Given the two-step process for manufacturing sulfur from "sour" natural gas: 2 H₂S(g)+ 3 O₂(g)→ 2 SO₂(g)+ 2 H₂O(g)
SO₂(g)+ 2 H₂S(g)→ 3 S(s)+ 2 H₂O(g)
What volume of H₂S at STP is necessary to produce 1.00 kg of sulfur?

Question

Quizplus · Accepted Answer

The molar mass of sulfur (S) is approximately 32.07 g/mol. To produce 1.00 kg (or 1000 g) of sulfur, the amount of sulfur in moles is calculated as follows: $ \frac{1000 \, \text{g}}{32.07 \, \text{g/mol}} \approx 31.2 \, \text{moles of S} $.From the second reaction, $ \text{SO}_2(g) + 2 \text{H}_2\text{S}(g) \rightarrow 3 \text{S}(s) + 2 \text{H}_2\text{O}(g) $, we see that 2 moles of $ \text{H}_2\text{S} $ produce 3 moles of sulfur. Therefore, to produce 31.2 moles of sulfur, the moles of $ \text{H}_2\text{S} $ needed are $ \frac{31.2 \, \text{moles of S} \times 2}{3} = 20.8 \, \text{moles of H}_2\text{S} $.At STP (Standard Temperature and Pressure), 1 mole of any gas occupies 22.4 liters. Therefore, the volume of $ \text{H}_2\text{S} $ needed is $ 20.8 \, \text{moles} \times 22.4 \, \text{L/mole} = 465.92 \, \text{L} $.However, this calculation only accounts for the $ \text{H}_2\text{S} $ used in the second step of the process. The first step also consumes $ \text{H}_2\text{S} $, which means the total amount of $ \text{H}_2\text{S} $ needed is actually higher.Given that the total sulfur produced involves both steps and that the initial calculation did not account for the $ \text{H}_2\text{S} $ used in the first step, the correct calculation should consider the overall stoichiometry of the process. The error in the explanation lies in not combining the reactions to find the total $ \text{H}_2\text{S} $ consumption.To correct the explanation: Combining both reactions to find the total $ \text{H}_2\text{S} $ consumption for the entire process is necessary. The overall reaction, after balancing, shows that to produce 3 moles of sulfur, 3 moles of $ \text{H}_2\text{S} $ are needed. Therefore, to produce 31.2 moles of sulfur, $ 31.2 \, \text{moles of H}_2\text{S} $ are required. The volume of $ \text{H}_2\text{S} $ at STP is $ 31.2 \, \text{moles} \times 22.4 \, \text{L/mole} = 698.88 \, \text{L} $, which rounds to approximately 698 L, making option C the correct answer.

Given the Two-Step Process for Manufacturing Sulfur from "Sour" Natural