UPSEE Solved Model Paper 7

Given:
No. of moles of CH4 = 1
No. of moles of unknown gas = 1
Area of orifice through which CH4 diffusing = 1 mm2
Time = 40 sec
Area of orifice through which unknown gas effusing = 2 mm2
Time = 10 sec
We have to find the molecular mass of unknown gas Let it be M
Molecular mass of CH4 = 16 g/mol
According to Graham's law of diffusion
r α Area of orifice (i)
where r = Rate of diffusion
Also,
r α

1

√M

... (ii)
where. M = Molecular mass
Thus, from equation (i) and equation (ii)

r1

r2

=

A1 √M1

A2 √M2

or

r1

r2

=

A1

A2

.√

M2

M1

... (iii)
Now,
Rat of diffusion r =

V

t

Thus, equation (iii) can be written as

V t1

V t2

=

A1

A2

.√

M2

M1

or

t2

t1

=

A1

A2

.√

M2

M1

On substituting the values in equation (i). we get

10

40

=

1

2

.√

M

16

2

4

=

√M

4

2 = √M
M = 4
Hence, option 'A' is correct.