Question

A sample of n2 effuses in 220 s. how long will the same size sample of cl2 take to effuse? a sample of n2 effuses in 220 s. how long will the same size sample of cl2 take to effuse? 86.8 s 388 s 350 s 558 s 138 s

Answer 1

Answer : The sample of $Cl_2$ effuses in, 350 seconds.

Solution : Given,

Effusion time of $N_2$ = 220 s

Molar mass of $N_2$ = 28 g/mole

Molar mass of $Cl_2$ = 71 g/mole

Rate of effusion : It is defined as the volume of gas effused in a given time 't'.

Formula used : $Rate=\frac{Volume}{Time}$

Or,

Rate of effusion : It is defined as the rate of effusion is directly proportional to the square root of the mass of the gas.

$\text{ Rate of effusion}\propto \frac{1}{\sqrt{\text{ Mass of gas}}}$

From the two expressions, we conclude that the relation between the time and the mass of gas is,

$\sqrt{M}\propto t$

or, $\sqrt{\frac{M_1}{M_2}}=\frac{t_1}{t_2}$     .........(1)

where,

$M_1$ = molar mass of $N_2$ gas

$M_2$ = molar mass of $Cl_2$ gas

$t_1$ = time of effusion of $N_2$ gas

$t_2$ = time of effusion of $Cl_2$ gas

Now put all the given values in equation (1), we get

$\sqrt{\frac{28g/mole}{71g/mole}}=\frac{220s}{t_2}$

By rearranging the terms, we get

$t_2=349.8s=350s$

Therefore, the sample of $Cl_2$ effuses in, 350 seconds.

Answer 2

According to Graham's gas effusion law, the rate effusion of N2 is 1.591 times greater than that of Cl2. To find the time, multiply the rate and the time. 220 x 1.591 = 350s.