In an experiment `100 mL` of hydrogen take 5 second and 100 mL of an unknown gas take 20 seconds to diffuse through a porous membrane. Determine the density of the unknown gas relative to that of hydrogen.

Explanation

To determine the density of the unknown gas relative to that of hydrogen, we can follow these steps:

### Step 1: Calculate the rate of diffusion for hydrogen.
The rate of diffusion can be calculated using the formula:
\[ \text{Rate} = \frac{\text{Volume}}{\text{Time}} \]
For hydrogen:
- Volume = 100 mL
- Time = 5 seconds

Substituting the values:
\[ \text{Rate of hydrogen} = \frac{100 \, \text{mL}}{5 \, \text{s}} = 20 \, \text{mL/s} \]

### Step 2: Calculate the rate of diffusion for the unknown gas.
Using the same formula for the unknown gas:
- Volume = 100 mL
- Time = 20 seconds

Substituting the values:
\[ \text{Rate of unknown gas} = \frac{100 \, \text{mL}}{20 \, \text{s}} = 5 \, \text{mL/s} \]

### Step 3: Apply Graham's Law of Effusion.
According to Graham's Law:
\[ \frac{\text{Rate of hydrogen}}{\text{Rate of unknown gas}} = \sqrt{\frac{\text{Density of unknown gas}}{\text{Density of hydrogen}}} \]
Substituting the rates we calculated:
\[ \frac{20 \, \text{mL/s}}{5 \, \text{mL/s}} = \sqrt{\frac{\text{Density of unknown gas}}{\text{Density of hydrogen}}} \]
This simplifies to:
\[ 4 = \sqrt{\frac{\text{Density of unknown gas}}{\text{Density of hydrogen}}} \]

### Step 4: Square both sides to eliminate the square root.
Squaring both sides gives:
\[ 16 = \frac{\text{Density of unknown gas}}{\text{Density of hydrogen}} \]

### Step 5: Solve for the density of the unknown gas.
This means:
\[ \text{Density of unknown gas} = 16 \times \text{Density of hydrogen} \]

### Conclusion
The density of the unknown gas is 16 times that of hydrogen.

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