1. 10.3 Equilibrium Constants
At equilibrium, the number of people riding up the lift and the number of people skiing down the slope are constant.
Learning Goal Calculate the equilibrium constant for a reversible reaction given the concentrations of reactants and products at equilibrium.

2. Equilibrium Constants
aA + bB cC + dD
An equilibrium constant for a reversible chemical reaction
multiplies the concentrations of the products together and divides by the concentrations of the reactants.
raises the concentration (moles/liter) of each species to a power that is equal to its coefficient in the balanced chemical equation.
Core Chemistry Skill Writing the Equilibrium Constant Expression

3. Guide to Writing an Equilibrium Expression

4. Study Check
Write an equilibrium expression for the following reaction: 2CO(g) + O2(g) 2CO2(g)

5. Solution
Write an equilibrium expression for the following reaction: 2CO(g) + O2(g) 2CO2(g) STEP 1 Write the balanced chemical equation. 2CO(g) + O2(g) 2CO2(g) STEP 2 Write the concentrations of the products as the numerator and the reactants as the denominator.

6. Solution
Write an equilibrium expression for the following reaction: 2CO(g) + O2(g) 2CO2(g) STEP 3 Write any coefficient in the equation as an exponent.

7. Calculating Equilibrium Constants
The equilibrium constant, Kc, is the numerical value obtained by substituting experimentally measured molar concentrations at equilibrium into the expression.
For example,
the Kc for the reaction of H2 and I2 is written as
H2(g) I2(g) 2HI(g)
the Kc expression is written as
Core Chemistry Skill Calculating an Equilibrium Constant

8. Calculating Equilibrium Constants
For example,
the concentrations of each species in Experiment 1 are [H2] = 0.10 M, [I2] = 0.20 M, and [HI] = 1.04 M, and the Kc is
in additional Experiments 2 and 3, the mixtures have different equilibrium concentrations for the system at equilibrium at the same temperature, but they have the same value of Kc.
Thus, a reaction at a specific temperature can have only one value for the equilibrium constant.

9. Calculating Equilibrium Constants
The units of Kc depend on the specific equation. In this example, the units of [M2]/[M2] cancel out to give a value of 54. In this text, the numerical value will be given without any units.

10. Guide to Calculating the Kc

11. Study Check
The decomposition of dinitrogen tetroxide forms nitrogen dioxide. N2O4(g) 2NO2(g) What is the numerical value of Kc at 100 °C if a reaction mixture at equilibrium contains 0.45 M N2O4 and 0.31 M NO2?

12. Solution
The decomposition of dinitrogen tetroxide forms nitrogen dioxide. N2O4(g) 2NO2(g) What is the numerical value of Kc at 100 °C if a reaction mixture at equilibrium contains 0.45 M N2O4 and 0.31 M NO2? STEP 1 State the given and needed quantities.
ANALYZE Given Need
THE PROBLEM M N2O Kc
0.31 M NO2
Equation
N2O4(g) NO2(g)

13. Solution
The decomposition of dinitrogen tetroxide forms nitrogen dioxide. N2O4(g) 2NO2(g) What is the numerical value of Kc at 100 °C if a reaction mixture at equilibrium contains 0.45 M N2O4 and 0.31 M NO2? STEP 2 Write the Kc expression for the equilibrium. STEP 3 Substitute equilibrium (molar) concentrations and calculate Kc.

14. Study Check
Given the following chemical reaction, H2(g) + I2(g) 2HI(g) what is the numerical value of Kc at 443 °C if the equilibrium concentrations are as follows? [H2] = 1.2 M [I2] = 1.2 M [HI] = 0.35 M

15. Solution
Given the following chemical reaction, H2(g) + I2(g) 2HI(g) what is the numerical value of Kc at 443 °C if the equilibrium concentrations are as follows? [H2] = 1.2 M [I2] = 1.2 M [HI] = 0.35 M STEP 1 State the given and needed quantities.
ANALYZE Given Need
THE PROBLEM M H2, 1.2 M I2, Kc
0.35 M HI
Equation
H2(g) + I2(g) 2HI(g)

16. Solution
Given the following chemical reaction, H2(g) + I2(g) 2HI(g) what is the numerical value of Kc at 443 °C if the equilibrium concentrations are as follows? [H2] = 1.2 M [I2] = 1.2 M [HI] = 0.35 M STEP 2 Write the Kc expression for equilibrium.

17. Solution
Given the following chemical reaction, H2(g) + I2(g) 2HI(g) what is the numerical value of Kc at 443 °C if the equilibrium concentrations are as follows? [H2] = 1.2 M [I2] = 1.2 M [HI] = 0.35 M STEP 3 Substitute equilibrium (molar) concentrations and calculate Kc.