Question

Consider the following reaction and associated equilibrium constant:

aA(g)+bB(g)⇌cC(g)

Kc = 4.5

Find the equilibrium concentrations of A, B, and C for a=1, b=1, and c=1. Assume that the initial concentrations of A and B are each 1.0 M and that no product is present at the beginning of the reaction.

Express your answer using two significant figures. Enter your answers separated by commas.

Answer 1

ICE Table:

                    [A]                 [B]                 [C]               

initial             1.0                 1.0                 0                 

change              -1x                 -1x                 +1x               

equilibrium         1.0-1x              1.0-1x              +1x               

Equilibrium constant expression is
Kc = [C]/[A]*[B]
4.5 = (1*x)/((1-1*x)(1-1*x))
4.5 = (1*x)/(1-2*x + 1*x^2)
4.5-9*x + 4.5*x^2 = 1*x
4.5-10*x + 4.5*x^2 = 0
This is quadratic equation (ax^2+bx+c=0)
a = 4.5
b = -10
c = 4.5

Roots can be found by
x = {-b + sqrt(b^2-4*a*c)}/2a
x = {-b - sqrt(b^2-4*a*c)}/2a

b^2-4*a*c = 19

roots are :
x = 1.595 and x = 0.6268

x can't be 1.595 as this will make the concentration negative.so,
x = 0.6268

At equilibrium:
[A] = 1.0-1x = 1.0-1*0.62679 = 0.37321 M
[B] = 1.0-1x = 1.0-1*0.62679 = 0.37321 M
[C] = +1x = +1*0.62679 = 0.62679 M

Answer:
[A] = 0.37 M
[B] = 0.37 M
[C] = 0.63 M