If rate of diffusion of A is 12 times that of B, what will be the density ratio of B and A?

Options

A. 12:1
B. 1:12
C. 144:1
D. 1:144

Explanation

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 are given that the rate of diffusion of gas A (Ra) is 12 times that of gas B (Rb).
- Mathematically, this can be expressed as:
\[ R_a = 12 R_b \]

2. **Using Graham's Law**:
- According to Graham's law, the relationship between the rates of diffusion and densities is given by:
\[ \frac{R_a}{R_b} = \sqrt{\frac{D_b}{D_a}} \]
- Here, \(D_a\) and \(D_b\) are the densities of gases A and B, respectively.

3. **Substituting the Known Values**:
- We can substitute the expression for \(R_a\) into Graham's law:
\[ \frac{12 R_b}{R_b} = \sqrt{\frac{D_b}{D_a}} \]
- This simplifies to:
\[ 12 = \sqrt{\frac{D_b}{D_a}} \]

4. **Squaring Both Sides**:
- To eliminate the square root, we square both sides of the equation:
\[ 12^2 = \frac{D_b}{D_a} \]
- This gives us:
\[ 144 = \frac{D_b}{D_a} \]

5. **Finding the Density Ratio**:
- Rearranging the equation gives us the density ratio:
\[ \frac{D_b}{D_a} = 144 \]
- This means that the density of gas B is 144 times that of gas A.

### Final Answer:
The density ratio of B to A is:
\[ D_b : D_a = 144 : 1 \]