At 200 K and 500 atm value of compressibility factor is 2.Then volume of the gas at the point will be

Options

A. 0.01 L
B. 0.09L
C. 0.065 L
D. 0.657 L

Explanation

To solve the problem, we will use the formula for the compressibility factor (Z):

\[ Z = \frac{PV}{RT} \]

Where:
- \( Z \) is the compressibility factor
- \( P \) is the pressure
- \( V \) is the volume of the gas
- \( R \) is the universal gas constant
- \( T \) is the temperature in Kelvin

### Step-by-Step Solution:

1. **Identify the given values:**
- Compressibility factor, \( Z = 2 \)
- Pressure, \( P = 500 \, \text{atm} \)
- Temperature, \( T = 200 \, \text{K} \)
- Universal gas constant, \( R = 0.082 \, \text{atm} \cdot \text{L} \cdot \text{mol}^{-1} \cdot \text{K}^{-1} \)

2. **Rearrange the formula to solve for volume \( V \):**
\[ V = \frac{ZRT}{P} \]

3. **Substitute the known values into the equation:**
\[ V = \frac{2 \times 0.082 \, \text{atm} \cdot \text{L} \cdot \text{mol}^{-1} \cdot \text{K}^{-1} \times 200 \, \text{K}}{500 \, \text{atm}} \]

4. **Calculate the numerator:**
\[ 2 \times 0.082 \times 200 = 32.8 \, \text{atm} \cdot \text{L} \cdot \text{mol}^{-1} \]

5. **Now, divide by the pressure:**
\[ V = \frac{32.8}{500} = 0.0656 \, \text{L} \]

6. **Final result:**
The volume of the gas at the given conditions is \( V = 0.0656 \, \text{L} \).