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青州's Question
Chemistry
Posted 10 months ago

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A 8.19−g8.19-\mathrm{g} sample of a Cu−Zn\mathrm{Cu}-\mathrm{Zn} alloy reacts with HCl\mathrm{HCl} acid to produce hydrogen gas. If the hydrogen gas has a volume of 1.45 L1.45 \mathrm{~L} at 20∘C20^{\circ} \mathrm{C} and 723mmHg723 \mathrm{mmHg}, what is the percent of Zn\mathrm{Zn} in the alloy? □\square %\%
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Answer from Sia
Posted 10 months ago
Solution
1
Convert pressure to atm: Convert the given pressure from mmHg to atm using the conversion factor 1 atm=760 mmHg1 \text{ atm} = 760 \text{ mmHg}
$ P_{\text{atm}} = \frac{723 \text{ mmHg}}{760 \text{ mmHg/atm}} = 0.9513 \text{ atm} $
2
Use the ideal gas law: Apply the ideal gas law PV=nRTPV = nRT to find the number of moles of hydrogen gas produced
$ n = \frac{PV}{RT} $ where $R = 0.0821 \text{ L atm mol}^{-1}\text{K}^{-1}$ and $T$ must be in Kelvin. $T = 20°C + 273.15 = 293.15 \text{ K}$.
$ n = \frac{(0.9513 \text{ atm})(1.45 \text{ L})}{(0.0821 \text{ L atm mol}^{-1}\text{K}^{-1})(293.15 \text{ K})} = 0.0569 \text{ mol} $
3
Relate moles of H2 to moles of Zn: The balanced chemical equation for the reaction of zinc with hydrochloric acid is Zn+2HCl→ZnCl2+H2Zn + 2HCl \rightarrow ZnCl_2 + H_2. From this, we know that 1 mole of Zn produces 1 mole of H2H_2
$ n_{\text{Zn}} = n_{H_2} = 0.0569 \text{ mol} $
4
Calculate the mass of Zn: Use the molar mass of Zn (65.38 g/mol65.38 \text{ g/mol}) to find the mass of Zn in the alloy
$ m_{\text{Zn}} = n_{\text{Zn}} \times \text{Molar mass of Zn} = 0.0569 \text{ mol} \times 65.38 \text{ g/mol} = 3.72 \text{ g} $
5
Determine the percentage of Zn in the alloy: Calculate the percentage by mass of Zn in the alloy using the mass of Zn and the total mass of the alloy
$ \text{Percentage of Zn} = \left( \frac{m_{\text{Zn}}}{m_{\text{alloy}}} \right) \times 100\% = \left( \frac{3.72 \text{ g}}{8.19 \text{ g}} \right) \times 100\% = 45.42\% $
Answer
45.42%
Key Concept
Using the ideal gas law to relate the volume of a gas to the amount of a reactant in a chemical reaction
Explanation
The volume of hydrogen gas produced in the reaction can be used to calculate the moles of hydrogen, which directly relates to the moles of zinc since they react in a 1:1 molar ratio. This allows us to find the mass and then the percentage of zinc in the alloy.

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