Question

in the gas-phase reaction A + B --> C + 2D, it was found that when 2 mole A, 1 mole B, and 3 mole D were mixed and allowed to come to equilibrium at 25^oC, the resulting mixture contained 0.79 mole C at a total pressure of 1 bar. calculate (a) the mole fractions of each species at equilibrium, (b) K_x (c) K and (d) delta_rG^o

Answer 1

A +          B   ------------------>      C    +    2D

2                      1                                 0               3          ----------------   initial

2 - x                1-x                              x               3 + 2x      ------------------ equilibrium

resulting mixture contain 0.79 moles of C

x = C moles = 0.79

moles of A = 2 - x = 2 - 0.79 = 1.21

moles of B = 1 - x = 1 - 0.79 = 0.21

moles of C = x = 0.79

moles of D = 3 + 2x = 3 + 2x0.79 = 4.58

total moles = moles of A + B + C +D

                  = 1.21 + 0.21 + 0.79 + 4.58

                  = 6.79

(a)

mole fraction of A = 1.21 / 6.79 = 0.178

mole fraction of B = 0.21 / 6.79 = 0.0309

mole fraction of C = 0.79 / 6.79 = 0.1163

mole fraction of D = 4.58 / 6.79 = 0.6745

(b)

Kx = [C][D]^2 / [A][B]

      = 0.1163 x 0.6745^2 / 0.178 x 0.0309

       = 9.62

(c)

K = [C][D]^2 / [A][B]

    = 0.79 x 4.58^2 / 1.21 x 0.21

    = 65.22

(d)

delta Go = - RT ln K

               = -8.314 x 10^-3 x 298 x ln 65.22

               = -10.35