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Chapter 5: Problem 72

A sample of zinc metal reacts completely with an excess of hydrochloric acid: $$ \operatorname{Zn}(s)+2 \mathrm{HCl}(a q) \longrightarrow \mathrm{ZnCl}_{2}(a q)+\mathrm{H}_{2}(g) $$ The hydrogen gas produced is collected over water at \(25.0^{\circ} \mathrm{C}\) using an arrangement similar to that shown in Figure \(5.15 .\) The volume of the gas is \(7.80 \mathrm{~L},\) and the pressure is \(0.980 \mathrm{~atm} .\) Calculate the amount of zinc metal in grams consumed in the reaction. (Vapor pressure of water at \(25^{\circ} \mathrm{C}=23.8 \mathrm{mmHg} .\) )

Short Answer

Expert verified
Approximately 20.12 grams of Zinc metal is consumed in the reaction.

Step by step solution

01

Convert given conditions to suitable units.

Convert the pressure of water vapor from mmHg to atm, by dividing the pressure in mmHg by 760 (mmHg equal to 1 atm). Vapor pressure of water at 25° C is 23.8 mmHg. So, \(P_{water}=23.8mmHg *\frac{1atm}{760mmHg} \approx 0.0313 atm\). Also, convert the temperature from Celsius to Kelvin - \( T = 25.0° C + 273.15 = 298.15 K \). The volume of the gas is given as 7.80 L.
02

Determine the pressure of dry hydrogen gas.

Subtract the vapor pressure of water from the total collected gas pressure to get the dry hydrogen pressure. Since the total collected gas pressure includes the water vapor pressure and dry hydrogen gas pressure. So, \(P_{H2}= P_{total}- P_{water}\), which would be approximately \(0.980 atm - 0.0313 atm = 0.9487 atm \).
03

Use Ideal Gas law to calculate the number of moles of hydrogen.

Use the ideal gas law \(PV=nRT\), where R is the ideal gas constant \(0.0821 L•atm/K•mol\). Substituting given values, \(n=\frac{PV}{RT} =\frac{0.9487 atm \times 7.80 L}{0.0821 L•atm/K•mol \times 298.15 K} ≈ 0.308 mol\). So, you have the number of moles of H2 gas collected to be approximately 0.308.
04

Apply stoichiometry to determine moles of Zinc.

According to the balanced chemical reaction, 1 mole of Zn reacts to produce 1 mole of H2. So, the moles of Zinc consumed is also 0.308 mol.
05

Convert moles of Zinc to grams.

Zinc has a molar mass of 65.38 g/mol. The amount of Zinc consumed in grams is the moles of Zinc multiplied by the molar mass of Zinc. \(0.308 mol \times 65.38 g/mol ≈ 20.12 grams \).

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