Question

Consider the following reaction: A(g)⇌B(g)+C(g) Find the equilibrium concentrations of A, B, and C for each of the following different values of Kc. Assume that the initial concentration of A in each case is 1.0 M and that the reaction mixture initially contains no products. Make any appropriate simplifying assumptions.

Part A: Kc= 1.0 Express your answer using two significant figures. Enter your answers numerically separated by commas.

Part B: Kc= 2.0×10⁻² Express your answer using two significant figures. Enter your answers numerically separated by commas.

Part C: Kc= 1.4×10⁻⁵ Express your answer using two significant figures. Enter your answers numerically separated by commas.

Answer 1

A(g)⇌B(g)+C(g)

Initial [A]=1.0M

Let equilibrium concentration of ,[A]eq=1.0-X

[B]=x

[C]=x

part A)kc=1.0=[B]eq [C]eq /[A]eq

           1.0=X^2/(1.0-X)

           1.0-X=X^2

             or, x^2+X-1.0=0

solving this quadratic equation for X of the form ax^2+bx+c=0 where x=[-b(b^2-4ac)^1/2]/2

x=[-1(5)^1/2]/2

or,x=0.62,-1.62

conc cant be negative so x=0.62M

x=0.62M=[B]eq=[C]eq

[Aeq]=1.0-x=1.0-0.62=0.38M

part B) kc=1.0=[B]eq [C]eq /[A]eq

           2.0 *10^-2=X^2/(1.0-X)

            2.0 *10^-2-(2.0 *10^-2X)=X^2

or,0.02-0.02x=x^2

x^2+0.02x-0.02=0

solving for x,

x=0.13, -0.15

x=0.13M=[B]eq=[C]eq

[A]eq=1.0-0.13=0.87M

part C) kc=1.0=[B]eq [C]eq /[A]eq

           1.4 *10^-5=X^2/(1.0-X) [ignore x<<<1.0]

             1.4 *10^-5=X^2/(1.0)

              1.4 *10^-5=X^2

                x^2=0.14*10^-4

                  x=0.37*10^-2M=[B]eq=[C]eq

              [A]eq=1.0-0.0037=1.00M(approx)