5.4c Determining Enthalpy Change: Calorimetry

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Tabulated ΔHrxn values are derived from experimental data. Experiments that measure heat exchange are referred to collectively as calorimetry experiments, and the measurement device is called a calorimeter. There are two important types of calorimetry experiments: constant-pressure calorimetry (also known as coffee cup calorimetry) and constant-volume calorimetry (also known as bomb calorimetry).

In constant-pressure calorimetry, the heat evolved or absorbed during a chemical change is measured under conditions in which the pressure does not change. This typically means that the chemical change is allowed to occur in a reaction vessel that is open to the atmosphere, and thus the pressure remains essentially constant. Under these conditions, the heat evolved or absorbed, q, is equal to the enthalpy change for the reaction, ΔH.

Heat exchange under conditions of constant pressure can be measured using a simple coffee cup calorimeter (Interactive Figure 5.4.2). The reaction vessel consists of two nested Styrofoam coffee cups that are covered with a lid. A thermometer measures the temperature change. Most coffee cup calorimetry experiments involve a solvent such as water and a stirring device ensures thorough mixing in the reaction vessel.

Due:
1/1/20 11:59 PM
Score: 0
A constant-pressure calorimeter

In a constant-pressure calorimetry experiment, the system consists of the chemicals undergoing change and the surroundings consist of the other contents of the calorimeter, the calorimeter itself, and all materials around the calorimeter. However, the calorimeter is designed to minimize energy transfer, so it is possible to assume that the surroundings consist only of the contents of the calorimeter. Therefore, the temperature change measured by the thermometer allows calculation of qsurroundings for a chemical change in a coffee cup calorimeter.

qsurroundings = (mass of calorimeter contents)(specific heat of solution)(ΔT)

Because 0 = qsystem + qsurroundings, the enthalpy change for a chemical process taking place in a coffee cup calorimeter is

ΔH = qsystem = -qsurroundings

In a typical experiment, enthalpy change is reported as kilojoules per mole of reactant (kJ/mol). Note that in constant-pressure calorimetry experiments, an increase in temperature indicates an exothermic reaction (qsurroundings is positive, qsystem and ΔH are negative) and a decrease in temperature indicates an endothermic reaction (qsurroundings is negative, qsystem and ΔH are positive). The sign conventions in constant-pressure calorimetry experiments are summarized in Table 5.4.1.

Table 5.4.1: Sign Conventions in Constant-Pressure Calorimetry
Exothermic reactions
  • Temperature increases (+ΔT)
  • +qsurroundings
  • qsystem
  • ΔH is negative
Endothermic reactions
  • Temperature decreases (-ΔT)
  • -qsurroundings
  • +qsystem
  • ΔH is positive
Example Problem: Use constant-pressure calorimetry to determine enthalpy change.

Ammonium chloride is very soluble in water. When 4.50 g NH4Cl is dissolved in 53.00 g of water, the temperature of the solution decreases from 20.40 °C to 15.20 °C. Calculate the enthalpy of dissolution of NH4Cl (in kJ/mol).

Assume that the specific heat of the solution is 4.18 J/g • °C and that the heat absorbed by the calorimeter is negligible.

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Video Solution

You are asked to calculate the enthalpy change for the dissolution of ammonium chloride.

You are given the masses of the solid and water, and the temperature change that occurs when the two are combined.

First calculate the energy change for the surroundings (qsolution) in the coffee cup calorimeter.

csolution = 4.18 J/g • °C
msolution = 4.50 g + 53.00 g = 57.50 g
ΔT = Tfinal - Tinitial = 15.20 °C - 20.40 °C = -5.20 °C
qsolution = m × csolution × ΔT = (57.50 g)(4.18 J/g • °C)(-5.20 °C) = -1250 J

Next calculate q for the dissolution of NH4Cl, qsystem.

qdissolution + qsolution = 0
qsolution = -qdissolution = 1250 J

Finally, calculate the amount of NH4Cl dissolved (in mol) and ΔH for the dissolution of NH4Cl (kJ/mol).

Is your answer reasonable? The temperature of the solution decreased, indicating an endothermic process and a positive value for ΔHdissolution.

