Question

Combining Equilibrium Constants.

It is possible to predict the equilibrium constant of a reaction by combining two or more reactions for which the value of K is known. When combining equilibrium constants, it is important to note the following:

When a reaction is reversed, its Kvalue is inverted; that is, Kreverse=1/Kforward.

When the coefficients of a reaction are multiplied by a factor, the Kvalue is raised to the power of that factor.

When reactions are added, their Kvalues are multiplied.

Part A

Determine the value of the equilibrium constant, Kgoal, for the reaction

N2(g)+H2O(g)⇌NO(g)+12N2H4(g),    Kgoal=?

by making use of the following information:

1. N2(g)+O2(g)⇌2NO(g),	K1 =	4.10×10−31
2. N2(g)+2H2(g)⇌N2H4(g),	K2 =	7.40×10−26
3. 2H2O(g)⇌2H2(g)+O2(g),	K3 =	1.06×10−10

Part B

Determine the equilibrium constant, Kgoal, for the reaction

4PCl5(g)⇌P4(s)+10Cl2(g),    Kgoal=?

by making use of the following information:

P4(s)+6Cl2(g)⇌4PCl3(g),       K1=2.00×1019

PCl5(g)⇌PCl3(g)+Cl2(g),       K2=1.13×10−2

Answer 1

A)

1. N2(g)+O2(g)⇌2NO(g),	K1 =	4.10×10−31
2. N2(g)+2H2(g)⇌N2H4(g),	K2 =	7.40×10−26
3. 2H2O(g)⇌2H2(g)+O2(g),	K3 =	1.06×10−10

N2(g)+H2O(g)⇌NO(g)+1/2N2H4(g),    Kgoal=?

Equation goal = 1/2(equation 1 + equation 2+ equation 3)

Kgoal = (K1 X K2 X K3 )^1/2 = (4.10 X 10^-31 X 7.40 X 10^-26 X 1.06 X 10^-10 )^1/2 = (32.16 X 10^-67)^1/2 = (3.126 X 10^-66)^1/2

= 1.77 X 10^-33

Part B:

4PCl5(g)⇌P4(s)+10Cl2(g),    Kgoal=?

1) P4(s)+6Cl2(g)⇌4PCl3(g),       K1=2.00×10¹⁹

2) PCl5(g)⇌PCl3(g)+Cl2(g),       K2=1.13×10⁻²

Equation goal = 4 X equation (2) - equation (1) = 4[PCl5(g)⇌PCl3(g)+Cl2(g)] - [ P4(s)+6Cl2(g)⇌4PCl3(g)]

=[ 4PCl5(g)⇌4PCl3(g)+4Cl2(g)]-[ P4(s)+6Cl2(g)⇌4PCl3(g)] = 4PCl5(g)⇌P4(s)+10Cl2(g)

Kgoal = (K2)⁴ / K1 = (1.13 X 10^-2)⁴ / 2.00×10¹⁹ = 0.815 X 10^-27