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Chapter 5: Problem 92

Some commercial drain cleaners contain two components: sodium hydroxide and aluminum powder. When the mixture is poured down a clogged drain, the following reaction occurs: $$2 \mathrm{NaOH}(a q)+2 \mathrm{Al}(s)+6 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow_{2 \mathrm{NaAl}(\mathrm{OH})_{4}(a q)+3 \mathrm{H}_{2}(g)}$$ The heat generated in this reaction helps melt away obstructions such as grease, and the hydrogen gas released stirs up the solids clogging the drain. Calculate the volume of \(\mathrm{H}_{2}\) formed at STP if \(3.12 \mathrm{~g}\) of \(\mathrm{Al}\) is treated with an excess of \(\mathrm{NaOH}\).

Short Answer

Expert verified
The volume of \(H_{2}\) formed at STP when 3.12 g of \(Al\) is treated with an excess of \(NaOH\) is approximately 3.89 L.

Step by step solution

01

Write down the balanced chemical equation

The balanced chemical equation is already provided: \[2 \mathrm{NaOH}(a q)+2 \mathrm{Al}(s)+6 \mathrm{H}_{2} \mathrm{O}(l) \rightarrow_{2} \mathrm{NaAl}(\mathrm{OH})_{4}(a q)+3 \mathrm{H}_{2}(g)\] This equation tells us that 2 moles of Al produce 3 moles of H2.
02

Convert mass of Al to moles

Using the molar mass of Al which is \(26.98 \, \mathrm{g/mol} \), the given mass of Al (3.12 g) can be converted to moles: \[\frac{3.12 \, \mathrm{g}}{26.98 \, \mathrm{g/mol}} \approx 0.116 \, \mathrm{mol} \, \mathrm{Al}\]
03

Use stoichiometric ratios to find moles of H2

From the balanced equation, 2 moles of Al produce 3 moles of H2. Therefore, the moles of H2 produced from 0.116 mol Al are: \(0.116 \, \mathrm{mol} \, \mathrm{Al} \times \frac{3 \, \mathrm{mol} \, \mathrm{H2}}{2 \, \mathrm{mol} \, \mathrm{Al}} \approx 0.174 \, \mathrm{mol} \, \mathrm{H2}\]
04

Convert moles of H2 to volume at STP

At standard temperature and pressure (STP), 1 mole of any gas occupies a volume of 22.4 L. Therefore, the volume of 0.174 mol H2 is: \(0.174 \, \mathrm{mol}\times 22.4 \, \mathrm{L/mol} \approx 3.89 \, \mathrm{L}\)

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Most popular questions from this chapter

The ozone molecules present in the stratosphere absorb much of the harmful radiation from the sun. Typically, the temperature and pressure of ozone in the stratosphere are \(250 \mathrm{~K}\) and \(1.0 \times 10^{-3} \mathrm{~atm},\) respectively. How many ozone molecules are present in \(1.0 \mathrm{~L}\) of air under these conditions?

Use the kinetic theory of gases to explain why hot air rises.

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At \(46^{\circ} \mathrm{C}\) a sample of ammonia gas exerts a pressure of \(5.3 \mathrm{~atm} .\) What is the pressure when the volume of the gas is reduced to one-tenth (0.10) of the original value at the same temperature?
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