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# 17.2: Thermochemical Equations

Difficulty Level: At Grade Created by: CK-12

## Lesson Objectives

• Define enthalpy, and know the conditions under which the enthalpy change in a reaction is equal to the heat absorbed or released.
• Describe the principles behind calorimetry, and be able to calculate the heat absorbed or released during a process that occurs in a calorimeter.
• Write and solve problems with thermochemical equations.

## Lesson Vocabulary

• calorimeter
• calorimetry
• enthalpy
• heat of reaction
• thermochemical equation

### Recalling Prior Knowledge

• How is specific heat used in calculating the heat absorbed or released in a process?
• What relationships are shown in a balanced chemical equation?

Heat is either absorbed or released during chemical reactions. In this lesson, you will learn about how heat changes are measured in the lab and how quantities of heat are represented in a chemical equation.

## Enthalpy

Heat changes in chemical reactions are most often measured in the laboratory under conditions in which the reacting system is open to the atmosphere. In that case, the system is at a constant pressure. Enthalpy (H) is the heat content of a system at constant pressure. Chemists routinely measure changes in the enthalpy of a chemical system as reactants are converted into products. The heat that is absorbed or released by a reaction at constant pressure is the same as the enthalpy change, which is given the symbol ΔH. Unless otherwise specified, all reactions in this text are assumed to take place at constant pressure. Therefore, heat and enthalpy change will be used interchangeably, and q = ΔH.

### Calorimetry

Calorimetry is the measurement of the transfer of heat into or out of a system during a chemical reaction or physical process. A calorimeter is an insulated container that is used to measure heat changes. The reactions that can most easily be analyzed in a calorimetry experiment involve only liquids or aqueous solutions. A frequently used and inexpensive calorimeter is a set of nested foam cups fitted with a lid to limit the heat exchange between the liquid in the cup and the air in the surroundings (Figure below). In a typical calorimetry experiment, specific volumes of the reactants are dispensed into separate containers, and the temperature of each is measured. They are then mixed into the calorimeter, which starts the reaction. The reactant mixture is stirred until the reaction is complete, and the temperature of the reaction is continuously monitored.

In a simple constant-pressure calorimeter, the temperature of a water-based reaction is monitored as the reaction takes place. The substances dissolved in the water are the system, and the water itself is the surroundings.

The key to all calorimetry experiments is the assumption that there is no heat exchange between the insulated calorimeter and the room. Consider the case of a reaction taking place between aqueous reactants. The water in which the solids have been dissolved is the surroundings, while the dissolved substances are the system. The temperature change that is measured is the temperature change that is occurring in the surroundings. If the temperature of the water increases as the reaction occurs, the reaction is exothermic. Heat was released by the system into the surrounding water. An endothermic reaction absorbs heat from the surroundings, so the temperature of the water decreases as heat leaves the surroundings to enter the system.

The temperature change of the water is measured in the experiment, and the specific heat of water can be used to calculate the heat absorbed by the surroundings (qsurr).

qsurr = m × cp × ΔT

In this equation, m is the mass of the water, cp is the specific heat of the water, and ΔT is Tf – Ti. The heat absorbed by the surroundings is equal, but opposite in sign, to the heat released by the system. Because the heat change is determined at constant pressure, the heat released by the system (qsys) is equal to the enthalpy change (ΔH).

qsys = ΔH = -qsurr = -(m × cp × ΔT)

The sign of ΔH is positive for an endothermic reaction and negative for an exothermic reaction.

Sample Problem 17.2: Calorimetry and Enthalpy Changes

In an experiment, 25.0 mL of 1.00 M HCl at 25.0°C is added to 25.0 mL of 1.00 M NaOH at 25.0°C in a foam cup calorimeter. As the reaction occurs, the temperature of the solution rises to 32.0°C. Calculate the enthalpy change (ΔH) in kJ for this reaction. Assume the densities of the solutions are 1.00 g/mL and that their specific heats are the same as that of pure water.

Step 1: List the known quantities and plan the problem.

Known

• cp = 4.18 J/g•°C
• Vfinal = 25.0 mL + 25.0 mL = 50.0 mL
• ΔT = 32.0°C – 25.0°C = 7.0°
• Density = 1.00 g/mL

Unknown

• ΔH = ? kJ

The volume and density can be used to find the mass of the solution after mixing. Then, calculate the change in enthalpy by using ΔH = qsys = −qsurr = −(m × cp × ΔT).

Step 2: Solve.

