillating tiles. The expected energy resolution for single hadrons is around σ E E ≈ 75 % E ⊕ 15 % subscript 𝜎 𝐸 𝐸 direct-sum percent 75 𝐸 percent 15 \frac{\sigma_{E}}{E}\approx\frac{75\%}{\sqrt{E}}\oplus 15\% divide start_ARG italic_σ start_POSTSUBSCRIPT italic_E end_POSTSUBSCRIPT end_ARG start_ARG italic_E end_ARG ≈ divide start_ARG 75 % end_ARG start_ARG square-root start_ARG italic_E end_ARG end_ARG ⊕ 15 % .

3.3 Forward Hadronic Calorimeter

The ePIC forward hadronic calorimeter, known as the Longitudinally-segmented Forward HCal (LFHCal), is designed to contain and precisely measure the high-energy hadrons produced in the forward region. The design leverages the SiPM-on-tile technology pioneered by the CALICE AHCal  [ 4 ] to provide fine spatial granularity, ideal for particle-flow algorithms. Each tower consists of steel absorber interleaved with 65 layers of eight square scintillator+SiPM tiles (See Fig.  5 ). The SiPM signals are ganged longitudinally into 7 readout channels, resulting in 56 readout channels per tower. The full detector contains 565,760 SiPMs readout via 60,928 channels of the HGCROC ASIC, developed for the CMS High Granularity Calorimeter  [ 11 ] . The LFHCal achieves an excellent energy resolution of around σ E E ≈ 44 % E ⊕ 6 % subscript 𝜎 𝐸 𝐸 direct-sum percent 44 𝐸 percent 6 \frac{\sigma_{E}}{E}\approx\frac{44\%}{\sqrt{E}}\oplus 6\% divide start_ARG italic_σ start_POSTSUBSCRIPT italic_E end_POSTSUBSCRIPT end_ARG start_ARG italic_E end_ARG ≈ divide start_ARG 44 % end_ARG start_ARG square-root start_ARG italic_E end_ARG end_ARG ⊕ 6 % . The innermost radius of the forward HCal, where the radiation load and particle energies are highest, consists of an "insert" section instrumented with hexagonal scintillating tiles. Detailed information on the insert section can be found in Refs.  [ 8 , 7 ] .

In summary, the ePIC calorimeter systems meet or exceed the challenging energy resolution requirements laid forth in the EIC Yellow Report, as can be seen in Fig.  6 . The ePIC collaboration is presently in the process of writing a technical design report that will provide detailed designs and projected performances of the calorimeters and other detector subsystems.

• [1] R. Abdul Khalek et al. Science Requirements and Detector Concepts for the Electron-Ion Collider: EIC Yellow Report. Nucl. Phys. A , 1026:122447, 2022.
• [2] M. Adinolfi et al. The KLOE electromagnetic calorimeter. Nucl. Instrum. Meth. A , 482:364–386, 2002.
• [3] J. K. Adkins et al. Design of the ECCE Detector for the Electron Ion Collider. 9 2022.
• [4] C. Adloff et al. Construction and Commissioning of the CALICE Analog Hadron Calorimeter Prototype. JINST , 5:P05004, 2010.
• [5] C. A. Aidala et al. Design and Beam Test Results for the sPHENIX Electromagnetic and Hadronic Calorimeter Prototypes. IEEE Trans. Nucl. Sci. , 65(12):2901–2919, 2018.
• [6] C. A. Aidala et al. Design and Beam Test Results for the 2-D Projective sPHENIX Electromagnetic Calorimeter Prototype. IEEE Trans. Nucl. Sci. , 68(2):173–181, 2021.
• [7] Miguel Arratia, Bruce Bagby, Peter Carney, Jiajun Huang, Ryan Milton, Sebouh J. Paul, Sean Preins, Miguel Rodriguez, and Weibin Zhang. Beam Test of the First Prototype of SiPM-on-Tile Calorimeter Insert for the EIC Using 4 GeV Positrons at Jefferson Laboratory. Instruments , 7(4):43, 2023.
• [8] Miguel Arratia et al. A high-granularity calorimeter insert based on SiPM-on-tile technology at the future Electron-Ion Collider. Nucl. Instrum. Meth. A , 1047:167866, 2023.
• [9] Tegan D. Beattie et al. Construction and Performance of the Barrel Electromagnetic Calorimeter for the GlueX Experiment. Nucl. Instrum. Meth. A , 896:24–42, 2018.
• [10] Isabella Brewer, Michela Negro, Nicolas Striebig, Carolyn Kierans, Regina Caputo, Richard Leys, Ivan Peric, Henrike Fleischhack, Jessica Metcalfe, and Jeremy Perkins. Developing the future of gamma-ray astrophysics with monolithic silicon pixels. Nucl. Instrum. Meth. A , 1019:165795, 2021.
• [11] J. D. González-Martínez. H2GCROC: Design and performance of a dedicated very front-end ASIC for SiPM readout of the CMS High Granularity Calorimeter. Nucl. Instrum. Meth. A , 1047:167863, 2023.
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Calorimetry ( AQA A Level Chemistry )

Revision note.

Chemistry Lead

Calorimetry

Measuring enthalpy changes.

• Calorimetry is the measurement enthalpy changes in chemical reactions
• A simple calorimeter can be made from a polystyrene drinking cup , a vacuum flask or metal can

A polystyrene cup can act as a calorimeter to find enthalpy changes in a chemical reaction

• The energy needed to increase the temperature of 1 g of a substance by 1 o C is called the specific heat capacity ( c ) of the liquid
• The specific heat capacity of water is 4.18 J g -1 o C -1
• The energy transferred as heat can be calculated by:

Equation for calculating energy transferred in a calorimeter

Worked example

Specific heat capacity calculations

In a calorimetry experiment, 2.50 g of methane is burnt in excess oxygen.

30% of the energy released during the combustion is absorbed by 500 g of water, the temperature of which rises from 25 °C to 68 °C

The specific heat capacity of water is 4.18 J g -1 °C −1   

What is the total energy released per gram of methane burnt?

Step 1: q = m x c x Δ T

             m (of water) = 500 g

             c (of water) = 4.18 J g -1 ° C -1

             Δ T (of water) = 68 o C - 25 o C

                                  = 43 o C

Step 2: q = 500 x 4.18 x 43

       = 89 870 J

Step 3:   This is only 30% of the total energy released by methane

Total energy x 0.3 = 89 870 J

Total energy = 299 567 J

Step 4:  This is released by 2.50 g of methane

Energy released by 1.00 g of methane = 299 567 ÷ 2.50

= 119 827 J = 120 000 J

= 120 kJ g -1

When new bonds are formed the amount of energy released is equal to the amount of energy absorbed when the same bonds are broken.

For example:

O 2 (g) → 2O (g)           E (O=O) = +498 kJ mol -1

2O (g) → O 2 (g)           E (O=O) = -498 kJ mol -1        

Aqueous solutions of acid, alkalis and salts are assumed to be largely water so you can just use the m and c values of water when calculating the energy transferred.

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