At room temperature, ammonia gas at 1 atm pressure and hydrogen chloride gas at P atm pressure are allowed to effuse through identical pin holes from opposite ends of a glass tube of one metre length and of uniform cross section. Ammonium chloride is first formed at a distance of 60 cm from the end through which HCl gas is sent in. What is the value of P?

Explanation

For Ammonia, `P_(1)= 1` atm, `M_(1)= 17`
For HCl gas, `P_(2)= P=`?, `M_(2)= 36.5`
If t is the time taken by the two gases to meet together and to form ammoniur chloride, Rate of diffusion of `NH_(3)(r_(1))= (100-60)/(t)= (40)/(t)`
(this is because the distance travelled by `NH_(3)` in the tube `=100-60cm`)
Rate of diffusion of HCl `(r_(2))= (60)/(t)`
For two gases at different pressures, Graham.s law of diffusion can be expressed as
`(r_(1))/(r_(2))= sqrt((M_(2))/(M_(1))).(P_(1))/(P_(2))`
Substituting, `((40)/(t))/((60)/(t))= sqrt((36.5)/(17)) xx (1)/(p)`
Hence, P= 2.198 atm