If rate of diffusion of A is 13 times that of B, what will be the density ratio of B and A?

Options

A. 169:1
B. 1:169
C. 1:13
D. 13:1

Explanation

To solve the problem, we need to use Graham's law of effusion/diffusion, 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. **Understand the relationship**:
We know from Graham's law that:
\[ \frac{r_A}{r_B} = \sqrt{\frac{d_B}{d_A}} \]
where \( r_A \) and \( r_B \) are the rates of diffusion of gases A and B, and \( d_A \) and \( d_B \) are their respective densities.

2. **Substitute the given values**:
According to the problem, the rate of diffusion of A is 13 times that of B:
\[ r_A = 13 r_B \]
Substituting this into the equation gives:
\[ \frac{13 r_B}{r_B} = \sqrt{\frac{d_B}{d_A}} \]
This simplifies to:
\[ 13 = \sqrt{\frac{d_B}{d_A}} \]

3. **Square both sides**:
To eliminate the square root, we square both sides:
\[ 13^2 = \frac{d_B}{d_A} \]
This results in:
\[ 169 = \frac{d_B}{d_A} \]

4. **Express the density ratio**:
Rearranging the equation gives us the density ratio:
\[ \frac{d_B}{d_A} = 169 \]
This means that the density of B is 169 times the density of A.

5. **Final result**:
Therefore, the density ratio of B to A is:
\[ d_B : d_A = 169 : 1 \]

### Conclusion:
The density ratio of B to A is 169:1.

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