$\mathrm{m=50.0 \ mL \times \dfrac{1.00 \ g}{1 \ mL}=50.0 \ g}$
ΔH = −(m × cp × ΔT) = -(50.0 g × 4.18 J/g•°C × 7.0°C) = -1463 J = -1.5 kJ

Step 3: Think about the result.

The enthalpy change is negative because the reaction releases heat to the surroundings, causing the temperature of the water to rise.

Practice Problems
1. A rock is heated and dropped into a foam cup calorimeter containing 35.0 mL of water at 21.4°C. The temperature of the water rises to 24.8°C. How many joules of heat were released by the rock?
2. A 100.0 g sample of an unknown metal is heated to 95.00°C. This hot metal is then placed into a foam cup calorimeter containing 50.0 g of water at 20.00°C. The water and metal come to a final temperature of 31.67°C. Calculate the specific heat of the metal, and use the table above (Table above) to identify it.

## Heats of Reaction

When methane gas is combusted, heat is released, making the reaction exothermic. Specifically, the combustion of 1 mol of methane releases 890.4 kilojoules of heat energy. This information can be shown as part of the balanced equation.

$\text{CH}_{4}{(g)}+2\text{O}_{2}{(g)} \rightarrow \text{CO}_{2}{(g)}+2\text{H}_2\text{O}{(l)}+890.4 \ \text{kJ}$

The equation tells us that 1 mol of methane combines with 2 mol of oxygen to produce 1 mol of carbon dioxide and 2 mol of water. In the process, 890.4 kJ is released, so it is written as a product of the reaction. A thermochemical equation is a chemical equation that includes the enthalpy change of the reaction. The process in the above thermochemical equation can be shown visually below (Figure below (A)).

(A) As reactants are converted to products in an exothermic reaction, enthalpy is released into the surroundings. The enthalpy change of the reaction is negative. (B) As reactants are converted to products in an endothermic reaction, enthalpy is absorbed from the surroundings. The enthalpy change of the reaction is positive.

In the combustion of methane example, the enthalpy change is negative because heat is being released by the system. Therefore, the overall enthalpy of the system decreases. The heat of reaction is the enthalpy change for a chemical reaction. In the case above, the heat of reaction is −890.4 kJ. The thermochemical reaction can also be written in this way:

$\text{CH}_{4}{(g)}+2\text{O}_{2}{(g)} \rightarrow \text{CO}_{2}{(g)}+2\text{H}_2\text{O}{(l)} \ \ \ \Delta \text{H}=-890.4 \ \text{kJ}$

Heats of reaction are typically measured in kilojoules. It is important to include the physical states of the reactants and products in a thermochemical equation, because the value of ΔH depends on those states.

Endothermic reactions absorb energy from the surroundings as the reaction occurs. When 1 mol of calcium carbonate decomposes into 1 mol of calcium oxide and 1 mol of carbon dioxide, 177.8 kJ of heat is absorbed. This process is shown visually above (Figure above (B)). When heat is absorbed during a reaction, it can be written as a reactant. The thermochemical reaction is shown below.

$\text{CaCO}_{3}{(s)}+\text{177.8 kJ} \rightarrow \text{CaO}{(s)}+\text{CO}_{2}{(g)}$

The reaction is endothermic, so the sign of the enthalpy change is positive.

$\text{CaCO}_{3}{(s)} \rightarrow \text{CaO}{(s)}+\text{CO}_{2}{(g)} \ \ \ \Delta \text{H}=177.8 \ \text{kJ}$

### Stoichiometry and Thermochemical Equations

Chemistry problems that involve enthalpy changes can be solved by techniques similar to stoichiometry problems. Refer again to the combustion reaction of methane. Since the reaction of 1 mol of methane releases 890.4 kJ, the reaction of 2 mol of methane would release 2 × 890.4 kJ = 1781 kJ. The reaction of 0.5 mol of methane would release 890.4 kJ / 2 = 445.2 kJ. As with other stoichiometry problems, the moles of a reactant or product can be linked to mass or volume.

Sample Problem 17.3: Calculating Enthalpy Changes

Sulfur dioxide gas reacts with oxygen to form sulfur trioxide in an exothermic reaction according to the following thermochemical equation.

$2\text{SO}_{2}{(g)}+\text{O}_{2}{(g)} \rightarrow 2\text{SO}_{3}{(g)}+198 \ \text{kJ}$

Calculate the enthalpy change that occurs when 58.0 g of sulfur dioxide is reacted with excess oxygen.

