If rate of diffusion of A is 3 times that of B, what will be the density ratio of A and B?

Explanation

To solve the problem of finding the density ratio of gases A and B given that the rate of diffusion of A is three times that of B, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Relationship**: The rate of diffusion of a gas is inversely proportional to the square root of its density. This is described by Graham's law of effusion/diffusion.

\[ \text{Rate of diffusion} \propto \frac{1}{\sqrt{\text{Density}}} \]

2. **Set Up the Equation**: Let \( R_a \) be the rate of diffusion of gas A and \( R_b \) be the rate of diffusion of gas B. According to the problem, we have:

\[ R_a = 3 R_b \]

3. **Apply Graham's Law**: According to Graham's law, we can express the relationship between the rates of diffusion and densities as:

\[ \frac{R_a}{R_b} = \sqrt{\frac{D_b}{D_a}} \]

where \( D_a \) and \( D_b \) are the densities of gases A and B, respectively.

4. **Substitute the Known Values**: Substitute \( R_a = 3 R_b \) into the equation:

\[ \frac{3 R_b}{R_b} = \sqrt{\frac{D_b}{D_a}} \]

This simplifies to:

\[ 3 = \sqrt{\frac{D_b}{D_a}} \]

5. **Square Both Sides**: To eliminate the square root, square both sides of the equation:

\[ 9 = \frac{D_b}{D_a} \]

6. **Rearrange to Find Density Ratio**: Rearranging this gives us the density ratio:

\[ \frac{D_a}{D_b} = \frac{1}{9} \]

Thus, the density ratio of A to B is \( 1:9 \).

### Final Answer:
The density ratio of A to B is \( 1:9 \).

---