Large amounts of Nitrogen gas (N2) are used in the manufacture of ammonia, princ

Question

Large amounts of Nitrogen gas (N2) are used in the manufacture of ammonia, principally for use in fertilizers. Suppose 120 kg of N2 gas is stored in a 1100.0 L metal cylinder at 280 degrees C.

a) Calculate the pressure of the gas, assuming ideal gas behavior.

b) Calculate the pressure of gas according to the van der Waals equation. For nitrogen, a = 1.39 L2-atm/mol^2. b=0.0391 L/mol.

c) Under the conditions of this problem, which correction dominates, the one for finite volume of gas molecules or the one for attractive interactions? Please explain (important)

Explanation / Answer

(a)

molecular weight of N2=14*2=28

No of moles n =120*10^3/28=4.286*10^3 moles

T=280+273=553K

V= 1100 L

R=.082 L atm K-1 mol-1

P=n*R*T/V=176.7 atm

(b)

For.van der Waals gas (P+n^2*a/V^2)(V-n*b)=n*R*T

V=1100L, a = 1.39 L2-atm/mol^2. b=0.0391 L/mol

Pressure correction n^2*a/V^2=4286^2*1.39/1100^2=21.1 atm

Volume correction n*b=4286*.0391=167.58L

P=4286*.082*553/(1100-4286*.0391)-4286^2*1.39/1100^2=187 atm

(c)

Pressure correction n^2*a/V^2=4286^2*1.39/1100^2=21.1 atm

% error in pressure =21.1/176.7*100= 12

% error in volume = 167.58/1100*100=15.2

So here pressure correction dominates

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