A sample of N₂O effuses from a container in 42 seconds. How long will it take the same amount of gaseous I₂ to effuse from the same container under identical conditions?

검증된 단계별 안내

Identify the problem as one involving effusion, which can be solved using Graham's Law of Effusion.

Recall Graham's Law of Effusion: \( \frac{\text{Rate of effusion of gas 1}}{\text{Rate of effusion of gas 2}} = \sqrt{\frac{M_2}{M_1}} \), where \( M_1 \) and \( M_2 \) are the molar masses of the gases.

Determine the molar masses of \( \text{N}_2\text{O} \) and \( \text{I}_2 \). \( \text{N}_2\text{O} \) has a molar mass of approximately 44 g/mol, and \( \text{I}_2 \) has a molar mass of approximately 254 g/mol.

Set up the equation using the given time for \( \text{N}_2\text{O} \) and solve for the time it takes for \( \text{I}_2 \) to effuse: \( \frac{42 \text{ s}}{t_{\text{I}_2}} = \sqrt{\frac{254}{44}} \).

Solve for \( t_{\text{I}_2} \) by rearranging the equation: \( t_{\text{I}_2} = 42 \text{ s} \times \sqrt{\frac{254}{44}} \).

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주요 개념

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Graham's Law of Effusion

Graham's Law states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass. This means that lighter gases effuse faster than heavier gases. In this question, we can use this principle to compare the effusion rates of N2O and I2, allowing us to calculate the time it takes for I2 to effuse based on the known time for N2O.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is a critical factor in Graham's Law, as the molar masses of the gases involved determine their rates of effusion. For N2O, the molar mass is approximately 44 g/mol, while for I2, it is about 254 g/mol, indicating that I2 is significantly heavier and will effuse more slowly.

Effusion

Effusion is the process by which gas molecules escape from a container through a small opening into a vacuum or another space. The rate of effusion is influenced by factors such as temperature and the size of the gas molecules. Understanding effusion is essential for solving the problem, as it allows us to apply Graham's Law to determine the time required for I2 to effuse based on the effusion time of N2O.

A sample of N2O effuses from a container in 42 seconds. How long will it take the same amount of gaseous I2 to effuse from the same container under identical conditions?