In this explainer, we will learn how to perform calorimetry experiments and use the results to calculate the enthalpy change for a chemical reaction.
Most chemical reactions, including those occurring in living organisms, will release energy or absorb energy when they take place. According to the law of conservation of energy, chemical reactions must lead to the conversion of energy from one category to another. Energy is transformed from one place to another, and it is neither created nor destroyed.
Law: The Law of the Conservation of Energy
The law of conservation of energy says that energy cannot be created or destroyed; it is only transferred.
In thermodynamics, the reaction of interest is contained within an area that we call the system. The area outside the system, which is where we make observations, is called the surroundings. An example of this terminology is shown below, where a reaction may be taking place inside a beaker.
An open system can exchange energy and matter with its surroundings, a closed system can exchange only energy with its surroundings, and an isolated system can exchange neither energy nor matter with its surroundings. An isolated system does not interact with its surroundings. A sealed thermos bottle that is thermally, mechanically, and electrically insulated from its surroundings is an example of an isolated system.
Chemical reactions that transfer energy as heat to the surroundings are described as exothermic reactions. Combustion reactions are examples of exothermic reactions. When a chemical reaction takes place in a system that absorbs energy as heat from the surroundings, it is described as an endothermic reaction. The gel ice packs that are contained in first aid kits contain chemicals that produce an endothermic reaction when mixed together.
The amount of heat that is transferred between the reaction system and the surroundings can be measured experimentally. To be able to calculate the energy transferred in these processes, we need to be able to relate the energy transferred to the amount of heating or cooling that is observed in the experiment.
Heat is the transfer of thermal energy between molecules and atoms in a system. This transfer of thermal energy is caused by a difference in temperature. Heat and temperature are closely associated, but they are fundamentally different. Temperature is the measure of the average kinetic energy of molecules. It can also be used to express how hot or cold a substance is.
Temperature is a measure of the average kinetic energy of matter in a system. It can also express how hot or cold a substance is.
When a substance is heated, energy is transferred to the molecules and atoms within the substance. The kinetic energy of these atoms and molecules is increased, and the temperature of the substance rises. The temperature change depends on the heat capacity of the substance. The heat capacity, , is defined as where is the quantity of energy measured in joules and is the temperature change in kelvins, or degrees Celsius. Since the size of a kelvin, K, is the same as that of a degree Celsius, the temperature change will be the same in either case.
Since heat capacity depends on the amount of substance being heated or cooled, it is known as an extensive property. The heat capacity may be used as an intensive property, in which case it is called the specific heat capacity. The specific heat capacity is defined as the heat capacity divided by the mass of the sample:
Specific heat capacity is measured in units of joules per kelvin per gram, or joules per degree Celsius per gram. Specific heat capacity is often simply referred to as specific heat.
Definition: Specific Heat Capacity
Also known as specific heat, this is the quantity of energy, measured in joules, required to raise the temperature of one gram of a substance by one degree Celsius.
Some values for the specific heat of different substances are seen in the table below. Liquid water has a relatively high specific heat when compared to other substances. If heat energy is supplied at a constant rate to liquid water, it will take longer to heat up through a given temperature when compared with the same mass of iron.
|Specific Heat Capacity ()||0.897||0.709||0.385||0.449||4.184||2.010|
If a known mass of a substance is heated at constant pressure so that no work is done against the surroundings, the quantity of heat energy gained can be calculated using the formula where is the energy, measured in joules.
The mass of the substance, , is measured in grams. , which is pronounced “delta T,” is the temperature change of the substance. can be calculated by subtracting the final temperature from the starting temperature and is measured with a thermometer. Numerically, will have the same value whether the final and starting temperatures are both measured in degrees Celsius or in kelvins.
The specific heat capacity, , is formally measured in units of . However, it is more common to use units of grams instead to give units of .
Example 1: Determining the Correct Formula to Use in order to Calculate the Heat Transferred in a Calorimetry Experiment
Which of the following equations can be used with the results from a calorimetry experiment to calculate the heat energy transferred during a chemical reaction?
The heat energy transferred during a chemical reaction is measured in joules. This quantity is denoted by the symbol .
The value of is found by multiplying together three other quantities. It is the product of the mass of the substance where the temperature changes and the specific heat capacity of the substance and the measured temperature change.
The mass of substance heated or cooled is denoted by . This is measured in grams. The specific heat capacity, or specific heat, of the substance is denoted by . This is measured in units of . The measured temperature change is given the symbol , which is pronounced “delta T.”
The only correct answer in which these quantities are seen correctly multiplied together is C.
Example 2: Calculating the Heat Transferred When a Mass of Water is Heated
In an experiment, it was found that a reaction resulted in 80 g of water changing temperature by . What is the value in joules for the heat energy transferred in this reaction? Use a value of for the specific heat capacity of water.
In this question, we are being asked to calculate the amount of heat energy transferred during a reaction that causes 80 g of water to change temperature by .
We can calculate the amount of heat energy, , transferred using the equation where is the mass in grams, is the specific heat capacity in units of , and is the change in temperature.
