The Graham's law of diffusion states that rate (r)∝
1
√M
Where, M is the molar mass. Also, rate (r)∝
volume(V)
time(t)
Let the given another gas be Z .
rSO2
rz
=
(V∕t)SO2
(V∕t)z
=
(1∕√M)SO2
(1∕√M)z
Rearranging the above formula we get.
VSO2×tz
Vz×tSO2
=√
Mz
MSO2
......(I) The molar mass of SO2 is 64g∕mol. The time can be converted to seconds as shown below. 1min=60seconds 5min=300 seconds Substitute the values in equation (I).
12×300
120×60
=√
Mz
64
1
4
=
Mz
64
Mz=
64
4
Mz=16g∕mol The molar mass of given gas is 16 g/mol.