Chemical Equilibrium Notes

Chemical Equilibrium

• Chemical equilibrium is achieved when the forward and reverse reactions occur at the same rate, resulting in constant reactant and product concentrations.

• Equilibrium applies to reaction extent, indicating product concentration after unlimited time or when no macroscopic change occurs.

• Many reactions reach chemical equilibrium, a dynamic state where reactant and product concentrations remain constant.

• Equilibrium equations use double arrows to show forward and reverse reactions.

How Chemical Reactions Occur

• Molecules must collide with enough energy and correct orientation for a reaction to occur via the transition state.

• Reaction Rates Affected By:

  • Higher temperatures: Higher speeds, more high-energy collisions, more bond breaking, faster reaction

  • Catalysts: Lower activation energy, less energy needed.

Equilibrium Constant

• For a reaction $aA + bB \rightleftharpoons cC + dD$, the equilibrium expression is: $K_{eq} = \frac{{\left[ C \right]^c \left[ D \right]^d}}{{\left[ A \right]^a \left[ B \right]^b}}$

• $K_{eq}$ is the equilibrium constant.

• $K_{eq}$ reflects the extent to which reactants or products dominate at equilibrium; it remains the same for a given temperature, regardless of initial amounts and has no units.

Heterogeneous Equilibria

• Homogeneous equilibria: involve one state.

• Heterogeneous equilibria: involve more than one state.

• Solids and pure liquids have constant concentrations, thus they don't affect equilibria and should be omitted from the $K_{eq}$ expression.

• Example: $PCl<em>5(s) \rightleftharpoons PCl</em>3(l) + Cl<em>2(g)$, $K</em>{eq} = [Cl_2]$

Le Châtelier’s Principle

• If a system at equilibrium is disturbed by changes in temperature, pressure, or concentration, it will shift to counteract the disturbance.

• Changes in Concentration:

  • Adding reactants shifts equilibrium to the product side.

  • Adding products shifts equilibrium to the reactant side.

  • Removing reactants shifts equilibrium to the reactant side.

  • Removing products shifts equilibrium to the product side.

• Changes in Volume:

  • Reducing volume (increasing pressure) shifts equilibrium towards fewer gas molecules.

  • Increasing volume (decreasing pressure) shifts equilibrium towards more gas molecules.

• Changes in Temperature:

  • Exothermic reactions (energy as a product): Adding energy shifts equilibrium to reactants, removing energy shifts it to products.

  • Endothermic reactions (energy as a reactant): Adding energy shifts equilibrium to products, removing energy shifts it to reactants.

Haber-Bosch Process

• Transformation of atmospheric nitrogen and hydrogen into ammonia for fertilizers.

• If $H<em>2$ is added to the system, $N</em>2$ will be consumed and more $NH_3$ will form.

Catalyst

• Catalysts increase both forward and reverse reaction rates, achieving equilibrium faster without altering the equilibrium composition.

• Disturbance Net Direction of Reaction Effect on Value of K

• Concentration

• Increase [reactant] Toward formation of product None

• Decrease [reactant] Toward formation of reactant None

• Increase [product] Toward formation of reactant None

• Decrease [product] Toward formation of product None

• Pressure

• Increase P (decrease V) Toward formation of fewer moles of gas None

• Decrease P (increase V) Toward formation of more moles of gas None

• Increase P (add inert gas, no change in V) None; concentrations unchanged None

• Temperature

• Increase T Toward absorption of heat Increases if ΔH{rxn} > 0 Decreases if ΔH{rxn} < 0

• Decrease T Toward release of heat Increases if ΔH{rxn} < 0 Decreases if ΔH{rxn} > 0

• Catalyst added None; forward and reverse rates increase equally equilibrium attained sooner; None

Applications Involving the Equilibrium Constant

• K_{eq} >> 1: product-favored

• K_{eq} << 1: reactant-favored

• Size of $K_{eq}$ and time needed to reach equilibrium aren't directly related

Calculating Equilibrium Concentrations

• Using equilibrium expressions to calculate unknown concentrations.

• Example: For $PCl<em>5(g) \rightleftharpoons PCl</em>3(g) + Cl<em>2(g)$, $K</em>{eq} = 0.0896$, solve for $[Cl_2]$ given other concentrations.

Solubility Equilibria

• Insoluble ionic compounds dissolve slightly in water, producing a small number of ions.

• Solid reactants are not included in $K_{sp}$ expressions.

• Solubility Product Constant ($K_{sp}$): Equilibrium expression for the dissolution of an ionic compound.

  • Example: $AgI(s) \rightleftharpoons Ag^+(aq) + I^-(aq)$, $K_{sp} = [Ag^+][I^-]$

• Molar solubility: Used to determine molar concentration of ions in solution (mol/L).