In the question, we are told that the mass of water is 80 g, the specific heat capacity of water is , and the change in temperature is .
Substituting the values into the equation gives
We can see by analyzing the units that grams, g, and degrees Celsius, , will cancel each other out to leave us with joules, J.
The final answer is 5 040 J.
In a laboratory, the temperature change caused by a reaction can be measured using a simple device known as a calorimeter. Experiments that measure the heat transferred by reactions are called calorimetry experiments.
Calorimetry is the study of heat transfer during physical and chemical changes.
A calorimeter is a device used for measuring energy transferred as heat during physical or chemical changes. It can be considered an isolated system.
A simple calorimeter consists of an insulated reaction container, a stirrer, and a thermometer. A polystyrene cup, supported in a beaker, with a close-fitting lid is often used as an insulated container for the reaction. The container is usually filled with a predetermined mass of water, which contains the reactants. A diagram of a simple calorimeter is shown below.
This type of calorimeter can be used to measure the heat energy change taking place in a reaction that happens in aqueous solution. Neutralization reactions and redox reactions may be studied using this type of apparatus. In this type of simple calorimeter, the insulated container is at atmospheric pressure, and the reaction takes place at constant pressure.
Example 3: Determining the Suitability of Experimental Apparatus for a Calorimetry Experiment
The diagram below shows the experimental setup for a simple calorimeter to measure the enthalpy change in certain reactions. For which type of reaction would this experimental apparatus not be suitable for measuring the change in enthalpy?
The type of calorimeter displayed in the diagram above is most suitable for measuring the enthalpy change for reactions that take place in aqueous solution, or in liquid media.
Dissolution reactions take place when a solute dissolves in a liquid solvent. An example of this is when an ionic compound, such as ammonium nitrate, dissolves in water to form hydrated ions.
Although displacement reactions can occur between solid reactants, they usually take place in water. An example of this type of reaction would be magnesium powder displacing copper in an aqueous copper sulfate solution.
Neutralization reactions take place between an acid and a base. The acid and the base are usually dissolved in water. In this case, the basic solution may be referred to as an alkali. These reactions are often encountered during a titration experiment in which an acid/base indicator is used.
Precipitation reactions involve the formation of an insoluble product from a combination of solutions. In these reactions, the solvent is frequently water.
All of the reactions described so far could be conducted inside a simple polystyrene-cup calorimeter, insulated with cotton wool.
Combustion reactions, which produce a flame of some sort, need a good supply of oxygen to ensure complete combustion. It would not be possible to heat a polystyrene cup directly with a flame, as it will catch fire, along with the cotton wool insulation. The polystyrene cup is not a good conductor of heat, and the oxygen supply to the flame would be limited inside the apparatus shown. The apparatus shown is not suitable for calorimetry experiments involving combustion. The correct answer is B.
For reactions such as the combustion of fuel, a different type of calorimeter is needed. Here, a constant-volume or combustion calorimeter is used. A simple diagram of a combustion calorimeter is show below.
Like the simple calorimeter, the combustion calorimeter contains water, a stirrer, and a thermometer. However, since the sample needs to be combusted, it cannot be placed directly into the water. Instead, the sample is placed inside a chamber, which can then be ignited remotely using the ignition wires.
As this chamber is also known as a bomb cell, the entire calorimeter is often referred to as a bomb calorimeter.
When using both the simple and bomb calorimeters, certain assumptions are made. These include the maximum temperature reflecting the amount of heat given off and that no heat escapes from the calorimeter to the surroundings. Finally, we also assume that the calorimeter itself, as well as the other equipment present such as the stirrer and thermometer, do not absorb any of the heat.
The bomb calorimeter is often used to find the calorific value of nutritional foods.
The joule (J) and the calorie (cal) can both be used as units of energy. The joule is the SI unit for energy. A joule is defined as the amount of thermal energy required to raise the temperature of 1 g of water by .
Joules can be converted into calories if they are divided by a value of 4.184, and calories can be converted into joules if they are multiplied by a value of 4.184.
The following conversion factors can also be used to convert between joules (J) and calories (cal):
One thousand calories can be defined as a kilocalorie (kcal). The relationship between the calorie and the kilocalorie is
A calorie is the quantity of energy needed to raise the temperature of one gram of water by one degree Celsius. It is equivalent to 4.184 J exactly.
An enthalpy change for a chemical reaction is usually calculated with units of kilojoules per mole. This is often referred to as the molar enthalpy change. The heat energy transferred during the chemical reaction must be linked to the number of moles of particles involved in the chemical reaction. For solid compounds, the moles reacting can be calculated from the mass of the limiting reagent used. For liquid solutions, the moles reacting can be calculated from the concentration of the solution and the volume taken. It is important that the molar enthalpy change is given the correct sign. For exothermic reactions, the molar enthalpy change is given a negative sign. For endothermic reactions, the molar enthalpy change is given a positive sign.
From experimental results, the molar enthalpy change can be calculated using the following equation: where is the number of moles reacting for the limiting reagent in the balanced chemical equation.
