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.

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

Guide to Writing an Equilibrium Expression

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

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.

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.

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

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.

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.

Guide to Calculating the Kc

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?

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 0.45 M N2O4 Kc 0.31 M NO2 Equation N2O4(g) 2NO2(g)

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.

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

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 1.2 M H2, 1.2 M I2, Kc 0.35 M HI Equation H2(g) + I2(g) 2HI(g)

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.

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.