Lesson

In this lesson, the focus is on calculating heat changes associated with phase changes and chemical changes at constant temperature. You will be using the formula

where q is the heat (or enthalpy) change, n is the number of moles of a species undergoing a change, and ΔH is the molar enthalpy value for the species.

Since moles are not directly measurable, you may be given an amount of a species in units of mass or volume. To convert from mass to moles, you will need to determine the molar mass of the species. If the species is a gas, then you will need to use the molar volume of a gas at STP (22.4 L/mol). 

Molar enthalpies for a number of species undergoing chemical or physical changes are known. Reference data may be found in your MHR textbook (see Table 16.2 p.642, Table 16.3 p.643, and Table 16.4 p.647).

Sample Exercise 1

Calculate the heat required to melt 50.0 g of ice at 0.0°C.

Answer

Plan a Strategy

  1. Calculate the molar mass of H2O and convert mass of ice to moles.
  2. Look-up the molar heat of fusion for ice, substitute into the heat formula and solve.
  3. Communicate the answer.

Step 1: Convert mass to moles.

The molar mass of water is 18.02 g/mol.

Step 2: Calculate the heat (enthalpy) change.

The molar heat of fusion for ice is 6.02 kJ/mol.

Step 3: Communicate the answer.

Melting 50.0 g of ice at 0.0°C requires +16.7 kJ of energy.

Notice the sign of the heat value. Melting (fusion) is an endothermic process - energy is required to break the intermolecular forces that hold water molecules together in the ice crystal. The energy absorbed by the ice becomes the potential energy of the liquid molecules.

This potential energy will be released if the melted water freezes. The amount of energy released as one mole of ice forms (6.02 kJ) is the same as the amount of energy required to melt one mole of ice (6.02 kJ). This relationship can be stated as:

.

Figure 16.16 on page 646 of MHR illustrates this relationship graphically.

Chemical Systems

Knowing the heat change associated with a chemical change involving one mole of a species allows you to calculate the heat change associated with any measured amount of that species.

Sample Exercise 2

Calculate the heat change that should occur when 10.4 g of calcium chloride is formed from its elements at SATP conditions.

Answer

Plan a Strategy

  1. Calculate the molar mass of CaCl2 and convert the given mass to moles.
  2. Look-up the molar heat of formation of CaCl2 at SATP conditions, substitute into the heat formula, and solve.
  3. Communicate the answer.

Step 1: Convert mass to moles.

Molar mass of CaCl2 = 1(40.08) + 2(35.45) = 110.98 g/mol

Step 2: Calculate the heat (enthalpy) change.

In Table 16.2, the molar enthalpy of formation for calcium chloride is  .

Step 3: Communicate the answer.

The formation of 10.4 g of calcium chloride at SATP conditions results in the release of 74.5 kJ of heat.

Sample Exercise 3

Calculate the heat change that should occur when 5.0 L of propane is burned at SATP conditions.

Answer

Plan a Strategy

  1. Convert the given volume to moles.
  2. Look-up the molar heat of combustion of C3H8 at SATP conditions, substitute into the heat formula, and solve.
  3. Communicate the answer.

Step 1: Convert volume to moles.

Molar volume of any gas at SATP conditions is 24.8 L/mol.

Step 2: Calculate the heat (enthalpy) change.

In Table 16.2, the molar enthalpy of combustion for propane is .

Step 3: Communicate the answer.

The combustion of 5.0 L of propane gas at SATP conditions results in the release of 470 kJ of heat.
 

Dissolving can be an exothermic or endothermic process depending on the nature of the interactions between the solute and the solvent.

Sample Exercise 4

Calculate the heat change that should occur when 4.00 g of ammonium nitrate dissociates in water. ΔHsoln = +25.7 kJ/mol.

Answer

Plan a Strategy

  1. Convert the given mass to moles.
  2. Substitute into the heat formula and solve.
  3. Communicate the answer.

Step 1: Convert mass to moles.

Molar mass of ammonium nitrate is 80.06 g/mol.

Step 2: Calculate the heat (enthalpy) change.

Step 3: Communicate the answer.

The heat change for dissolving 4.00 g of ammonium nitrate is +1.28 kJ.

Simple calorimetry is used to determine ΔHsoln. In such cases, the solute mixes with the surroundings (calorimeter water). Because of this, you have to add the mass of solute to the mass of the calorimeter water when calculating q. Unless the specific heat capacity of the solution is provided, you assume that the specific heat of the solution is equal to that of water. This assumption would be considered to be a source of error in a quantitative analysis.

Sample Exercise 5

The addition of 5.32 g of lithium perchlorate to 100.0 mL of calorimeter water resulted in a temperature change from 20.44°C to 23.45°C in the calorimeter. Calculate the molar enthalpy of solution formation for lithium perchlorate.

Answer
Plan a strategy.
  1. Calculate m for calorimeter water.
  2. Calculate qcalorimeter.
  3. Apply first law of thermodynamics.
  4. Calculate ΔHsoln.
  5. Communicate the answer.

Step 1: Calculate the mass of the calorimeter water.

