For the diffusion of a gas at pressure P, the rate of diffusion is expressed by

Answer

To solve the question regarding the expression for the rate of diffusion of a gas at pressure P, we can follow these steps:

### Step-by-Step Solution:

1. **Understand Graham's Law of Diffusion**:
Graham's law states that the rate of diffusion of a gas is inversely proportional to the square root of its molar mass (molecular weight). This means that lighter gases diffuse faster than heavier gases.

2. **Write the Mathematical Expression**:
According to Graham's law, the relationship can be expressed mathematically as:
\[ \text{Rate of diffusion} (r) \propto \frac{1}{\sqrt{M}} \]
where \( M \) is the molar mass of the gas.

3. **Include the Pressure Factor**:
While Graham's law primarily focuses on the molar mass, the rate of diffusion can also be affected by the pressure of the gas. At constant temperature, the rate of diffusion can be expressed as:
\[ r = k \cdot \frac{P}{\sqrt{M}} \]
where \( k \) is a constant that depends on the conditions of the experiment.

4. **Final Expression**:
Therefore, the expression for the rate of diffusion of a gas at pressure \( P \) can be summarized as:
\[ r = k \cdot \frac{P}{\sqrt{M}} \]