Question

If 0.15 mol of I2 vapor can effuses through an opening in a heated vessel in 36 sec, how long will it take 0.15 mol of Cl2 to effuse under the same conditions?

Answer 1

Answer: The amount of time required by chlorine gas to effuse is 19 seconds.

Explanation:

Rate of a gas is defined as the amount of gas displaced in a given amount of time.

$\text{Rate}=\frac{n}{t}$

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,

$\left(\frac{\frac{n_{Cl_2}}{t_{Cl_2}}}{\frac{n_{I_2}}{t_{I_2}}}\right)=\sqrt{\frac{M_{I_2}}{M_{Cl_2}}}$

We are given:

Moles of iodine gas = 0.15 moles

Moles of chlorine gas = 0.15 moles

Time taken by iodine gas = 36 seconds

Molar mass of iodine gas = 254 g/mol

Molar mass of chlorine gas = 71 g/mol

Putting values in above equation, we get:

$\left(\frac{\frac{0.15}{t_{Cl_2}}}{\frac{0.15}{36}}\right)=\sqrt{\frac{254}{71}}\\\\\frac{0.15}{t_{Cl_2}}\times \frac{36}{0.15}=1.89\\\\t=19s$

Hence, the amount of time required by chlorine gas to effuse is 19 seconds.