Answer : The sample of [tex]Cl_2[/tex] effuses in, 350 seconds.
Solution : Given,
Effusion time of [tex]N_2[/tex] = 220 s
Molar mass of [tex]N_2[/tex] = 28 g/mole
Molar mass of [tex]Cl_2[/tex] = 71 g/mole
Rate of effusion : It is defined as the volume of gas effused in a given time 't'.
Formula used : [tex]Rate=\frac{Volume}{Time}[/tex]
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.
[tex]\text{ Rate of effusion}\propto \frac{1}{\sqrt{\text{ Mass of gas}}}[/tex]
From the two expressions, we conclude that the relation between the time and the mass of gas is,
[tex]\sqrt{M}\propto t[/tex]
or, [tex]\sqrt{\frac{M_1}{M_2}}=\frac{t_1}{t_2}[/tex] .........(1)
where,
[tex]M_1[/tex] = molar mass of [tex]N_2[/tex] gas
[tex]M_2[/tex] = molar mass of [tex]Cl_2[/tex] gas
[tex]t_1[/tex] = time of effusion of [tex]N_2[/tex] gas
[tex]t_2[/tex] = time of effusion of [tex]Cl_2[/tex] gas
Now put all the given values in equation (1), we get
[tex]\sqrt{\frac{28g/mole}{71g/mole}}=\frac{220s}{t_2}[/tex]
By rearranging the terms, we get
[tex]t_2=349.8s=350s[/tex]
Therefore, the sample of [tex]Cl_2[/tex] effuses in, 350 seconds.
