Chemical Equilibrium

Reversible Reactions and Dynamic Equilibrium

• Very few chemical reactions proceed in only one direction (non-reversible).
• Most reactions are reversible to some extent: reactants form products, and products can revert to reactants.
• Equilibrium is reached when the rate of forward and reverse reactions are equal, and reactant/product concentrations remain constant.
  • Dynamic equilibrium means that the forward and reverse reactions are still occurring, but there is no net change in concentration of reactants or products.

Characteristics of Equilibrium State

• Closed system.
  • No exchange of matter with the surroundings.
• Rate of forward reaction equals the rate of reverse reaction.
• Equilibrium can be approached from either direction.
• Concentrations of reactants and products, pressure, and colors are constant.
  • Macroscopic properties are constant, even though the system is dynamic on a molecular level.

The Equilibrium Law

• For any equilibrium at a given temperature, the ratio of products to reactants, each raised to the power of their coefficients in the balanced equation, is a constant (Kc).
• $aA(aq) + bB(aq) ⇌ cC(aq) + dD(aq)$
• $𝐾c = \frac{[C]^c[D]^d}{[A]^a[B]^b}$
  • [A], [B], [C], and [D] are the equilibrium concentrations of reactants and products in mol/L (molarity).
  • a, b, c, and d are the stoichiometric coefficients for the balanced reaction.
• The unit of Kc varies from one equilibrium to another
• Equilibrium expression in terms of partial pressure:
• $𝐾p = \frac{(PC)^c(PD)^d}{(PA)^a(PB)^b}$
  • PA, PB, PC, and PD are the equilibrium partial pressures of reactants and products.
• Kp indicates pressure, atm or kPa
• For the reverse reaction:
  • $K1 = \frac{1}{K_{-1}}$

Homogeneous and Heterogeneous Equilibrium

• Homogeneous Equilibrium: All reacting species are in the same phase.
  • Example: $N<em>2(g) + 3H</em>2(g) ⇌ 2NH_3(g)$
• Heterogeneous Equilibrium: Reactants and products are in different phases; "concentration" is an intrinsic properties.
  • Example: $CaCO<em>3(s) ⇌ CaO(s) + CO</em>2(g)$
• $𝐾p = 𝐾c(RT)^{Δn}$, where $Δn$ is moles of gaseous products - moles of gaseous reactants.
  • R is the ideal gas constant (0.0821 L atm / (mol K) or 8.314 J / (mol K)).
  • T is the temperature in Kelvin.
• ICE table is used to calculate concentrations.
  • ICE stands for Initial, Change, Equilibrium.
  • Used to determine equilibrium concentrations when initial concentrations and the equilibrium constant are known.

Equilibrium Constant and Position of Equilibrium

• If product concentrations are low relative to reactants, equilibrium lies to the left, and Kc/Kp is small.
  • Kc/Kp < 1 indicates that reactants are favored at equilibrium.
• If product concentrations are high relative to reactants, equilibrium lies to the right, and Kc/Kp is large.
  • Kc/Kp > 1 indicates that products are favored at equilibrium.

Reaction Quotient and Equilibrium

• Reaction quotient (Q) is calculated with initial concentrations to determine if a system is at equilibrium.
  • Q is calculated using the same formula as Kc, but with non-equilibrium concentrations.
• Q = Kc: system is in equilibrium.
• Q < Kc: reaction shifts right to reach equilibrium.
• Q > Kc: reaction shifts left to reach equilibrium.

Le Chatelier’s Principle

• If external conditions change, equilibrium shifts to maintain the equilibrium constant.
  • System adjusts to minimize the effect of the stress.
• Adjustments include changes in the net direction of the reaction.
• External stresses: catalyst presence, concentration changes, pressure changes, temperature changes.

Factors Affecting Chemical Equilibrium

• Catalyst: increases reaction rate, reduces time to reach equilibrium, no effect on Kc or Kp.
  • Catalysts lower the activation energy for both forward and reverse reactions.
• Concentration: adding reactants shifts the reaction towards products, and vice versa.
  • Removing products shifts the reaction towards products, and vice versa.
• Pressure: affects equilibrium when there's an overall volume change.
  • Changing the pressure by adding an inert gas has no effect on the equilibrium position.
  • Only changes in pressure due to changes in volume or addition of gaseous reactants or products affect equilibrium.
  • Increasing pressure shifts equilibrium to the side with fewer gas moles.
• Temperature: increasing shifts equilibrium in the endothermic direction.
  • Decreasing shifts equilibrium in the exothermic direction.

Effect of Temperature on Equilibrium

• The van’t Hoff equation shows the effect of temperature on the equilibrium constant, KC
• $lnK_c = -\frac{ΔH}{RT} + C$
  • ΔH is the standard enthalpy change of the reaction.
  • R is the ideal gas constant.
  • T is the temperature in Kelvin.
  • C is a constant.
• Exothermic reaction: equilibrium constant decreases with increasing temperature
  • Increasing temperature favors the reverse reaction.
• Endothermic reaction: equilibrium constant increases with increasing temperature
  • Increasing temperature favors the forward reaction.

Chemical Equilibrium in the Industry

• Optimal conditions are NOT necessarily the conditions that will give the maximum amount of products, but the most cost-effective
  • Balancing yield, rate, and cost is crucial in industrial processes.
• Haber Process: produces ammonia, $N<em>2(g) + 3H</em>2(g) ⇌ 2NH_3(g)$, $ΔH= ‒92 kJmol‒1$
  • High pressure (200 atm) and