Equilibrium constants are crucial in chemistry, providing a quantitative measure of reaction equilibrium. They indicate relative concentrations of reactants and products, predict reaction directions, and enable calculations of equilibrium concentrations or pressures.

Calculating equilibrium constants involves using the law of mass action and balanced chemical equations. The reaction quotient Q helps determine reaction direction by comparing it to K. Applications include solubility calculations, pH determination, and industrial process optimization.

Equilibrium Constants

Significance of equilibrium constants

• Equilibrium constants provide a quantitative measure of the position of equilibrium in a reversible chemical reaction
• Indicate the relative concentrations of reactants and products at equilibrium (acetic acid and acetate ion in a buffer solution)
• Allow prediction of the direction of a reaction based on initial concentrations or pressures (formation of ammonia from nitrogen and hydrogen gases)
• Enable calculation of equilibrium concentrations or pressures when initial conditions are known (solubility of a sparingly soluble salt)
• Facilitate comparison of the extent of different reactions under similar conditions (formation of nitrogen oxides at high temperatures)

Calculation of equilibrium constants

• Equilibrium constant expressions are derived from the law of mass action and depend on the balanced chemical equation
• For a general reaction $aA + bB \rightleftharpoons cC + dD$, the concentration-based equilibrium constant is $K_c = \frac{[C]^c[D]^d}{[A]^a[B]^b}$
• The pressure-based equilibrium constant, $K_p$, is used for gaseous equilibria and is expressed as $K_p = \frac{(P_C)^c(P_D)^d}{(P_A)^a(P_B)^b}$
• Equilibrium constants are calculated by substituting equilibrium concentrations or pressures into the appropriate expression (dissociation of dinitrogen tetroxide into nitrogen dioxide)
• $K_c$ and $K_p$ are related by the equation $K_p = K_c(RT)^{\Delta n}$, where $\Delta n$ is the change in moles of gas in the reaction (synthesis of ammonia from nitrogen and hydrogen)

Reaction direction from quotients

• The reaction quotient $Q$ has the same form as the equilibrium constant expression but uses non-equilibrium concentrations or pressures
• Comparing $Q$ to $K$ determines the direction of a reaction to reach equilibrium:
  1. If $Q < K$, the reaction shifts to the right, forming more products (dissolution of a slightly soluble salt)
  2. If $Q > K$, the reaction shifts to the left, forming more reactants (precipitation of a slightly soluble salt)
  3. If $Q = K$, the reaction is at equilibrium, and no net change occurs (saturated solution of a slightly soluble salt)
• Reaction quotients are useful for predicting the direction of a reaction and determining how to alter conditions to favor a desired outcome (optimizing product yield in an industrial process)

Applications in chemical equilibria

• Homogeneous equilibria involve reactants and products in the same phase, typically gaseous or aqueous (ionization of a weak acid in water)
  • The equilibrium constant expression includes concentrations of all species
• Heterogeneous equilibria involve reactants and products in different phases (decomposition of calcium carbonate into calcium oxide and carbon dioxide)
  • Pure solids and liquids are omitted from the equilibrium constant expression as their concentrations are constant
• Problem-solving strategies:
  1. Write a balanced chemical equation for the reaction
  2. Set up the appropriate equilibrium constant expression
  3. Substitute known values and solve for unknown concentrations or pressures
  4. Calculate $Q$ and compare it to $K$ to determine the reaction direction
• Applications include:
  • Calculating solubility of sparingly soluble salts (silver chloride in water)
  • Determining the pH of buffer solutions (acetic acid and sodium acetate)
  • Predicting the formation of precipitates (mixing solutions of lead nitrate and potassium iodide)
  • Optimizing conditions for industrial processes (Haber-Bosch process for ammonia synthesis)