If rate of diffusion of A is 15 times that of B, what will be the density ratio of B and A?

Options

A. 225:1
B. 1:225
C. 15:1
D. 1:15

Explanation

To solve the problem of finding the density ratio of B and A given that the rate of diffusion of A is 15 times that of B, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the relationship between diffusion rate and density:**
The rate of diffusion is inversely proportional to the square root of the density of the gas. This relationship can be expressed mathematically as:
\[ \frac{R_A}{R_B} = \sqrt{\frac{D_B}{D_A}} \]
where \(R_A\) and \(R_B\) are the rates of diffusion of gases A and B, respectively, and \(D_A\) and \(D_B\) are their densities.

2. **Substitute the given information:**
We know that the rate of diffusion of A is 15 times that of B:
\[ R_A = 15 R_B \]
Substituting this into the equation gives:
\[ \frac{15 R_B}{R_B} = \sqrt{\frac{D_B}{D_A}} \]
Simplifying this, we find:
\[ 15 = \sqrt{\frac{D_B}{D_A}} \]

3. **Square both sides to eliminate the square root:**
Squaring both sides of the equation results in:
\[ 15^2 = \frac{D_B}{D_A} \]
This simplifies to:
\[ 225 = \frac{D_B}{D_A} \]

4. **Express the density ratio:**
Rearranging the equation gives us the density ratio of B to A:
\[ \frac{D_B}{D_A} = 225 \]
Therefore, the density ratio of B to A is:
\[ D_B : D_A = 225 : 1 \]

### Final Answer:
The density ratio of B to A is 225:1.