Testing Ammonia is among the top ten synthesized compounds. Its many uses includ

Question

Testing Ammonia is among the top ten synthesized compounds. Its many uses include the manufacture of ammonium nitrate and other fertilizers. Ammonia decomposes at high temperatures. In an experiment to explore this behavior, 2.000 moles of gaseous NH3 are sealed in a rigid 1-liter vessel. The vessel is heated at 800 K and some of the NH3 decomposes in the following reaction: The system eventually reaches equilibrium and is found to contain 1.740 mole of NH3. What are the values of Kp and Kc for the decomposition reaction at 800 K?

Explanation / Answer

                                             2NH3 <---> N2 + 3 H2
initial:                                     2 mol         0         0
at equilibrium:           2-2x           x           3x
Given number of moles of NH3 at equilibrium = 1.74 mol
so, 2-2x = 1.74
x= 0.13 mol

number of moles of N2= x = 0.13 mol
[N2] = number of moles/volume = 0.13/1 =0.13 M
p(N2)= n*R*T/V             {since : P*V= n*R*T}
          = 0.13*0.0821*800 / 1
           =8.5384 atm

number of moles of H2= 3x = 3*0.13 = 0.39 mol
[H2] = number of moles/volume = 0.39/1 =0.39 M
p(H2)= n*R*T/V             {since : P*V= n*R*T}
          = 0.39*0.0821*800 / 1
           = 25.62 atm

number of moles of NH3 = 1.74 mol
[NH3] = number of moles/volume = 1.74/1 =1.74 M
p(NH3)= n*R*T/V             {since : P*V= n*R*T}
          = 1.74*0.0821*800 / 1
           = 114.28 atm

Kc = [N2] [H2]^3 /[NH3]^2
     = (0.13) * (0.39)^3 / (1.74)^2
     =2.55*10^-3

Kp =p(N2) p(H2)^3 /p(NH3)^2
    =(8.5384) * (25.62)^3 / (114.28)^2
    = 11.4

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