Suppose that nitrogen gas and hydrogen gas are mixed in a container of constant

Question

Suppose that nitrogen gas and hydrogen gas are mixed in a container of constant volume at 700 K and in the presence of a catalyst such that the initial partial pressures of nitrogen gas is 2.0 atm and the initial partial pressure of hydrogen gas is 6.0 atm. Under these conditions equilibrium between the reactants and the product ammonia is established. The equilibrium constant, KP, for this reaction at 700 K is 1.0 x 10-4. Compute partial pressures of the three gases when equilibrium is established

Explanation / Answer

the reaction is given by

N2 + 3H2 ----> 2NH3

now

the equilibrium constant is given by

Kp = [pNH3]^2 / [pN2] [pH2]^3

now

consider the reaction

N2 + 3H2 ---> 2NH3

using ICE table

inital partial pressures of N2 , H2 and NH3 are 2 , 6 ,0

change in partial pressures of N2 , H2 , NH3 are -x , -3x ,+2x

equilibirum partial pressures of N2 , H2 , NH3 are 2-x ,6-3x ,2x

Kp = [pNH3]^2 / [pN2] [pH2]^3

Kp = ( 2x)^2 / (2-x) (6-3x)^3

Kp =4x2 / (2-x) [3(2-x)]^3

Kp = 4x2 / 27 (2-x)^3

assuming x <<< 2

we get

Kp = 4x2 / 216

10-4 = 4x2 / 216

x = 0.074

now

At equilibrium

pN2 = 2- x = 2-0.074 = 1.926 atm

pH2 = 6 - 3x = 6- 3(0.074) = 5.778 atm

pNH3 = 2x =2 (0.074) = 0.148 atm

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