How many of g of S are required to produce 20 moles and 30 g of `H_(2)SO_(4)` respectively?

Options

A. 320g, 6.42g
B. 640g,9.79g
C. 240g,3.23g
D. None of these

Explanation

To determine how many grams of sulfur (S) are required to produce 20 moles and 30 grams of sulfuric acid (H₂SO₄), we can follow these steps:

### Step 1: Calculate the amount of sulfur needed for 20 moles of H₂SO₄.

1. **Identify the molar mass of sulfur (S)**: The molar mass of sulfur is approximately 32 grams per mole.
2. **Determine the amount of sulfur in one mole of H₂SO₄**: Each mole of H₂SO₄ contains 1 mole of sulfur.
3. **Calculate the total amount of sulfur for 20 moles of H₂SO₄**:
\[ \text{Mass of S} = \text{Number of moles of H₂SO₄} \times \text{Mass of S in one mole of H₂SO₄} \]
\[ \text{Mass of S} = 20 \, \text{moles} \times 32 \, \text{g/mole} = 640 \, \text{g} \]

### Step 2: Calculate the amount of sulfur needed for 30 grams of H₂SO₄.

1. **Identify the molar mass of H₂SO₄**: The molar mass of H₂SO₄ is approximately 98 grams per mole.
2. **Determine the ratio of sulfur in H₂SO₄**: Since 98 grams of H₂SO₄ contains 32 grams of sulfur, we can set up a proportion to find the amount of sulfur in 30 grams of H₂SO₄.
3. **Calculate the amount of sulfur in 30 grams of H₂SO₄**:
\[ \text{Mass of S} = \left(\frac{32 \, \text{g S}}{98 \, \text{g H₂SO₄}}\right) \times 30 \, \text{g H₂SO₄} \]
\[ \text{Mass of S} = \frac{32 \times 30}{98} \approx 9.79 \, \text{g} \]

### Final Results:
- For 20 moles of H₂SO₄, you need **640 grams of sulfur**.
- For 30 grams of H₂SO₄, you need approximately **9.79 grams of sulfur**.