Concept: Graham's Law of Effusion dictates that the rate at which a gas escapes through a small hole is inversely proportional to the square root of its molar mass.
Formula: $$ \text{Rate} \propto \frac{1}{\sqrt{M}} $$
Solution: - To find the fastest deflating balloon, we must find the gas with the lowest molar mass.
- Molar mass of \( \text{O}_2 = 32 \text{ g/mol} \).
- Molar mass of \( \text{N}_2 = 28 \text{ g/mol} \).
- Molar mass of \( \text{He} = 4 \text{ g/mol} \).
- Molar mass of \( \text{H}_2 = 2 \text{ g/mol} \).
- Because Hydrogen (\( \text{H}_2 \)) is the lightest gas, it will effuse through the micropores of the balloon at the highest velocity, deflating first.
Why other options are incorrect: They possess higher molar masses, meaning their molecules move slower and escape the balloon more slowly.
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