Example 4: Calculating a Molar Enthalpy Change from Experimental Data
When 50 mL of water containing 0.5 M at was mixed with 50 mL of water containing 0.5 M at , the highest temperature recorded was .
- What is the value of for this reaction? Use a value of for the specific heat capacity of water. Give your answer in joules.
- If is the limiting reagent, what is the value of in kilojoules per mole of ? [, , ]
- The balanced equation for the reaction is What is the molar enthalpy change for each mole of consumed? Give your answer as a whole number.
We use the equation to calculate the joules of energy transferred to the water in this reaction.
The total volume of liquid in the container is . We assume that this liquid has a density of 1 g/mL. The mass of liquid is therefore .
The temperature change is .
Using the equation, . This equates to 2 520 J.
The moles of reacting can be calculated by multiplying the concentration of the solution and the volume taken in litres.
The moles of is . So, .
Since , this equates to kJ. So, .
We now divide the kilojoules by the moles of reacting:
Since we have calculated the moles of as 0.025 mol, we can use the mole ratio seen in the balanced equation to establish the moles of consumed. For each mole of consumed, half the number of moles of is consumed, as these species react in a ratio. We have mol of consumed.
To find the molar enthalpy change for each mole of , we divide by .
This equates to .
We must give the answer a negative sign, as heat is transferred from the system to the surroundings. This is evident, as there was a temperature rise during the reaction. To the nearest whole number, the answer is kJ/mol.
Example 5: Calculating the Heat Change per Gram of Fuel from Experimental Data
In an experiment, 80 g of water was measured and placed into a copper container, and its temperature was recorded. A spirit lamp containing a fuel was weighed and then placed underneath the copper container. The wick of the spirit lamp was lit, and the water was heated until the temperature reached . The flame was then extinguished, and the final temperature of the water was recorded. The spirit lamp was then also weighed. The results are listed in the table below.
|Initial temperature of water ()||Final temperature of water ()||Mass of spirit lamp before heating (g)||Mass of spirit lamp after heating (g)|
- What is the value of , the heat energy transferred, in the experiment? Give your answer in units of kilojoules and to 1 decimal place. Use a value of for the specific heat capacity of water.
- What is the heat change per gram of fuel? Give your answer in units of kilojoules per gram of fuel.
In this part of the question, we are being asked to calculate the amount of heat energy transferred to 80 g of water when a fuel is combusted.
We can calculate the amount of heat energy () transferred using the following equation: where is the mass in grams, is the specific heat capacity in units of , and is the change in temperature.
From the question we are told that the mass of water is 80 g and that the specific heat capacity of water is 4.18. However, we will need to use the data in the table to calculate the change in temperature:
Substituting the values into the equation gives
We can see by analyzing the units that grams, g, and degrees Celsius, , will cancel each other out to leave us with joules, J.
However, the question asks for the value to be given in units of kilojoules and to 1 decimal place. To convert from joules to kilojoules, we must divide the value by 1 000:
Rounding this value to 1 decimal place gives us our final answer of 9.6 kJ.
Having determined the amount of heat that is transferred when the fuel is combusted, we now need to determine how much this is per gram of fuel.
In order to calculate this value, we need to know the amount of fuel that is burned during the experiment. From the table provided in the question, we can calculate the difference in mass of the spirit lamp before and after heating:
This result tell us that burning 1.5 g of the fuel produces 9.6 kJ of heat. Therefore, in order to determine the amount of heat produced per gram of fuel, we will divide the amount of heat produced by the mass of fuel burned:
The final answer is 6.4 kJ/g of fuel.
It is important to realize the limitations of calorimetry experiments carried out using simple apparatus in a laboratory. The calorimeter is not a perfectly isolated system, and heat transfer to the surrounding air and surfaces is inevitable. As a result, the measured temperature change will usually be less than it would be if there were no heat transfers. This will lead to the calculated value for a molar enthalpy change being lower than the actual value.
When combustion experiments are conducted, heat transfer to the surrounding air is more significant and large experimental errors may be encountered. Incomplete combustion frequently occurs in simple laboratory experiments. Incomplete combustion experiments leave sooty deposits on calorimeters. Less energy is released by the combustion reaction in these conditions. This will lead to lower experimental values for molar enthalpies of combustion, compared with accepted data, measured under standard conditions.
Let’s summarize what we have looked at in this explainer.
- The law of conservation of energy states that energy cannot be created or destroyed; it is only transferred.
- In an open system, both energy and matter are exchanged with the surroundings, while in a closed system, only energy can be exchanged.
- In an isolated system, neither energy nor matter can be exchanged with the surroundings.
- The specific heat capacity of a substance is the quantity of energy, measured in joules, required to raise the temperature of one gram of the substance by one degree Celsius.
- A simple calorimeter consists of an insulated cup, a lid, and a thermometer to record the temperature of the contents.
- The heat energy transferred, in joules, is calculated using the equation .
- The molar enthalpy change, , can be calculated by dividing the heat energy transferred by the moles of substance reacting.
- It is impossible to completely insulate the calorimeter cup from the surroundings. Heat loss to, or heat transfer from, the surroundings will cause experimental errors.