Question

Under certain conditions, neon (Ne) gas diffuses at a rate of 4.5 centimeters per second. Under the same conditions, an unknown gas diffuses at a rate of 10.1 centimeters per second. What is the approximate molar mass of the unknown gas?

Answer 1

Mv^2 = const 
m ~ 1/v^2 

(4.5/10.1)^2 = 0.198 

20.2 * 0.198 = 4.0 g/mol (Helium)

Answer 2

Answer: 4 g/mol

Explanation:

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

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

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

Molar mass of neon =  20 g/mol

Molar mass of unknown gas = ?g/mol

For the rate of diffusion of neon to unknown gas (X), we write the expression:

$\frac{Rate_{Ne}}{Rate_{X}}=\sqrt{\frac{M_{X}}{M_{Ne}}}$

$\frac{4.5}{10.1}=\sqrt{\frac{M_{X}}{20}$

${M_{X}}=4g/mol$

Hence, the approximate molar mass of the unknown gas is 4 g/mol