A 10.0 L cylinder contains 370 g of N₂. What is the difference in the pressure at 27°C calculated using van der Waals equation, and the pressure calculated using the ideal gas equation?

Question

Quizplus · Accepted Answer

First, we need to calculate the pressure using the ideal gas equation:

PV=nRT

n= m/MW = 370 g / 92.14 g/mol = 4.01 mol

P = (4.01 mol)(0.0821 L·atm/K·mol)(27+273 K)/(10.0 L) = 10.5 atm

Next, we need to calculate the pressure using van der Waals equation:

a = 4(1.37)^2(0.414)/27 = 0.115 atm·L^2/mol^2
b = 0.0866 L/mol

(P + a(n/V)^2)(V - nb) = nRT

(P + 0.115(4.01/10.0)^2)(10.0 - 0.0866*4.01) = 4.01*0.0821*(27+273)

P = 9.88 atm

The difference in pressure between the two equations is:

ΔP = Pvan der Waals - Pideal gas = 9.88 atm - 10.5 atm = -0.62 atm

Therefore, the answer is B) 0.620 atm, since it is the closest value to the calculated difference.

A 100 L Cylinder Contains 370 G of N2

A 100 L Cylinder Contains 370 G of N₂