Equilibrium

Equilibrium Constant Calculations

This section covers calculations involving equilibrium constants ( $ K $ ). We’ll break it down by type of equilibrium.

1. $ K_c $ (Equilibrium Constant in terms of concentration):

• Definition: $ K_c = \frac{[Products]]}{[Reactants]]} $ where the bracketed terms represent the equilibrium concentrations raised to the power of their stoichiometric coefficients.
• Example: For the reaction $ aA + bB \rightleftharpoons cC + dD $ , $ K_c = \frac{[C]]^c[D]]^d}{[A]]^a[B]]^b} $
• **ICE Tables:** Use ICE (Initial, Change, Equilibrium tables to organize information and solve for equilibrium concentrations when some are known. (ICE Table Examples]])
• Calculations: Often involve solving quadratic or cubic equations. Approximations can be made if $ K $ is very small or very large. (Approximation Techniques)
• Units: $ K_c $ has units that depend on the stoichiometry of the reaction. Usually omitted for simplicity.

2. $ K_p $ (Equilibrium Constant in terms of partial pressures):

• Definition: Similar to $ K_c $ , but uses partial pressures of gases instead of concentrations. $ K_p = \frac{P_{products}}{P_{reactants}} $
• Relationship to $ K_c $ : $ K_p = K_c(RT)^{\Delta n} $ , where R is the ideal gas constant, T is the temperature in Kelvin, and $ \Delta n $ is the change in the number of moles of gas (moles of gaseous products - moles of gaseous reactants). K_p and K_c Relationship
• Calculations: Similar to $ K_c $ calculations, but using partial pressures.

3. $ K_w $ (Ion-Product Constant for Water):

• Definition: $ K_w = [H_3O^+]][OH^-]] = 1.0 \times 10^{-14} $ at 25°C. (Water Autoionization)
• pH and pOH: Related to $ K_w $ by: $ pH + pOH = 14 $ at 25°C. (pH and pOH Calculations)

4. Heterogeneous Equilibria:

• Definition: Equilibria involving reactants and products in different phases (e.g., solids, liquids, gases).
• ** $ K $ expression:** Pure solids and liquids are excluded from the $ K $ expression because their concentrations are essentially constant. Heterogeneous Equilibria Examples

5. Calculating Equilibrium Concentrations:

• Often requires solving equilibrium expressions which can range from simple algebraic equations to more complex systems requiring numerical methods. Solving Equilibrium Expressions

Linked Notes:

• ICE Table Examples
• Approximation Techniques
• K_p and K_c Relationship
• Water Autoionization
• pH and pOH Calculations
• Heterogeneous Equilibria Examples
• Solving Equilibrium Expressions