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Chapter 11: Problem 71

Zinc metal reacts with hydrochloric acid to form hydrogen gas via the reaction \(\mathrm{Zn}(s)+2 \mathrm{HCl}(a q) \rightarrow \mathrm{ZnCl}_{2}(a q)+\mathrm{H}_{2}(g)\) How many grams of zinc would be required to produce enough hydrogen gas to fill a 50.0-L cylinder to a pressure of \(10.0 \mathrm{~atm}\) at \(25.0^{\circ} \mathrm{C}\) ?

Short Answer

Expert verified
To produce enough hydrogen gas to fill a 50.0 L cylinder to a pressure of 10.0 atm at 25.0 °C, we would require approximately 1331.36 grams of zinc metal.

Step by step solution

01

Determine moles of hydrogen gas using the Ideal Gas Law

The Ideal Gas Law is given by \(PV = nRT\), where: P - pressure, V - volume, n - number of moles, R - the Ideal Gas constant, T - temperature in Kelvin. First, we need to convert the given temperature to Kelvin by adding 273.15: \(25.0°C + 273.15 = 298.15 K\) Next, we rearrange the Ideal Gas Law equation to solve for the number of moles (n): \(n = \frac{PV}{RT}\) Substituting the given values (P = 10.0 atm, V = 50.0 L, T = 298.15 K, and using R = 0.0821 L·atm/mol·K as the gas constant): \(n = \frac{10.0 \, \text{atm} \cdot 50.0 \, \text{L}}{0.0821\, \frac{\text{L} \cdot \text{atm}}{\text{mol} \cdot \text{K}} \cdot 298.15 \, \text{K}} \approx 20.37 \, \text{moles}\)
02

Convert moles of hydrogen gas to moles of zinc metal using stoichiometry

Using the given balanced chemical equation: \(\mathrm{Zn}(s)+2 \mathrm{HCl}(a q) \rightarrow \mathrm{ZnCl}_{2}(a q)+\mathrm{H}_{2}(g)\) We have a 1:1 ratio of Zn to H₂, so the moles of Zn required will be equal to the moles of H₂ needed. 20.37 moles of H₂ = 20.37 moles of Zn.
03

Convert moles of zinc metal to grams

To find the mass of zinc metal required, we need to multiply the number of moles of zinc by its molar mass (65.38 g/mol): \(20.37 \, \text{moles Zn} \times 65.38 \, \frac{\text{g}}{\text{mol}} \approx 1331.36 \, \text{g}\) Thus, 1331.36 grams of zinc metal are required to produce enough hydrogen gas to fill a 50.0 L cylinder to a pressure of 10.0 atm at 25.0 °C.

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