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 the ideal gas law, which states that for a given amount of gas at constant temperature, the product of pressure and volume is constant. This can be expressed mathematically as:

\[ P_1 V_1 = P_2 V_2 \]

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Initial pressure, \( P_1 = 5.3 \, \text{atm} \)
- Initial volume, \( V_1 = V \) (we will assume the initial volume as \( V \))
- Final volume, \( V_2 = \frac{1}{10} V_1 = \frac{1}{10} V \)

2. **Set Up the Equation**:
- According to the ideal gas law, we can set up the equation:
\[ P_1 V_1 = P_2 V_2 \]

3. **Substitute the Known Values**:
- Substitute \( P_1 \), \( V_1 \), and \( V_2 \) into the equation:
\[ 5.3 \, \text{atm} \times V = P_2 \times \left(\frac{1}{10} V\right) \]

4. **Cancel Out the Volume**:
- Since \( V \) appears on both sides of the equation, we can cancel it out:
\[ 5.3 \, \text{atm} = P_2 \times \frac{1}{10} \]

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

### Final Answer:
The pressure when the volume of the gas is reduced to one-tenth of the original value at the same temperature is **53 atm**.