Which of the following statements is(are) correct for a gas X having molar mass 5g and density 0.3g/litre at 0.5 atmospheric pressure at 300 K?

Options

A. The gas “X” will behave ideally
B. The force of attraction will dominate over the force of repulsion among the gas molecules
C. The force of repulsion will dominate over the force of attraction among the gas molecules
D. None of these

Explanation

To solve the problem regarding the gas X with a molar mass of 5 g, density of 0.3 g/litre, pressure of 0.5 atm, and temperature of 300 K, we can follow these steps:

### Step 1: Calculate the Volume of the Gas
We know that density (d) is given by the formula:
\[ d = \frac{m}{V} \]
Where:
- \( m \) = mass of the gas
- \( V \) = volume of the gas

Rearranging the formula to find volume:
\[ V = \frac{m}{d} \]

Substituting the values:
- \( m = 5 \, \text{g} \)
- \( d = 0.3 \, \text{g/L} \)

Calculating the volume:
\[ V = \frac{5 \, \text{g}}{0.3 \, \text{g/L}} = 16.67 \, \text{L} \]

### Step 2: Calculate the Compressibility Factor (Z)
The compressibility factor \( Z \) is given by the formula:
\[ Z = \frac{PV}{RT} \]

Where:
- \( P = 0.5 \, \text{atm} \)
- \( V = 16.67 \, \text{L} \)
- \( R = 0.0821 \, \text{L atm/(mol K)} \)
- \( T = 300 \, \text{K} \)

Substituting the values into the formula:
\[ Z = \frac{(0.5 \, \text{atm})(16.67 \, \text{L})}{(0.0821 \, \text{L atm/(mol K)})(300 \, \text{K})} \]

Calculating:
\[ Z = \frac{8.335}{24.63} \approx 0.338 \]

### Step 3: Analyze the Value of Z
The value of \( Z \) indicates the behavior of the gas:
- If \( Z = 1 \), the gas behaves ideally.
- If \( Z < 1 \), the gas shows negative deviation from ideal behavior, indicating that attractive forces between gas molecules are significant.
- If \( Z > 1 \), the gas shows positive deviation from ideal behavior.

Since \( Z \approx 0.338 \) which is less than 1, we conclude that the gas X does not behave ideally and exhibits significant attractive forces between its molecules.

### Conclusion
Based on the calculated compressibility factor, we can conclude that the gas X has a compressibility factor less than 1, indicating it behaves non-ideally due to the dominance of attractive forces among its molecules.