The densities of hydrogen and oxygen are 0.09 and 1.44 g `L^(-1)`. If the rate of diffusion of hydrogen is 1 then that of oxygen in the same units will be

Options

A. 4
B. `1//4`
C. 16
D. `1//16`

Explanation

To solve the problem, we will use Graham's law of effusion, which states that the rate of diffusion of a gas is inversely proportional to the square root of its density. The formula can be expressed as:

\[ \frac{\text{Rate of diffusion of gas 1}}{\text{Rate of diffusion of gas 2}} = \sqrt{\frac{\text{Density of gas 2}}{\text{Density of gas 1}}} \]

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Density of Hydrogen (H₂) = 0.09 g/L
- Density of Oxygen (O₂) = 1.44 g/L
- Rate of diffusion of Hydrogen = 1 (as given)

2. **Set Up the Ratio Using Graham's Law:**
\[ \frac{\text{Rate of diffusion of O₂}}{\text{Rate of diffusion of H₂}} = \sqrt{\frac{\text{Density of H₂}}{\text{Density of O₂}}} \]

3. **Substitute the Known Values:**
\[ \frac{\text{Rate of diffusion of O₂}}{1} = \sqrt{\frac{0.09}{1.44}} \]

4. **Calculate the Right Side:**
- First, calculate the fraction:
\[ \frac{0.09}{1.44} = 0.0625 \]
- Now, take the square root:
\[ \sqrt{0.0625} = 0.25 \]

5. **Determine the Rate of Diffusion of Oxygen:**
\[ \text{Rate of diffusion of O₂} = 0.25 \]

### Final Answer:
The rate of diffusion of oxygen is 0.25.