Step 1: List the known quantities and plan the problem.

Known

• mass of SO2 = 58.0 g
• molar mass of SO2 = 64.07 g/mol
• ΔH = −198 kJ for the reaction of 2 mol SO2

Unknown

• ΔH = ? kJ

The calculation requires two steps. First, the mass of SO2 is converted to moles. Then, mol SO2 is multiplied by the conversion factor (−198 kJ/2 mol SO2).

Step 2: Solve.

$\Delta \text{H}=58.0 \ \text{g SO}_2 \times \dfrac{1 \ \text{mol SO}_2}{64.07 \ \text{g SO}_2} \times \dfrac{-198 \ \text{kJ}}{2 \ \text{mol SO}_2}=-89.6 \ \text{kJ}$

The mass of sulfur dioxide is slightly less than 1 mol. Since 198 kJ is released for every 2 mol of SO2 that reacts, the heat released when about 1 mol reacts is one half of 198. The 89.6 kJ is slightly less than half of 198. The sign of ΔH is negative because the reaction is exothermic.

Practice Problem
1. Given the reaction below for the decomposition of mercury(II) oxide:
1. What is ΔH when 0.750 mol of HgO fully reacts?
2. A certain reaction produces 28.4 g of Hg. How much heat was absorbed in this reaction?
3. What volume of oxygen gas at STP is produced in a reaction that absorbs 432 kJ of heat?

## Lesson Summary

• Enthalpy is the heat content of a system. When a chemical reaction or physical process occurs at constant pressure, the heat absorbed or released by the system is equal to the enthalpy change of the system.
• A calorimeter is an insulated device used in the laboratory to measure the enthalpy change during a reaction.
• Thermochemical equations show the heat that is either absorbed or released during a reaction. The enthalpy change (ΔH) for a reaction can be used as a conversion factor in solving problems.

## Lesson Review Questions

### Reviewing Concepts

1. What experimental condition is required for the heat change in a reaction to be numerically equal to the enthalpy change (ΔH)?
2. Why is a foam cup used as a calorimeter rather than a glass beaker?
3. What are some possible sources of error that would be present in an experiment where a foam cup is used as a calorimeter?
4. When 1 mol of nitrogen gas reacts with 3 mol of hydrogen gas, 2 mol of ammonia gas is produced and 92.6 kJ of heat is released. Write the thermochemical equation.

### Problems

1. Given the following reaction for the formation of water from hydrogen and oxygen gases: What is the ΔH for the following reactions?
1. $\text{H}_{2}{(g)}+1/2 \text{O}_{2}{(g)} \rightarrow \text{H}_2\text{O}{(l)}$
2. $2\text{H}_2\text{O}{(l)} \rightarrow 2\text{H}_{2}{(g)}+\text{O}_{2}{(g)}$
2. 100. mL of 0.500 M HCl is mixed with 100. mL of 0.500 M NaOH in a foam cup calorimeter. The initial temperatures of both solutions are 22.50°C. After the reaction occurs, the temperature rises to 26.00°C. Calculate the enthalpy change for the reaction. Assume the densities of the solutions are 1.00 g/mL and the specific heat is 4.18 J/g°C.
3. An ice cube is dropped into a foam cup calorimeter containing 95.0 mL of water at 20.0°C. The temperature drops to 13.7°C as the ice cube melts. How much total heat (in kJ) was released by the water into the ice cube?
4. 66.80 g of lead is heated to 155°C and then placed into a foam cup calorimeter containing 70.0 mL of water at 15.2°C. Assuming no heat loss, calculate the final temperature of the water and lead.
5. Given the balanced equation below for the highly exothermic reaction of aluminum with oxygen to form aluminum oxide:
1. What is the value of ΔH when 1.00 mol of aluminum reacts?
2. What is the value of ΔH when 5.23 g of aluminum reacts?
3. What is the value of ΔH when 6.17 L of oxygen gas at STP reacts with excess aluminum?
4. A certain reaction releases 6881 kJ of heat. What mass of aluminum oxide was produced in the reaction?
6. Propane gas combusts according to the following equation. 45.1 L of propane at 0.915 atm is combusted at 513.°C. How much heat is released in the reaction? Assume the propane is an ideal gas.

## Points to Consider

Enthalpy changes always accompany changes in state.

• What are the heat of fusion and heat of vaporization, and how can they be used to solve problems?
• What is the heat of solution?

Aug 02, 2012

Feb 16, 2015

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