Question

A sample of N2 gas is observed to effuse through a pourous barrier in 3.81 minutes. Under the same conditions, the same number of moles of an unknown gas requires 6.68 minutes to effuse through the same barrier. The molar mass of the unknown gas is _______ g/mol.

Answer 1

To determine the molar mass of the unknown gas, we can use Graham's law of effusion. The rate of effusion of a gas is inversely proportional to the square root of its molar mass. Using the given rates of effusion for N2 gas and the unknown gas, we can solve for the molar mass of the unknown gas using Graham's law.

Step-by-step explanation:

To determine the molar mass of the unknown gas, we can use 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. In this case, we are given that the same number of moles of the unknown gas takes 6.68 minutes to effuse, while N2 gas takes 3.81 minutes. So, we can set up an equation using Graham's law:

Rate of effusion for N2 gas / Rate of effusion for unknown gas = Square root of the molar mass of unknown gas / Square root of the molar mass of N2 gas

Plugging in the values: 3.81 / 6.68 = √(molar mass of unknown gas) / √(28 g/mol)

Now, we can solve for the molar mass of the unknown gas:

√(molar mass of unknown gas) = √(28 g/mol) × (3.81 / 6.68)

Molar mass of unknown gas = (√(28 g/mol) × (3.81 / 6.68))²

Calculating this expression will give you the molar mass of the unknown gas