# Solving Problems with Calorimetry

## Calculating the heat produced by a chemical or physical change involves measuring the temperature of a sample before and after the change.

#### Key Points

• Calorimetry is the science of measuring the heat of chemical reactions or physical changes. It involves measurements made with calorimeters.

• The heat of the reaction is the negative of the amount of heat gained by the calorimeter. The calorimeter may be made of more than one component, such as a bomb and a water bath.

• The amount of heat gained by the calorimeter is also a product of the heat capacity of the calorimeter and the change in temperature of the sample undergoing a chemical or physical change.

• The above two points can be applied to calculate the heat of reaction given a temperature change.

#### Terms

• A process where two chemicals are combined to produce heat.

• The enthalpy change in a chemical reaction; the amount of heat that a systems gives up to its surroundings so it can return to its initial temperature.

#### Figures

1. ##### Bomb Calorimeter

This is the picture of a typical setup of bomb calorimeter.

## Solving Problems with Calorimetry

### Review

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.

### Calorimeters

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 (Figure 1).

### 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
• Thermometer
• 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).

<equation contenteditable="false">$Q_{reaction}=-Q_{calorimeter}$ where $Q_{calorimeter}=Q_{bomb}+Q_{water}$

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:

$Q_{calorimeter}=C_{calorimeter}\Delta T$

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

$Q=mc\Delta T$ where $c=\frac{C}{m}$

### Example

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.

Given:

• 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:

$Q_{calorimeter}=C_{calorimeter}\Delta T=(4.9 \ kJ/^{\circ}C)(27.64 - 23.42)^{\circ}C=(4.90 \times 4.22)\ kJ = 20.7 \ kJ$

Plug into the first equation: $Q_{reaction}=-Q_{calorimeter}$

$Q_{reaction}=-Q_{calorimeter} =-20.7 \ kJ$

### 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

$Q=mc\Delta T$

$Q_{lead}=(0.128 \ J/(g \ ^{\circ}C) )\times 150 \ g \ \times (28.8^{\circ}C-100^{\circ}C)=-1370 \ J$

$Q_{water}=(4.184 \ J/(g \ ^{\circ}C) )\times 50 \ g \ \times (28.8^{\circ}C-22^{\circ}C)=1420 \ J$

$Q_{calorimeter}=-(Q_{lead}+Q_{water})=-(1420 \ J + - 1370 \ J)=-50 \ J$

#### Key Term Glossary

calorimeter
An apparatus for measuring the heat generated or absorbed by either a chemical reaction, change of phase or some other physical change.
##### Appears in these related concepts:
calorimetry
The science of measuring the heat absorbed or evolved during the course of a chemical reaction or change of state.
##### Appears in these related concepts:
chemical reaction
A process, involving the breaking or making of interatomic bonds, in which one or more substances are changed into others.
##### Appears in these related concepts:
combustion
A process where two chemicals are combined to produce heat.
##### Appears in these related concepts:
Component
A part of a vector. For example, horizontal and vertical components.
##### Appears in these related concepts:
conversion
a change between different units of measurement for the same quantity.
##### Appears in these related concepts:
energy
A quantity that denotes the ability to do work and is measured in a unit dimensioned in mass × distance²/time² (ML²/T²) or the equivalent.
##### Appears in these related concepts:
enthalpy
the total amount of energy in a system, including both the internal energy and the energy needed to displace its environment
##### Appears in these related concepts:
equation
An assertion that two expressions are equal, expressed by writing the two expressions separated by an equal sign; from which one is to determine a particular quantity.
##### Appears in these related concepts:
heat
energy transferred from one body to another by thermal interactions
##### Appears in these related concepts:
heat capacity
The amount of heat energy needed to raise the temperature of an object or unit of matter by one degree Celsius; in units of joules per kelvin (J/K).
##### Appears in these related concepts:
heat of reaction
The enthalpy change in a chemical reaction; the amount of heat that a systems gives up to its surroundings so it can return to its initial temperature.
##### Appears in this related concept:
mass
The quantity of matter which a body contains, irrespective of its bulk or volume. It is one of four fundamental properties of matter. It is measured in kilograms in the SI system of measurement.
##### Appears in these related concepts:
pressure
the amount of force that is applied over a given area divided by the size of that area
##### Appears in these related concepts:
specific heat
The ratio of the amount of heat needed to raise the temperature of a unit mass of substance by a unit degree to the amount of heat needed to raise that of the same mass of water by the same amount.
##### Appears in these related concepts:
thermal energy
The internal energy of a system in thermodynamic equilibrium due to its temperature.
##### Appears in these related concepts:
work
A measure of energy expended in moving an object; most commonly, force times displacement. No work is done if the object does not move.