## Chapter 3

## Q. 3.23

One way of producing hydrogen for use in hydrogen powered vehicles is the water–gas shift reaction:

H_{2}O(g) + CO(g) → H_{2}(g) + CO_{2}(g)

At 200°C, the reaction produces a 96% yield. How many grams of H_{2}O and CO are needed to generate 176 g of H_{2} under these conditions?

## Step-by-Step

## Verified Solution

**Collect and Organize** This is a stoichiometry problem like Sample Exercises 3.12 and 3.13, except that the yield of reaction is only 96%.

**Analyze** We need to convert the mass of H_{2} we wish to make into moles of H_{2}, and then we use the mole ratios of H_{2}:CO and H_{2}:H_{2}O to find the amount of reactants we need. To produce 176 g of H_{2} by using a reaction that produces 96% of the theoretical yield, we consider the theoretical yield to be 96% of the total yield we need. Then by analogy to Sample Exercise 3.13, we can calculate the amount of both reactants needed.

**Solve**

1. The number of moles of H_{2} we wish to produce is:

176 \sout{g H_{2}} \times \frac{1 mol H_{2}}{2.016 \sout{g H_{2}}} =87.3 mol H_{2}

However, since the reaction produces only 96% of the theoretical yield, we need to base our calculation on what 100% yield would be if 87.30 moles is 96% of the theoretical yield:

87.30 mol = 0.96x x = 91 mol

2. Using the mole ratios of H_{2}:H_{2}O and H_{2}:CO, we find the number of moles of H_{2}O and CO:

91 \sout{mol H_{2}} \times \frac{1 mol H_{2}O}{1 \sout{mol H_{2}}} =91 mol H_{2}O 91 \sout{mol H_{2}} \times \frac{1 mol CO}{1 \sout{mol H_{2}}} =91 mol CO

3. We convert from moles of reactants to the mass of the reactants by multiplying by the molar mass:

91 \sout{mol H_{2}O} \times \frac{18.02 g H_{2}O}{1 \sout{mol H_{2}O}} =1.6 \times 10^{3} g H_{2}O

91 \sout{mol CO} \times \frac{28.01 g CO}{1 \sout{mol CO}}= 2.5 \times 10^{3} g CO

As a check of our answers, let’s calculate how much H_{2} would be produced from 91 moles of CO if the reaction proceeded in 100% yield:

91 \sout{mol CO} \times \frac{1 \sout{mol H_{2}}}{1 \sout{mol CO}} \times \frac{2.016 g H_{2}}{1 \sout{mol H_{2}}} =183 g H_{2}

The percent yield is

\frac{176 g H_{2}}{183 g H_{2}} \times 100\% = 96\%

**Think About It **On a large scale, any yield less than 100% could be a significant cost for rare and expensive reactants.