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# 17.9: Stoichiometric Calculations and Enthalpy Changes

Difficulty Level: At Grade Created by: CK-12
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Practice Stoichiometric Calculations and Enthalpy Changes
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What will it cost?

There is a growing concern about the damage to the environment from emissions from manufacturing plants. Many companies are taking steps to reduce these harmful emissions by adding equipment that will trap the pollutants. In order to know what equipment (and how many) to order, studies need to be done to measure the amount of product currently produced. The since pollution is often both particulate and thermal, energy changes need to be determined in addition to the amounts of products released.

### Stoichiometric Calculations and Enthalpy Changes

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 released 890.4 kJ, the reaction of 2 mol of methane would release 2×890.4 kJ=1781 kJ\begin{align*}2 \times 890.4 \text{ kJ} = 1781 \text{ kJ}\end{align*}. The reaction of 0.5 mol of methane would release 890.4 kJ2=445.2 kJ\begin{align*}\frac{890.4 \text{ kJ}}{2}= 445.2 \text{ kJ}\end{align*}. As with other stoichiometry problems, the moles of a reactant or product can be linked to mass or volume.

#### Sample Problem: Calculating Enthalpy Changes

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

2SO2(g)+O2(g)2SO3(g)+198 kJ\begin{align*}2\text{SO}_2(\text{g}) + \text{O}_2(\text{g}) \rightarrow 2\text{SO}_3(\text{g})+198 \text{ kJ}\end{align*}

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 SO2 = 58.0 g
• molar mass SO2 = 64.07 g/mol
• ΔH=198 kJ for the reaction of 2 mol SO2\begin{align*}\Delta H = -198 \text{ kJ for the reaction of } 2 \text{ mol SO}_2 \end{align*}

Unknown

• ΔH=? kJ\begin{align*}\Delta H = ? \text{ kJ} \end{align*}

The calculation requires two steps. The mass of SO2 is converted to moles. Then the mol SO2 is multiplied by the conversion factor of (198 kJ2 mol SO2)\begin{align*}\left(\frac{-198 \text{ kJ}}{2 \text{ mol SO}_2} \right)\end{align*}.

Step 2: Solve.

ΔH=58.0 g SO2×1 mol SO264.07 g SO2×198 kJ2 mol SO2=89.6 kJ\begin{align*}\Delta H=58.0 \text{ g SO}_2 \times \frac{1 \text{ mol SO}_2}{64.07 \text{ g SO}_2} \times \frac{-198 \text{ kJ}}{2 \text{ mol SO}_2}=-89.6 \text{ kJ}\end{align*}

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\begin{align*}\Delta H\end{align*} is negative because the reaction is exothermic.

#### Summary

• Calculations of energy changes in enthalpy equations are described.

#### Practice

Work on the problems at the site below. No peaking at the answers.

#### Review

Questions

1. What do you need to determine to solve enthalpy stoichiometry problems?
2. If I react 1.75 moles of methane, how much energy will be involved?
3. I ran a reaction producing sulfur dioxide and releasing 267.3 kJ of energy. How many moles of sulfur dioxide were involved in the reaction?

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