Question

A gas evolved from the fermentation of glucose is found to effuse through a porous barrier in 15.0 min. Under the same conditions of temperature and pressure, it takes an equal volume of N2 12.0 min to effuse through the same barrier. Calculate the molar mass of the gas and suggest what the gas might be.

Answer 1

According to Graham's law of effusion, the molar mass of the unknown gas can be estimated based on the ratio of effusion rates. The molar mass of the unknown gas is approximately 80.46 g/mol, which is closest to the molar mass of XeF4 (131.29 g/mol).

Step-by-step explanation:

According to Graham's law of effusion, the rate of effusion of a gas is inversely proportional to the square root of the mass of its particles. In this case, if N2 takes 12.0 minutes to effuse, and the unknown gas takes 15.0 minutes to effuse, we can set up the following proportion: (sqrt(molar mass of N2))/(sqrt(molar mass of unknown gas)) = (effusion rate of unknown gas)/(effusion rate of N2).

Since the rate of effusion of hydrogen is 8.97 times faster than the unknown gas, the square root of the molar mass of the unknown gas is approximately 8.97 times greater than that of hydrogen. Therefore, the molar mass of the unknown gas is approximately (8.97)^2 = 80.46 g/mol. From the periodic table, we can see that the closest molar mass to this value is that of XeF4, which is 131.29 g/mol. Therefore, the gas is likely to be XeF4.