Question

It takes 167 s for an unknown gas to effuse through a porous wall and 99 s for the same volume of n2 gas to effuse at the same temperature and pressure. what is the molar mass of the unknown gas?

Answer 1

Answer : The molar mass of the unknown gas will be 79.7 g/mol

Explanation : To solve this question we can use graham's law;

Now we can use nitrogen as the gas number 2, which travels faster than gas 1;

So, 167 / 99 = 1.687 So the nitrogen gas is 1.687 times faster that the unknown gas 1

We can compare the rates of both the gases;

So here, Rate of gas 2 / Rate of gas 1 = $\sqrt{(molar mass 1 / molar mass 2)}$

Now, 1.687 = square root [$\sqrt{(molar mass 1) / (28.01 g/mol N_{2})}$ ]

When we square both the sides we get;

2.845 = (molar mass 1) / (28.01 g/mol N2)

On rearranging, we get,

2.845 X (28.01 g/mol N2) = Molar mass 1

So the molar mass of unknown gas will be = 79.7 g/mol