If rate of diffusion of A is 6 times that of B, what will be the density ratio of A and B?

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. **Understand the relationship between rate of diffusion and density**:
According to Graham's law, the rates of diffusion of two gases (A and B) can be expressed 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, and \( D_a \) and \( D_b \) are their respective densities.

2. **Substitute the given information**:
We know from the problem that the rate of diffusion of A is 6 times that of B:
\[ R_a = 6R_b \]
Substituting this into the equation gives:
\[ \frac{6R_b}{R_b} = \sqrt{\frac{D_b}{D_a}} \]

3. **Simplify the equation**:
The \( R_b \) cancels out:
\[ 6 = \sqrt{\frac{D_b}{D_a}} \]

4. **Square both sides**:
To eliminate the square root, we square both sides:
\[ 36 = \frac{D_b}{D_a} \]

5. **Rearrange to find the density ratio**:
Rearranging the equation gives us:
\[ \frac{D_a}{D_b} = \frac{1}{36} \]
This means that the density of A is 1 part for every 36 parts of density of B.

6. **Express the density ratio**:
Therefore, the density ratio of A to B can be expressed as:
\[ D_a : D_b = 1 : 36 \]

### Final Answer:
The density ratio of A to B is \( 1 : 36 \).