The Haber process { 2 N2(g) + 3 H2(g) <-> 2 NH3(g) } has a Kp of 4.34 x 10^3 at

Question

The Haber process { 2 N2(g) + 3 H2(g) <-> 2 NH3(g) } has a Kp of 4.34 x 10^3 at 300 K. Calculate the pressure of ammonia that is present at equilibrium if we start with 10 atm of nitrogen and 20 atm of hydrogen gas. Predict whether this concentration would increase or decrease if the original mixture was contained in a 5 L metal bottle and the mixture was allowed to expand into a second 5 L bottle, resulting in a total volume of 10 L. Verify your prediction by calculating the new pressure of ammonia.

Explanation / Answer

Initially, there is 10 atm of N2 and 20 atm of Hydrogen gas

At Equilibrium 2x= Pressure of Ammonia

At Equilibrium Pressures : N2= 10-2x H2= 20-3x

KP= [NH3]2/ {[N2][H2]3 =(2x)3/ [(10-2x)*(20-3x)3=4.32*10-3

This equation when solved using solver gives x=2.043atm

At Equilibrium pressure of ammonia =2*2.043= 4.086 atm

b) When the volume is increased, the pressure decreases and the reaction shifts in a directino where there is an increase in pressure , i.e the reacrtion shfits to backward direction leading to less formation of NH3 at Equilibrium

When expanded in to 10L

New pressures are from P1V1= P2V2 ( at consttant temperature )

New pressures N2 : 10*5/10= 5 atm and H2= 10 atm

Kp now is (2x)3/ (5-2x)*(10-3x)3   = 4.34*10-3

x=0.885 and Equilibrium pressure = 2*0.885=1.77 atm

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