Due: 1/1/20 11:59 PM
Score: 0
Due: 1/1/20 11:59 PM
Score: 0

Although most constant-pressure calorimetry experiments are performed in a laboratory, Interactive Figure 5.4.3 shows how you can use this type of experiment to determine practical information about a heat source in your home.

Due:
1/1/20 11:59 PM
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How hot is this fire?

Many constant-pressure calorimetry experiments assume that no heat is transferred to the calorimeter or to the outside surroundings. A more precise experiment is performed using constant-volume calorimetry. Constant-volume experiments can be performed using a bomb calorimeter (Interactive Figure 5.4.4), a reaction vessel designed to measure the energy change involved in combustion reactions.

Due:
1/1/20 11:59 PM
Score: 0
A constant-volume calorimeter

The chemical reaction studied in a bomb calorimeter takes place inside a sealed steel vessel (the bomb) that is completely surrounded by a water bath, and an insulated jacket surrounds the water bath. The temperature change of the chemical reaction is determined by measuring the temperature change of the water surrounding the bomb.

Because the reaction studied in a bomb calorimetry experiment takes place in a sealed bomb, this is a constant-volume calorimetry experiment, not a constant-pressure experiment. Under constant volume conditions, the heat evolved or absorbed by a chemical change, q, is equal to the change in energy, ΔE, not the change in enthalpy, ΔH. However, the difference between ΔE and ΔH is quite small for most chemical reactions.

The heat evolved in a bomb calorimeter combustion reaction (qreaction) is absorbed by the steel bomb (qbomb) and the water in the water bath (qwater).

0 = qreaction + qbomb + qwater

The heat absorbed by the steel bomb is calculated from the temperature change of the water bath (ΔT) and the bomb heat capacity (cbomb, J/°C). The heat absorbed by the water bath is calculated from the mass of water, the specific heat of water, and the water bath temperature change.

Quick Check 5.5
Due:
1/1/20 11:59 PM
Score: 0
Click the above link to answer a question about calorimetry.
Example Problem: Use constant-volume calorimetry to determine energy change.

A 0.444-g sample of sucrose (C12H22O11) is burned in a bomb calorimeter and the temperature increases from 20.00 °C to 22.06 °C. The calorimeter contains 748 g of water, and the bomb has a heat capacity of 420. J/°C. Calculate ΔE for the combustion reaction per mole of sucrose burned (kJ/mol).

C12H22O11(s) + 12 O2(g) → 12 CO2(g) + 11 H2O(ℓ)

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Video Solution

You are asked to calculate the energy change (in kJ/mol sucrose) for the combustion of sucrose.

You are given the mass of sucrose and bomb calorimeter data (mass of the water, temperature change of the water, and calorimeter heat capacity).

First, calculate the energy absorbed by the water bath and the bomb.

Water bath:

cwater = 4.184 J/g • °C
mwater = 748 g
ΔT = Tfinal - Tinitial = 22.06 °C - 20.00 °C = 2.06 °C
qwater = m × cwater × ΔT = (748 g)(4.184 J/g • °C)(2.06 °C) = 6450 J

Bomb:

cbomb = 420. J/°C
ΔT = Tfinal - Tinitial = 22.06 °C - 20.00 °C = 2.06 °C
qbomb = cbomb × ΔT = (420. J/g • °C)(2.06 °C) = 865 J

Next, calculate the energy released by the combustion reaction.

0 = qreaction + qbomb + qwater
qreaction = -(qbomb + qwater) = -(6450 J + 865 J) = -7320 J

Finally, calculate the amount (in mol) of sucrose burned in the combustion reaction and the energy change for the reaction.

Because the difference between ΔE and ΔH is quite small, this energy change can be taken as the enthalpy of combustion (ΔHcomb) for sucrose.

Is your answer reasonable? This is an exothermic reaction; temperature increased, and qreaction and ΔE are negative. In addition, the combustion of a hydrocarbon typically produces a large amount of energy per mole of compound.

Due: 1/1/20 11:59 PM
Score: 0
Due: 1/1/20 11:59 PM
Score: 0
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