Question

it takes 145 seconds for 1.00 milliliter of n2(g) to effuse from a certain porous container. given that it takes 230 seconds for 1.00 milliliter of an unknown gas to effuse under the same temperature and pres- sure, calculate the molecular mass of the unknown gas.

Answer 1

The rate of effusion of a gas is inversely proportional to the square root of its molar mass. The Graham's law of effusion equation is given by:

Rate of effusion of gas 1 / Rate of effusion of gas 2 = √(Molar mass of gas 2 / Molar mass of gas 1)

In this case, let's denote the nitrogen gas as "N2" and the unknown gas as "X."

Given:

Time for N2: t_N2 = 145 seconds

Time for unknown gas X: t_X = 230 seconds

We can set up the ratio of the rates of effusion and use it to find the ratio of the molar masses:

(Rate of effusion of N2 / Rate of effusion of X) = √(Molar mass of X / 28.02 g/mol)

Now, plug in the given values:

145 / 230 = √(Molar mass of X / 28.02 g/mol)

Solve for the molar mass of X:

Molar mass of X = (145 / 230)^2 * 28.02 g/mol

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