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

Options

A. 960g,9.79g
B. 450g,4.48g
C. 320g,3.23g
D. None of these

Explanation

To solve the problem of how many grams of sulfur (S) are required to produce 30 moles and 30 grams of H₂SO₄ respectively, we can follow these steps:

### Step 1: Calculate the grams of sulfur needed for 30 moles of H₂SO₄.

1. **Identify the molar mass of H₂SO₄**:
- The molar mass of H₂SO₄ is 98 g/mol.
- Each mole of H₂SO₄ contains 1 mole of sulfur (S), which has a molar mass of 32 g/mol.

2. **Calculate the total grams of sulfur in 30 moles of H₂SO₄**:
- Since 1 mole of H₂SO₄ contains 32 g of sulfur, then:
\[ \text{Grams of S in 30 moles of H₂SO₄} = 30 \, \text{moles} \times 32 \, \text{g/mole} = 960 \, \text{g} \]

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

1. **Determine the proportion of sulfur in H₂SO₄**:
- From the molar mass, we know that in 98 g of H₂SO₄, there are 32 g of sulfur.

2. **Set up the ratio to find grams of sulfur in 30 g of H₂SO₄**:
- Using the ratio of sulfur to H₂SO₄:
\[ \text{Grams of S in 30 g of H₂SO₄} = \left(\frac{32 \, \text{g}}{98 \, \text{g}}\right) \times 30 \, \text{g} \]
- Calculate:
\[ \text{Grams of S} = \frac{32 \times 30}{98} \approx 9.79 \, \text{g} \]

### Final Answers:
- For 30 moles of H₂SO₄, 960 g of sulfur is required.
- For 30 g of H₂SO₄, approximately 9.79 g of sulfur is required.

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