Solving Problems with Calorimetry
Previously we discussed the theoretically underpinnings of calorimetry and the equations necessary to calculate the heat created or absorbed by a chemical reaction or physical change. Calorimetry is widely used in chemistry to measure the enthalpy change of chemical reactions, but can be applied to any situation that involves a change in temperature and heat production. In this section, we will view the topic from a practical standpoint, introducing some examples.
There are two types of calorimeter: constant-volume calorimeters and constant-pressure calorimeters, which eponymously describe the experimental condition in which they are used. A coffee-cup calorimeter is often used since it is simpler than a bomb calorimeter, but to measure the heat evolved in a combustion reaction, constant volume or bomb calorimetry is ideal. A constant volume calorimeter is also more accurate than a coffee-cup calorimeter, but it is more difficult to use since it requires a well-built reaction container that is able to withstand large amounts of pressure changes that happen in many chemical reactions .
Structure of the Constant Volume Calorimeter
In a constant volume calorimeter, the system is sealed or isolated from its surroundings, and this accounts for why its volume is fixed and there is no volume-pressure work done. A bomb calorimeter structure consists of the following:
- Steel bomb which contains the reactants
- Water bath in which the bomb is submerged
- A motorized stirrer
- Wire for ignition
All of these components are contained within the double-walled outer part of the calorimeter. After the initial temperature of the water is measured, the heated wire inside the bomb starts the reaction. After the reaction completes, the final temperature of the water is measured, and then the change in temperature of the reactants can be calculated. Through the reaction, the temperature rises due to the conversion from chemical energy to thermal energy.
Determining Heat of Reaction
The amount of heat that the system gives up to its surroundings so that it can return to its initial temperature is the heat of reaction. The heat of reaction is just the negative of the thermal energy gained by the calorimeter and its contents (Qcalorimeter) through the combustion reaction (we can generalize this to any type of reaction).
If the constant volume calorimeter is set up the same way as before, (same steel bomb, same amount of water, etc.) then the heat capacity of the calorimeter can be measured using the following familiar formula:
Where Ccalorimeter is the heat capacity of the calorimeter. The heat capacity of the calorimeter can be determined by conducting an experiment.
Sometimes instead of the total heat capacity, we deal with the specific heat, so the equation above becomes
1.150 g of sucrose goes through combustion in a bomb calorimeter. If the temperature rose from 23.42°C to 27.64°C and the heat capacity of the calorimeter is 4.90 kJ/°C, then determine the heat of combustion of sucrose in kJ.
- mass of C12H22O12 : 1.150 g
- Tinitial: 23.42°C
- Tfinal: 27.64°C
- Heat of Capacity: 4.90 kJ/°C
Using the second equation above:
Plug into the first equation:
Another Example (Constant Pressure)
If 150 g of lead at 100°C were placed in a calorimeter with 50 g of water at 28.8°C and the resulting temperature of the mixture was 22°C, what are the values of Qlead, Qwater and Qcalorimeter? (Knowing that the specific heat of water is 4.184 J/g °C and the specific heat of lead is 0.128 J/g °C)
For lead, we know that: m = 150 g, Ti = 100°C, Tf = 28.8°C, cl (specific heat of lead) = 0.128 J/g °C
For water: m= 50 g, Ti = 22°C, Tf = 28.8°C, cw = 4.184 J/g °C