Question

50ml of gas A effuse through a pin - hole in 146 seconds. The same
volume of CO 2 under identical conditions effuse in 115 seconds. Calculate
the molecular mass of A.

Answer 1

t1/t2 = (M1/M2)^1/2
146/115 = (M1/44)^1/2
1.61 = M1/44
M1 = 70.91

Answer 2

Thus the molecular mass of A is 71 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:

$\frac{rate_A}{rate_B}=\sqrt{\frac{M_B}{M_A}}$

$rate=\frac{volume}{time}$

Rate is volume effused per unit time. Since, the volumes are same, the formula could be written as:

$\frac{t_B}{t_A}=\sqrt{\frac{M_B}{M_A}}$

$\frac{t_{CO_2}}{t_A}=\sqrt{\frac{M_{CO_2}}{M_A}}$

$\frac{115}{146}=\sqrt{\frac{44}{M_A}}$

$M_A=71g/mol$

Thus the molecular mass of A is 71 g/mol

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