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

Answer

To solve the problem, we need to use the relationship between the rate of diffusion and the density of gases. The rate of diffusion of a gas is inversely proportional to the square root of its density.

Let's break down the solution step by step:

### Step 1: Understand the relationship between rate of diffusion and density
The rate of diffusion (R) of a gas is inversely proportional to the square root of its density (d). Mathematically, this can be expressed as:
\[ R \propto \frac{1}{\sqrt{d}} \]
This means:
\[ \frac{R_A}{R_B} = \sqrt{\frac{d_B}{d_A}} \]

### Step 2: Substitute the given information
From the problem, we know that the rate of diffusion of gas A (R_A) is 6 times that of gas B (R_B). Therefore, we can write:
\[ R_A = 6 R_B \]

### Step 3: Set up the equation using the relationship
Substituting \(R_A\) into the relationship we derived:
\[ \frac{6 R_B}{R_B} = \sqrt{\frac{d_B}{d_A}} \]
This simplifies to:
\[ 6 = \sqrt{\frac{d_B}{d_A}} \]

### Step 4: Square both sides to eliminate the square root
To eliminate the square root, we square both sides of the equation:
\[ 6^2 = \frac{d_B}{d_A} \]
This gives us:
\[ 36 = \frac{d_B}{d_A} \]

### Step 5: Express the density ratio
From the equation \(36 = \frac{d_B}{d_A}\), we can express the density ratio of B to A as:
\[ \frac{d_B}{d_A} = 36:1 \]

### Conclusion
The density ratio of gas B to gas A is 36:1.

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