Consider the following reaction and associated equilibrium constant: a A( g ) b

Question

Consider the following reaction and associated equilibrium constant:
aA(g)bB(g), Kc = 1.5

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.

[A], [B] = ?M

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.

[A], [B] = ?M

Part C

Find the equilibrium concentrations of A and B for a = 2 and b = 1. Assume that the initial concentration of Ais 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.

[A], [B] = ?M

Explanation / Answer

K = B^b / A^a

1.5 = B^b / A^a

A)

1.5 = B/A

A = 1-x

B= 0+x

1.5 = x/(1-x)

1.5 -1.5x = x

2.5x = 1.5

x = 1.5/2.5 = 0.6

then

A = 1-x = 1-0.6 = 0.4

B= 0+x = 0.6

B)

1.5 = B^2/A^2

B = 0 +2x

A = 1-2x

1.5 = (2x)^2 / (1-2x)^2

sqrt(1.5) = 2x/(1-2x)

2/sqrt(1.5) x = 1-2x

x(2/sqrt(1.5) + 2) = 1

x = 1/((2/sqrt(1.5) + 2) = 0.27525

B = 0 +2x = 2*0.27525 = 0.5505

A = 1-2x = 1-2*0.27525 = 0.4495

C)

1.5 = B/A^2

B = 0 +x

A = 1-2x

1.5 = x/(1-2x)^2

1-4x +4x^2 = 0.66x

4x^2 -4.66x +1 = 0

x = 0.2836

B = 0 +x = 0.2836

A = 1-2x = 1-2*0.2836 = 0.4328

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