Question

The molar mass of argon is 40 g/mol. what is the molar mass of a gas if it effuses at 0.91 times the speed of argon gas?

Answer 1

To determine the molar mass of the unknown gas, we use Graham's Law of Effusion where it relates the effusion rates of two gases with their molar masses. It is expressed as r1/r2 = √M2/M1. We calculate as follows:
Let 1 = argon gas      2 = unknown gas
r2 = 0.91r1r1/r2 = 1/0.91
1/0.91 = √M2/M1 = √M2/40M2 = 48.30 g/mol

Answer 2

Answer : The molar mass of a gas is, 48.3 g/mole

Solution : Given,

Molar mass of argon gas = 40 g/mole

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

$R\propto \sqrt{\frac{1}{M}}$

or,

$\frac{R_1}{R_2}=\sqrt{\frac{M_2}{M_1}}$

where,

$R_1$ = rate of effusion of a gas

$R_2$ = rate of effusion of argon gas

$M_1$ = molar mass of a gas

$M_2$ = molar mass of argon gas

As per question,

$R_1=0.91\times R_2$

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

$\frac{0.91\times R_2}{R_2}=\sqrt{\frac{40g/mole}{M_1}}$

$M_1=48.30g/mole$

Therefore, the molar mass of a gas is, 48.3 g/mole