Question

a pure sample of methane is found to effuse through a porus barrier in 1.50 minutes under the same coditions an equal number of molecules of an unknown gas effuses through the barrier in 4.73 onutes. what is the molar mass of the unkown gass?

Answer 1

To find the molar mass of the unknown gas, apply Graham's Law using the given effusion times for methane and the unknown gas, with methane's molar mass known to be 16.04 g/mol. Calculate the ratio of the effusion rates, square it, and solve for the unknown gas's molar mass.

Step-by-step explanation:

The question involves calculating the molar mass of an unknown gas based on the rate of effusion through a porous barrier. According to Graham's Law of effusion, the rate at which a gas effuses is inversely proportional to the square root of its molar mass (rate of effusion ∝ 1/sqrt(molar mass)). The problem states that methane (CH4) effuses in 1.50 minutes, and an unknown gas effuses in 4.73 minutes. We can use rate1 / rate2 = sqrt(molar mass2 / molar mass1) to find the molar mass of the unknown gas, with methane's molar mass being approximately 16.04 g/mol.

Here's the calculation:

1. Calculate the ratio of effusion rates: rateCH4 / rateunknown = timeunknown / timeCH4 = 4.73 / 1.50.
2. Apply Graham's Law: (rateCH4 / rateunknown)2 = molar massunknown / molar massCH4.
3. Solve for molar massunknown.

Thus, the molar mass of the unknown gas can be calculated using the derived rate ratio and methane's known molar mass.