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According to the following reaction, how many grams of sulfur are formed when 37.4 g of water are formed?

[tex]\[ 2 \, \text{H}_2\text{S} (g) + \text{SO}_2 (g) \rightarrow 3 \, \text{S} (s) + 2 \, \text{H}_2\text{O} (l) \][/tex]

A. 99.8 g S
B. 66.6 g S
C. 56.1 g S
D. 44.4 g S
E. 14.0 g S

Answer :

To find out how many grams of sulfur are formed when 37.4 g of water are produced, we can follow these steps using the balanced chemical equation:

1. Equation Analysis:
The balanced equation is:
[tex]\[
2 \text{H}_2\text{S(g)} + \text{SO}_2\text{(g)} \rightarrow 3 \text{S(s)} + 2 \text{H}_2\text{O(l)}
\][/tex]

2. Molar Masses:
- Molar mass of water (Hâ‚‚O) ≈ 18.02 g/mol
- Molar mass of sulfur (S) ≈ 32.07 g/mol

3. Moles of Water:
First, calculate the moles of water formed:
[tex]\[
\text{moles of H}_2\text{O} = \frac{\text{mass of H}_2\text{O}}{\text{molar mass of H}_2\text{O}} = \frac{37.4 \text{ g}}{18.02 \text{ g/mol}}
\][/tex]
Moles of Hâ‚‚O ≈ 2.07 moles

4. Stoichiometry of the Reaction:
From the equation, 2 moles of Hâ‚‚O are produced per reaction cycle, and this corresponds to the formation of 3 moles of sulfur (S). Therefore, the moles of sulfur formed are:
[tex]\[
\text{moles of S} = \left(\frac{3 \text{ moles of S}}{2 \text{ moles of H}_2\text{O}}\right) \times \text{moles of H}_2\text{O}
\][/tex]
Moles of S ≈ 3.11 moles

5. Mass of Sulfur:
Finally, we convert the moles of sulfur to grams:
[tex]\[
\text{mass of S} = \text{moles of S} \times \text{molar mass of S} = 3.11 \text{ moles} \times 32.07 \text{ g/mol}
\][/tex]
Mass of sulfur ≈ 99.8 g

Therefore, approximately 99.8 grams of sulfur are formed when 37.4 grams of water are produced, which matches the result in the options given. The correct answer is 99.8 g S.

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