Explain the relationship between the rate of effusion of a gas and its molar mass. Methane gas (CH4) effuses 3.4 times faster than an unknown gas. Determine the molar mass of the unknown gas. Show your work or explain your answer, giving specific values used to determine the answer.

Answer : The molar mass of unknown gas is 184.96 g/mole.

Solution : Given,

Effusion rate of methane gas is 3.4 times faster than an unknown gas. That means,

Molar mass of methane, = 16 g/mole

According to Graham's law of effusion, the rate of effusion of a gas in inversely proportional to the square root of the mass of a gas.

where,

R = rate of effusion of a gas

M = Molar mass of a gas

By rearranging the above formula, we get

Now put all the given values in this formula, we get molar mass of unknown gas.

Therefore, the molar mass of unknown gas is 184.96 g/mole.