The densities of two gases are in the ratio of 1:16. The ratio of their rates of diffusion is

Options

A. `16:1`
B. `4:1`
C. `1:4`
D. `1:16`

Explanation

To solve the problem of finding the ratio of the rates of diffusion of two gases with a density ratio of 1:16, we can follow these steps:

### Step 1: Understand Graham's Law of Diffusion
According to Graham's law, the rate of diffusion of a gas is inversely proportional to the square root of its density. This can be expressed mathematically as:
\[ \text{Rate of diffusion} \propto \frac{1}{\sqrt{\text{Density}}} \]

### Step 2: Set Up the Given Information
We are given that the densities of two gases are in the ratio of:
\[ \text{Density}_1 : \text{Density}_2 = 1 : 16 \]
This means we can denote:
\[ \text{Density}_1 = 1 \quad \text{and} \quad \text{Density}_2 = 16 \]

### Step 3: Apply Graham's Law to Find the Rates of Diffusion
Using Graham's law, we can express the rates of diffusion for the two gases:
\[ \text{Rate of diffusion}_1 \propto \frac{1}{\sqrt{\text{Density}_1}} = \frac{1}{\sqrt{1}} = 1 \]
\[ \text{Rate of diffusion}_2 \propto \frac{1}{\sqrt{\text{Density}_2}} = \frac{1}{\sqrt{16}} = \frac{1}{4} \]

### Step 4: Calculate the Ratio of the Rates of Diffusion
Now we can find the ratio of the rates of diffusion:
\[ \frac{\text{Rate of diffusion}_1}{\text{Rate of diffusion}_2} = \frac{1}{\frac{1}{4}} = 4 \]

### Step 5: Write the Final Ratio
Thus, the ratio of the rates of diffusion of the two gases is:
\[ \text{Rate of diffusion}_1 : \text{Rate of diffusion}_2 = 4 : 1 \]

### Conclusion
The final answer is that the ratio of the rates of diffusion of the two gases is **4:1**.

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