If rate of diffusion of A is 11 times that of B, what will be the density ratio of B and A?

Options

A. 121:1
B. 1:121
C. 11:1
D. 1:11

Explanation

To solve the problem, we need to find the density ratio of gases A and B based on their rates of diffusion. The relationship between the rate of diffusion and density is given by 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**:
According to Graham's law, the rate of diffusion (R) of two gases is related to their densities (d) as follows:
\[ \frac{R_A}{R_B} = \sqrt{\frac{d_B}{d_A}} \]
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. **Given Information**:
We know that the rate of diffusion of A is 11 times that of B:
\[ R_A = 11 R_B \]

3. **Substituting the Given Values**:
Substitute \( R_A \) into the Graham's law equation:
\[ \frac{11 R_B}{R_B} = \sqrt{\frac{d_B}{d_A}} \]
This simplifies to:
\[ 11 = \sqrt{\frac{d_B}{d_A}} \]

4. **Square Both Sides**:
To eliminate the square root, square both sides of the equation:
\[ 11^2 = \frac{d_B}{d_A} \]
This gives:
\[ 121 = \frac{d_B}{d_A} \]

5. **Finding the Density Ratio**:
Rearranging the equation gives us the density ratio:
\[ d_B = 121 d_A \]
Therefore, the ratio of the densities of B to A is:
\[ \frac{d_B}{d_A} = 121:1 \]

### Final Answer:
The density ratio of B to A is \( 121:1 \).

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