The rate of diffusion of a gas is directly proportional to the square root of ………………… .

Answer

To solve the question regarding the rate of diffusion of a gas, we need to understand the relationship between the rate of diffusion and the factors that influence it.

### Step-by-Step Solution:

1. **Understanding the Rate of Diffusion**:
The rate of diffusion (R) of a gas is influenced by several factors, including its molecular mass (M), temperature (T), pressure (P), and the cross-sectional area (A) through which it diffuses.

2. **Using Graham's Law of Effusion**:
According to Graham's law, the rate of diffusion of a gas is inversely proportional to the square root of its molar mass. This can be expressed mathematically as:
\[ R \propto \frac{1}{\sqrt{M}} \]
where R is the rate of diffusion and M is the molecular mass of the gas.

3. **Considering Temperature**:
The rate of diffusion is also directly proportional to the square root of the temperature (T) in Kelvin. This can be expressed as:
\[ R \propto \sqrt{T} \]

4. **Combining the Relationships**:
Therefore, we can conclude that the rate of diffusion of a gas is directly proportional to the square root of the temperature and inversely proportional to the square root of the molecular mass:
\[ R \propto \sqrt{T} \quad \text{and} \quad R \propto \frac{1}{\sqrt{M}} \]

5. **Final Answer**:
The rate of diffusion of a gas is directly proportional to the square root of the temperature (T) and inversely proportional to the square root of the molecular mass (M). Thus, the answer to the question is:
- The rate of diffusion of a gas is directly proportional to the square root of **temperature (T)**.