Exercise 14 49 Consider the following reaction and associated equilibrium consta

Question

Exercise 14 49 Consider the following reaction and associated equilibrium constant aA(g) bB(g), Kc = 4.0 Part A Find the equilibrium concentrations of A and B for a = 1 and b = 1. Assume that the initial concentration of A is 1.0 M and that no B is present at the beginning of the reaction Express your answers using two significant figures separated by a comma. Part B Find the equilibrium concentrations of A and B for a = 2 and b = 2. Assume that the initial concentration of A is 1.0 M and that no B is present at the beginning of the reaction. Express your answers using two significant figures separated by a comma. Part C Find the equilibrium concentrations of A and B for a = 2 and b = 1. Assume that the initial concentration of A is 1.0 M and that no B is present at the beginning of the reaction. Express your answers using two significant figures separated by a comma.

Explanation / Answer

aA <-> bB

K = 4

a)

if a = 1 and b = 1

A = 0.1 and B = 0 at the begining

Then

Kc = [B]^b / [A]^a

[B] = 0 + x

[A] = 0.1 - x

substitue in K

Kc = [B]^b / [A]^a

4 = (x) / (0.1-x)

4(0.1-x) = x

0.4 - 4x = x

5x = 0.4

x = 0.4/5 = 0.08

Substitute in equilibrium concnetrations

[B] = 0 + x = 0.08

[A] = 0.1 - 0.08 = 0.02

b)

a = 2 and b = 2

[A] = 0.1 and [B] = 0

then in equilibrium

[A] = 0.1-2x

[B] = 0+2x

Substitute in K in equilirbrium

Kc = [B]^2 / [A]^2

4 = (2x)^2 / (0.1-2x)^2

solve for x

sqrt(4) = sqrt((2x)^2 / (0.1-2x)^2)

2 = 2x / (0.1-2x)

0.2-4x = 2x

6x = 0.2

x = 0.2/6 = 0.03333

Substitue in Equilbirium concentrations

[A] = 0.1-2x = 0.1 - 2*0.03333 = 0.0333

[B] = 0+2x = 0 +2*0.03333 = 0.0666

c)

a = 2 and b = 1

then

K = [B] / [A]^2

[A] = 0.1

[B] = 0

in equilibrium

[A] = 0.1 - x

[B] = +x

susbtitute in K

K = [B] / [A]^2

4 = (x) / (0.1-x)^2

(0.1-x) ^2 = x/4

0.01 -0.2x + x^2 = 0.25x

0.01 - 0.45x + x^2 = 0

x = 0.0234

substiute in equilibrium concentrations

[A] = 0.1 - x = 0.1-0.0234 = 0.0.766

[B] = +x = 0.0234

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