At `27^(@)C` a sample of ammonia gas exerts a pressure of 5.3 atm. What is the pressure when the volume of the gas is reduced to one-tenth of the original value at the same temperature ?

Options

A. 0.53 atm
B. 5.3atm
C. 53 atm
D. None of these

Explanation

To solve the problem, we will use Boyle's Law, which states that the pressure of a gas is inversely proportional to its volume when the temperature is constant. The mathematical representation of Boyle's Law is given by:

\[ P_1 V_1 = P_2 V_2 \]

Where:
- \( P_1 \) = initial pressure
- \( V_1 \) = initial volume
- \( P_2 \) = final pressure
- \( V_2 \) = final volume

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Initial pressure, \( P_1 = 5.3 \, \text{atm} \)
- The volume is reduced to one-tenth of the original value, so \( V_2 = \frac{V_1}{10} \).

2. **Set Up the Equation Using Boyle's Law:**
- According to Boyle's Law:
\[ P_1 V_1 = P_2 V_2 \]

3. **Substitute the Known Values:**
- We know that \( V_2 = \frac{V_1}{10} \). Substitute this into the equation:
\[ 5.3 \, \text{atm} \cdot V_1 = P_2 \cdot \left(\frac{V_1}{10}\right) \]

4. **Simplify the Equation:**
- Cancel \( V_1 \) from both sides (assuming \( V_1 \neq 0 \)):
\[ 5.3 = \frac{P_2}{10} \]

5. **Solve for \( P_2 \):**
- Multiply both sides by 10 to isolate \( P_2 \):
\[ P_2 = 5.3 \times 10 = 53 \, \text{atm} \]

6. **Final Answer:**
- The pressure when the volume of the gas is reduced to one-tenth of the original value at the same temperature is:
\[ P_2 = 53 \, \text{atm} \]