The rates of diffusion of gases `A` and `B` of molecular mass `36` and `64` are in the ratio

Options

A. `9 : 16`
B. `4 : 3`
C. `3 : 4`
D. `16 : 9`

Explanation

To find the ratio of the rates of diffusion of gases A and B with molecular masses of 36 and 64 respectively, we can use Graham's law of diffusion. Here’s the step-by-step solution:

### Step 1: Write 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 molecular mass. Mathematically, it can be expressed as:

\[ \frac{\text{Rate of A}}{\text{Rate of B}} = \sqrt{\frac{M_B}{M_A}} \]

where \( M_A \) and \( M_B \) are the molecular masses of gases A and B, respectively.

### Step 2: Substitute the Molecular Masses
Given:
- Molecular mass of gas A, \( M_A = 36 \)
- Molecular mass of gas B, \( M_B = 64 \)

Substituting these values into Graham's law gives:

\[ \frac{\text{Rate of A}}{\text{Rate of B}} = \sqrt{\frac{64}{36}} \]

### Step 3: Simplify the Square Root
Now, simplify the fraction inside the square root:

\[ \frac{64}{36} = \frac{16}{9} \]

Taking the square root:

\[ \sqrt{\frac{16}{9}} = \frac{\sqrt{16}}{\sqrt{9}} = \frac{4}{3} \]

### Step 4: Write the Ratio of Rates
From the previous step, we have:

\[ \frac{\text{Rate of A}}{\text{Rate of B}} = \frac{4}{3} \]

This means that the rates of diffusion of gases A and B are in the ratio of 4:3.

### Step 5: Conclusion
Thus, the final answer is:

\[ \text{Rate of A : Rate of B} = 4 : 3 \]