If rate of diffusion of A is 10 times that of B, what will be the density ratio of B and A?

Options

A. 10:1
B. 100:1
C. 1:100
D. 1:10

Explanation

To solve the problem, we will 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 Given Information**:
We know that the rate of diffusion of gas A (Ra) is 10 times that of gas B (Rb). This can be expressed as:
\[ R_a = 10 R_b \]

2. **Apply Graham's Law**:
According to Graham's law:
\[ \frac{R_a}{R_b} = \sqrt{\frac{D_b}{D_a}} \]
where \(D_a\) and \(D_b\) are the densities of gases A and B, respectively.

3. **Substitute the Known Values**:
From the first step, we substitute \(R_a\) in the equation:
\[ \frac{10 R_b}{R_b} = \sqrt{\frac{D_b}{D_a}} \]
This simplifies to:
\[ 10 = \sqrt{\frac{D_b}{D_a}} \]

4. **Square Both Sides**:
To eliminate the square root, we square both sides:
\[ 10^2 = \frac{D_b}{D_a} \]
This gives us:
\[ 100 = \frac{D_b}{D_a} \]

5. **Express the Density Ratio**:
Rearranging the equation gives us the density ratio of B to A:
\[ \frac{D_b}{D_a} = 100 \]
Therefore, the density ratio of B to A is:
\[ D_b : D_a = 100 : 1 \]

### Final Answer:
The density ratio of B to A is \(100 : 1\).

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