Question

A sample of N2 gas is contaminated with a gas (A) of unknown molar mass. The partial pressure of each gas is known to be 200 tore at 25 degrees Celsius. The gas are allowed to Effuse through a pinhole, and it is found that has A escapes at 4 times the rate of N2. The molar mass of gas A is:
A. 1.75 g/mol
B. 448 g/mol
C. 112 g/mol
D. 7.01 g/mol
E. None of these

Answer 1

Answer: The molar mass of gas A is 1.75 g/mol

Explanation:

To calculate the rate of diffusion of gas, we use Graham's Law.

This law states that the rate of effusion or diffusion of gas is inversely proportional to the square root of the molar mass of the gas. The equation given by this law follows the equation:

$\text{Rate of effusion}\propto \frac{1}{\sqrt{\text{Molar mass of the gas}}}$

So,

$\frac{\text{Rate}_A}{\text{Rate}_{N_2}}=\sqrt{\frac{M_{N_2}}{M_{A}}}$

We are given:

Molar mass of nitrogen gas = 28 g/mol

Molar mass of A gas = ? g/mol

Putting values in above equation, we get:

$\frac{\text{Rate}_A}{\text{Rate}_{N_2}}=\sqrt{\frac{28}{M_{A}}}\\4=\sqrt{\frac{28}{M_{A}}}$

$M_{A}=1.75g/mol$

Thus molar mass of gas A is 1.75 g/mol