Question

Identify the correct statements from the following:

For an ideal gas, the compressibility factor is 1.0.

The kinetic energy of NO (g) (molar mass = 30 g mol^-1) at T(K) is \( x \) J mol^-1. The kinetic energy of N₂O₄ (g) (molar mass = 92 g mol^-1) at T(K) is \( 2x \) J mol^-1.

The rate of diffusion of a gas is inversely proportional to the square root of its density.

 

• A. I, III
• B. II, III only
• C. I, III only
• D. I, II only

Hint:

For an ideal gas, the compressibility factor \( Z = 1 \). Also, Graham's law of diffusion relates the rate of diffusion to the square root of the density of the gas.

Answer 1

The Correct Option is C

Step 1: Let's evaluate each statement. 

Statement I: For an ideal gas, the compressibility factor \( Z \) is defined as: \[ Z = \frac{P V_m}{R T} \] For an ideal gas, this value is 1.0, so Statement I is true. 

Step 2: Now consider Statement II. The kinetic energy \( E_k \) of a gas molecule is given by: \[ E_k = \frac{3}{2} R T \] The kinetic energy is directly proportional to temperature for a given substance. The relationship given in the question, where the kinetic energy of N_2O_4 is twice that of NO at the same temperature, is consistent with this law. So Statement II is also true. 

Step 3: Statement III states that the rate of diffusion of a gas is inversely proportional to the square root of its density. This is a correct statement according to Graham's law of diffusion: \[ \text{Rate of diffusion} \propto \frac{1}{\sqrt{\text{Density}}} \] Thus, Statement III is also true.

 Step 4: All statements I, II, and III are true. Therefore, the correct answer is option (3), which includes statements I and III.