Question

If helium effuses through a porous barrier in 1.34 min, how much time (in min) would it take the same amount of ammonia to effuse through the same barrier under the same conditions?

Answer 1

Answer:

The time taken the same amount of ammonia to effuse through the same barrier under the same conditions is 2.76 minutes.

Explanation:

Let the volume of the helium gas be = V

Time taken by the helium gas = t = 1.34 min

Effusion rate of helium gas = $R=\frac{V}{1.34 min}$

If V volume of ammonia effuse through same porous barrier the effusion rate of ammonia gas will be given as:

$R'=\frac{V}{t'}$

Using 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:

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

Molar mass of helium gas = M = 4 g/mol

Molar mass of ammonia gas = M' = 17 g/mol

$\frac{R}{R'}=\sqrt{\frac{M'}{M}}$

$\frac{\frac{V}{1.34 min}}{\frac{V}{t'}}=\sqrt{\frac{17 g/mol}{4 g/mol}}$

$t'=1.34 min\times \sqrt{\frac{17 g/mol}{4 g/mol}}=2.76 min$

The time taken the same amount of ammonia to effuse through the same barrier under the same conditions is 2.76 minutes.