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Answer :
Final answer:
The molar mass of the unknown gas can be determined using Graham's law of effusion. By comparing the effusion times of the unknown gas and carbon dioxide, we can calculate the molar mass of the unknown gas. The molar mass of the unknown gas is equal to the molar mass of carbon dioxide divided by 1.081.
Explanation:
To determine the molar mass of the unknown gas, we can use Graham's law of effusion. According to the law, the rate of effusion of a gas is inversely proportional to the square root of its molar mass. Let's denote the unknown gas as Gas X and carbon dioxide as Gas CO2.
We are given that it takes Gas X 42.4 s to effuse, and it takes CO2 39.4 s to effuse for the same volume. Using Graham's law of effusion, we can set up the following equation:
Rate of effusion of Gas X / Rate of effusion of CO2 = √(Molar mass of CO2 / Molar mass of Gas X)
Substituting the given values:
42.4 s / 39.4 s = √(Molar mass of CO2 / Molar mass of Gas X)
Squaring both sides of the equation:
(42.4 s / 39.4 s)^2 = (Molar mass of CO2 / Molar mass of Gas X)
Calculating the left side of the equation:
(42.4 / 39.4)^2 = 1.081
Therefore, the molar mass of Gas X is equal to the molar mass of CO2 divided by 1.081.
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