Answer to Question #109614 in General Chemistry for Jonathan

Question

A 51 g sample of N2 (Nitrogen) gas has a volume of 32 L at 33°C.
i. Calculate the pressure using the Ideal Gas Law.
ii. Calculate the corrected pressure using the Van der Waals Equation.
a=1.351 atm×L2 b=0.0387 L
mol2 mol

Answer 1

T=33+273=306 K

Mr(N2) = 14*2=28

n=51/28=1.82 mol

i. Ideal Gas Law : pV=m(N2)/Mr(N2) *RT

p_i=m(N2)*R*T/(Mr(N2) *V_i)=(51*8.314*306) / (28*32)=144.8 kPa

ii.  Van der Waals Equation: [ p_r + a*(n/V)²](V_r - n*b)=nRT

V_i=Vr - n*b, so [ p_r + a*(n/V)2]V_i=nRT

p_r= (nRT)/(V-n*b) - a*(n/V)² = (1.82*8.314*306)/(32) - 1.351*(1.82/32)² = 144.69 kPa