A sample of solid NH4HS is placed in an empty container and sealed. When heated

Question

A sample of solid NH4HS is placed in an empty container and sealed. When heated to 25 C, the solid decomposes as follows : NH4HS (s) = NH3 (g) + H2S (g) The pressure of the container is monitored until it reaches a constant value of .659 atm, and some solid remains as well. a) Write the expression for Kp and calculate its value b) How do we know equilibrium has been established? c) After equilibrium has been established, extra NH3 (g) is added such that the pNH3 is twice that of H2S. What is the pressure of NH3 after equlibrium is reestablished? d) Calculate Kc.

Explanation / Answer

a) Write the expression for Kp and calculate its value

First, Kp:

Kp = P-NH3 * P-H2S

P final = 0.659 atm

Note that this implies:

Ptotal = P-NH3 + P-H2S

and, due to sotichioemtry

P-NH3 = P-H2S

So

Ptotalx = 2x = 0.659

x = 0.659/2 = 0.3295

substitute

Kp = 0.3295/*0.3295

kp = 0.10857025

b) How do we know equilibrium has been established?

The equilibrium has been stablished since:

"until it reaches a constant value of .659 atm,"

meaning, that no reaction/shift will occur

the Rate of change is 0, so this is in equilbirium

c) After equilibrium has been established, extra NH3 (g) is added such that the pNH3 is twice that of H2S. What is the pressure of NH3 after equlibrium is reestablished?

Recalcualte equilbrium:

initially:

P-NH3 = 2*0.3295 = 0.659 atm

P-H2S = 0.3295 atm

after equilibrium shifts:

P-NH3 = 2*0.3295 = 0.659 atm - x

P-H2S = 0.3295 atm - x

substitute in Kp

Kp = P-NH3 * P-H2S

0.10857025 = (0.659 -x) * (0.3295 -x)

solve for x

0.10857025 = (0.659 *0.3295 ) -(0.3295 +0.659 )x + x^2

x^2 -0.9885x + ( 0.2171405-0.10857025 ) = 0

x^2 - 0.9885*x + 0.108570 = 0

x = 0.1222 or 0.866 ; the later can't be since it is too large, will give negative, so choose 0.122

P-NH3 = 2*0.3295 = 0.659 atm - x = 0.659-0.1222 = 0.5368

P-H2S = 0.3295 atm - x = 0.3295 -0.1222 = 0.2073

Proof:

Kp = 0.5368*0.2073 = 0.11127; which is pretty near to 0.10857025, so this must be true

P-NH3 = 0.5368 atm

d) Calculate K

Kc from:

Kp = Kc*(RT)^dn

dn = 2 moles of gas, so n = 2

Kp = Kc*(RT)^dn

0.10857025 = Kc*(0.082*298)^2

Kc = (0.10857025 ) / ((0.082*298)^2) = 0.00018182

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