A sample of HCl is introduced at one end of a 1meter tube.A sample of gas with a molecular weight of 34.5 is introduced at the other. calculate where the two gases meet.

Question

it asks to use Graham's Law

Answer 1

Hi Lauren K.

Graham's law states that the rate of effusion/diffusion of a gas is inversely related to the square of its molar mass. Put in the form of an equation, we have ...

rate gas₁ / rate gas₂ = √MW_gas2 / √MW_gas1

Let's call HCl gas₁ and the other gas we'll call gas₂ of X

MW HCl = molecular weight HCl = 36.46 g/mol

MW X = 34.5 g/mol

rate HCl/rate X = sqrt34.5 / sqrt 36.46

rate HCl/rate X = 5.87 / 6.04

rate HCl / rate X = 0.972

This means the rate of movement of HCl in the tube is 0.972 times that the movement of gas X, or the rate of movement of gas X is 1.03 times that of HCl. This makes sense since the molar mass of HCl is greater than that of gas X so the HCl should move slower.

The gases will thus meet at the end closer to where the HCl started. Since the tube is 1 meter in length, the 2 gases should meet at 0.493 meters from the HCl end or 0.507 meters from the gas X end.

X / 1 - X = 1.03 (ratio of gas X to HCl)

x = 1.03 - 1.03x

x = 0.507 meters or 0.493 meters from HCl end