The rate of diffusion of two gases A and B is in the ratio of `1 : 4` and that of B and C in the ratio of `1 : 3`. The rate of diffusion of C with respect to A is

Options

A. `(1)/(12)`
B. 12
C. 6
D. 4

Explanation

To solve the problem, we need to find the rate of diffusion of gas C with respect to gas A, given the ratios of diffusion rates between gases A, B, and C.

### Step-by-Step Solution:

1. **Identify the Given Ratios**:
- The rate of diffusion of gases A and B is given as:
\[ \frac{r_A}{r_B} = \frac{1}{4} \]
- The rate of diffusion of gases B and C is given as:
\[ \frac{r_B}{r_C} = \frac{1}{3} \]

2. **Express the Rates in Terms of a Common Variable**:
- From the first ratio, we can express \( r_A \) in terms of \( r_B \):
\[ r_A = \frac{1}{4} r_B \]
- From the second ratio, we can express \( r_B \) in terms of \( r_C \):
\[ r_B = \frac{1}{3} r_C \]

3. **Substitute \( r_B \) into the Expression for \( r_A \)**:
- Substitute \( r_B \) from the second equation into the expression for \( r_A \):
\[ r_A = \frac{1}{4} \left(\frac{1}{3} r_C\right) \]
- This simplifies to:
\[ r_A = \frac{1}{12} r_C \]

4. **Find the Ratio of \( r_C \) to \( r_A \)**:
- To find \( \frac{r_C}{r_A} \), we can rearrange the equation:
\[ \frac{r_C}{r_A} = 12 \]

5. **Conclusion**:
- The rate of diffusion of gas C with respect to gas A is:
\[ \frac{r_C}{r_A} = 12 \]

### Final Answer:
The rate of diffusion of C with respect to A is 12.

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