If rate of diffusion of A is 9 times that of B, what will be the density ratio of B and A?

Answer

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.

### Step-by-step Solution:

1. **Understanding the Given Information**:
- We know that the rate of diffusion of gas A (ra) is 9 times that of gas B (rb).
- Mathematically, this can be expressed as:
\[ r_a = 9 \cdot r_b \]

2. **Using Graham's Law**:
- According to Graham's law, the relationship between the rates of diffusion and densities of two gases can be expressed as:
\[ \frac{r_a}{r_b} = \sqrt{\frac{d_b}{d_a}} \]
- Here, \(d_a\) is the density of gas A and \(d_b\) is the density of gas B.

3. **Substituting the Known Values**:
- We substitute \(r_a\) with \(9 \cdot r_b\) in the equation:
\[ \frac{9 \cdot r_b}{r_b} = \sqrt{\frac{d_b}{d_a}} \]
- This simplifies to:
\[ 9 = \sqrt{\frac{d_b}{d_a}} \]

4. **Squaring Both Sides**:
- To eliminate the square root, we square both sides of the equation:
\[ 9^2 = \frac{d_b}{d_a} \]
- This results in:
\[ 81 = \frac{d_b}{d_a} \]

5. **Finding the Density Ratio**:
- The density ratio of B to A can be expressed as:
\[ \frac{d_b}{d_a} = 81 \]
- This means that the density of gas B is 81 times that of gas A.

### Final Answer:
The density ratio of B to A is \(81:1\).