The rate of diffusion of two gases X and Y is in the ration of `1:5` and that of Y and Z in the ratio of `1:6`. The ratio of the rate of diffusion of Z with respecte to X is `:`

Options

A. `5//6`
B. `1//30`
C. `6//5`
D. 30

Answer

To solve the problem, we need to find the ratio of the rate of diffusion of gas Z with respect to gas X, given the rates of diffusion of gases X, Y, and Z.

### Step-by-step Solution:

1. **Understand the Given Ratios:**
- The rate of diffusion of gases X and Y is given as \( R_X : R_Y = 1 : 5 \). This can be expressed mathematically as:
\[ \frac{R_X}{R_Y} = \frac{1}{5} \]
- The rate of diffusion of gases Y and Z is given as \( R_Y : R_Z = 1 : 6 \). This can be expressed as:
\[ \frac{R_Y}{R_Z} = \frac{1}{6} \]

2. **Express \( R_Y \) in terms of \( R_X \):**
- From the first ratio, we can express \( R_Y \) in terms of \( R_X \):
\[ R_Y = 5R_X \]

3. **Express \( R_Z \) in terms of \( R_Y \):**
- From the second ratio, we can express \( R_Z \) in terms of \( R_Y \):
\[ R_Z = 6R_Y \]

4. **Substitute \( R_Y \) into the equation for \( R_Z \):**
- Now, substitute \( R_Y = 5R_X \) into the equation for \( R_Z \):
\[ R_Z = 6(5R_X) = 30R_X \]

5. **Find the ratio of \( R_Z \) to \( R_X \):**
- Now we can find the ratio of the rate of diffusion of Z with respect to X:
\[ \frac{R_Z}{R_X} = \frac{30R_X}{R_X} = 30 \]

### Final Answer:
The ratio of the rate of diffusion of Z with respect to X is \( 30 : 1 \).

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