`P_(4)S_(3) + 8O_(2) to P_(4)O_(10) + 3SO_(2)`
Calculate mass of `P_(4)S_(3)` is required at least 9.6 gm of each product.

Answer

To solve the problem, we need to calculate the mass of \( P_4S_3 \) required to produce at least 9.6 grams of each product, \( P_4O_{10} \) and \( SO_2 \), from the reaction:

\[ P_4S_3 + 8O_2 \rightarrow P_4O_{10} + 3SO_2 \]

### Step 1: Calculate the molar masses of the compounds involved.

1. **Molar mass of \( P_4O_{10} \)**:
- Phosphorus (P): 30.97 g/mol, so \( 4 \times 30.97 = 123.88 \) g/mol
- Oxygen (O): 16.00 g/mol, so \( 10 \times 16.00 = 160.00 \) g/mol
- Total: \( 123.88 + 160.00 = 283.88 \) g/mol

2. **Molar mass of \( SO_2 \)**:
- Sulfur (S): 32.07 g/mol
- Oxygen (O): 16.00 g/mol, so \( 2 \times 16.00 = 32.00 \) g/mol
- Total: \( 32.07 + 32.00 = 64.07 \) g/mol

3. **Molar mass of \( P_4S_3 \)**:
- Phosphorus (P): 30.97 g/mol, so \( 4 \times 30.97 = 123.88 \) g/mol
- Sulfur (S): 32.07 g/mol, so \( 3 \times 32.07 = 96.21 \) g/mol
- Total: \( 123.88 + 96.21 = 220.09 \) g/mol

### Step 2: Determine the moles of products needed.

To find the number of moles of each product required to produce at least 9.6 grams:

1. **Moles of \( P_4O_{10} \)**:
\[ \text{Moles of } P_4O_{10} = \frac{9.6 \text{ g}}{283.88 \text{ g/mol}} \approx 0.0338 \text{ moles} \]

2. **Moles of \( SO_2 \)**:
\[ \text{Moles of } SO_2 = \frac{9.6 \text{ g}}{64.07 \text{ g/mol}} \approx 0.150 \text{ moles} \]

### Step 3: Relate moles of products to moles of \( P_4S_3 \).

From the balanced equation:
- 1 mole of \( P_4S_3 \) produces 1 mole of \( P_4O_{10} \) and 3 moles of \( SO_2 \).

Using the stoichiometry:
1. For \( P_4O_{10} \):
\[ \text{Moles of } P_4S_3 \text{ required} = 0.0338 \text{ moles} \]

2. For \( SO_2 \):
\[ \text{Moles of } P_4S_3 \text{ required} = \frac{0.150 \text{ moles of } SO_2}{3} \approx 0.0500 \text{ moles} \]

### Step 4: Determine the greater requirement.

Since we need to satisfy both products, we take the larger number of moles:
- \( 0.0500 \) moles of \( P_4S_3 \) is required to produce enough \( SO_2 \).

### Step 5: Calculate the mass of \( P_4S_3 \) required.

Using the molar mass of \( P_4S_3 \):
\[ \text{Mass of } P_4S_3 = 0.0500 \text{ moles} \times 220.09 \text{ g/mol} \approx 11.0045 \text{ g} \]

### Final Answer:
The mass of \( P_4S_3 \) required to produce at least 9.6 grams of each product is approximately **11.00 grams**.

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