Question

A sample of Ne with a pressure of 0.443 atm and a temperature of 297K is introduced into one side of a porous barrier. After 220 seconds, the pressure of Ne on the other side of the barrier is 0.233atm. When 0.443atm of an unknown gas is subjected to the same process at 297 K, the pressure is found to be 0.111atm after 220 seconds. Calculate the density of the unknown gas.

Answer 1

rate of diffusion of unknown gas, A = rA
rate of diffusion of unknown gas, Ne = rNe
Moles of A diffused in time t = nA
Moles of Ne diffused in time t = nNe
pressure of diffused A = pA= 0.111 atm
pressure of diffused Ne = pNe = 0.233 atm
Molar mass of A = MW(A)
Molar mass of Ne = MW(Ne) = 20.18 g/mol

rA/rNe = nA/nNe = pA/pNe
But rate of diffusion is inversely proportional to square root of temperature.
rA/rNe = (MW(Ne)/MW(A))^0.5

(MW(Ne)/MW(A))^0.5 = pA/pNe

MW(A) = MW(Ne)*(pNe/pA)^2 = 20.18*(0.233/0.111)^2= 88.9 g/mol

Density of gas A at 0.443 atm and a temperature of 297K, rho = MW(A)*n/V = MW(A)*P/(R*T)
gas constant, R = 0.0821 L atm/K

Density of gas A = MW(A)*P/(R*T) = 88.9*0.443/(0.0821*297) = 1.615 L