Since lithium perchlorate has high solubility in water, it dissociates completely into lithium ions and perchlorate ions. It mixes evenly with the calorimeter water. The mass of the calorimeter water increases. Assuming the density of pure water is 1 g/mL, the mass of water is 100.0 g. When the mass of solute dissolves, the total mass of the mixture in the calorimeter is 105.32 g.

Step 2: Calculate qcalorimeter.

Step 3: Apply first law of thermodynamics.

Step 4: Calculate ΔHsoln.

Calculate the molar mass of LiClO4: 6.94 + 35.45 + 4(16.00) = 106.39g/mol.

Step 5: Communicate the answer.

The molar enthalpy of solution formation for lithium perchlorate is -26.5 kJ/mol.

Calculating ΔH

When a new substance is discovered, its properties have to be determined and reported. For enthalpy changes alone, the list can be extensive ΔHfus, ΔHvap, ΔHcomb, ΔHsoln, and so on.

Sample Exercise 6

By simple calorimetry, the heat change for melting 0.1000 mol of a new top secret compound, X2-J, at its melting point was found to be 1.337 kJ. Calculate the heat of molar enthalpy of fusion for compound X2-J.

Answer

Plan a Strategy

  1. Rearrange the molar enthalpy formula to solve for ΔHfus, substitute and solve.
  2. Communicate the answer.

Step 1: Rearrange formula and solve.

Step 2: Communicate the answer.

The molar enthalpy of fusion of X2-J is 13.37 kJ/mol.

The molar heat of reaction for a compound can be determined given a mass and a heat change.

Sample Exercise 7

A 5.00 g sample of benzene was burned at SATP conditions resulting in the release of 209.2 kJ of heat. Calculate the molar heat of combustion for benzene.

Answer

Plan a Strategy

  1. Convert the given mass to moles.
  2. Substitute into the molar enthalpy formula, and solve.
  3. Communicate the answer.

Step 1: Convert mass to moles.

Molar mass of benzene is 78.12 g/mol.

Step 2: Calculate the heat (enthalpy) change.

Step 3: Communicate the answer.

The molar heat of combustion of benzene is -3267 kJ/mol.

During an enthalpy change, the temperature of the species in a system does not change. For this reason, a temperature change in the surroundings is measured and used to find the heat change for the surroundings. Then, by application of the first law of thermodynamics, the enthalpy change of the system is known.

Sample Exercise 8

A 2.00 g sample of methanol was burned at SATP conditions resulting in heat gain of 45.3 kJ in the surroundings. Calculate the molar enthalpy of combustion for methanol.

Answer

Plan a Strategy

  1. Convert the given mass to moles.
  2. Apply the first law of thermodynamics.
  3. Substitute into the molar enthalpy formula, and solve.
  4. Communicate the answer.

Step 1: Convert mass to moles.

Molar mass of methanol is 32.05 g/mol.

Step 2: Apply the First Law of Thermodynamics

Step 3: Calculate the heat (enthalpy) change.

Step 4: Communicate the answer.

The molar heat of combustion of methanol is -726 kJ/mol.
 

Given the number of variables in the formulas used to perform calculations above, you may be asked challenging questions in which calculate the mass of a substance that will undergo a change when a certain amount of heat is absorbed or released.

Sample Exercise 9

A 945.6 g chunk of ice at 0.0°C absorbs 68.6 kJ of heat. Calculate the mass of ice that remains.

Answer

Plan a Strategy

  1. Calculate the number of moles of water that can be melted.
  2. Convert the moles of water to mass.
  3. Subtract the moles melted from the original mass.
  4. Communicate the answer.

Step 1: Use the heat formula to calculate the moles of water melted

Step 2: Convert moles to mass

Step 3: By subtraction find the mass of ice that remains.

945.6 g  -  205.34419 g  =  740.25581 g  =  740.3 g

Step 4: Communicate the answer.

The mass of ice that remains is 740.3 g.

Activity

Textbook Readings

MHR

  • pages 643-644: Calculating Enthalpy Changes
  • pages 645-647: Enthalpy Changes and Changes of State
  • pages 647-648: Enthalpy of Solution
  • page 648: Heat Absorbed or Released a Physical Change
Textbook Practice Items

MHR

  • page 645: items 19, 20, 21a-c, 22 and 23
  • pages 648-649: items 24, 25, 26, 27a-c, 28 and 29
  • pages 649-650: items 3, 5 and 8a-b
  • page 658: items 13, 14a-b, 15, 16a-c, 17a-c and 18a-c
More Practice Items
  1. Given that ΔHvap for ammonia, NH3, is +23.4 kJ/mol, calculate the heat change for condensing 10.0 g of ammonia?
  2. Calculate mass of sodium hydroxide will cause the release of 11.13 kJ of heat when dissolved in water. ΔHsoln for sodium hydroxide is -44.51 kJ/mol.
  3. Calculate the molar enthalpy of vaporization of ammonia if 34.25 kJ of heat is absorbed to vaporize 25.0 g of ammonia.
  4. Calculate the amount of heat required to melt the remaining ice in Sample Exercise 7.
  5. A puncture in the tubing of a refrigerator can cause severe frostbite as chloroethane vaporizes. Use this thermochemical equation to calculate the heat absorbed when 23.6 g of chloroethane (molar mass = 64.52 g/mol) vaporizes at its boiling point.

Test Yourself

There is no self test for this lesson.