A sample of Br2(g) takes 10.0 min to effuse through a membrane. How long would it take the same number of moles of Ar(g) to effuse through the same membrane?

5 minutes

(rate1/rate2) = sqrt(molar mass 1/molar mass 2)

To answer this question, we need to use Graham's law of effusion, which states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass.

Let's consider the two gases involved: Br2(g) and Ar(g).

1. Find the molar masses:
- Molar mass of Br2 = 2 * atomic mass of Br = 2 * 79.90 g/mol = 159.80 g/mol
- Molar mass of Ar = 39.95 g/mol

2. Calculate the square roots of the molar masses:
- Square root of molar mass of Br2 = √(159.80 g/mol) ≈ 12.64 g/mol
- Square root of molar mass of Ar = √(39.95 g/mol) ≈ 6.32 g/mol

3. Calculate the ratio of the square roots:
- Ratio = (Square root of molar mass of Br2) / (Square root of molar mass of Ar)
- Ratio = 12.64 g/mol / 6.32 g/mol ≈ 2

According to Graham's law of effusion, the ratio of the rates of effusion for two gases is equal to the ratio of the square roots of their molar masses. Therefore, the rate of effusion of Ar gas is twice that of Br2 gas.

4. Now, we use the information given in the question to find the time it takes for Ar to effuse.
- Given: Time for Br2 to effuse = 10.0 min

Since the rate of effusion of Ar is twice that of Br2, the time required for Ar to effuse through the same membrane would be half that of Br2.

5. Calculate the time for Ar to effuse:
- Time for Ar = (Time for Br2) / 2 = 10.0 min / 2 = 5.0 min

Therefore, it would take 5.0 minutes for the same number of moles of Ar(g) to effuse through the same membrane.

12 minutes

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