UPSEE Solved Model Paper 7

Given
Container x has circular hole
Container y has square hole
Radius of circular hole = Length of square
No of moles of g as in x = 2 No. of moles of gas in y
Let the length of square be 'a'
Now,
Area of square = (side)2
= a2
Area of circle = π(Radius)2
= πa2
According to Graham 's law of diffusion:
Rate of diffusion α p × A .. (i)
where, p = Pressure
A = Area of hole
Now. greater the no of moles of gas. greater will be the pressure exerted by them.
Thus,
Pressure in container x = 2 × pressure in container y
Let the pressure in container y be p.
∴ pressure in container x = 2p
Substituting values in equation (i). w e get
Rate of diffusion of gas from container x α 2p × π × a2 (ii)
Rate of diffusion of gas from container y α p × a2 (iii)
Dividing equation (ii) by (iii), we get
=

2p×πa2

pa2

= 2π
Hence, option 'A' is correct