📚Study Guide: Equilibrium
Unit 7: Equilibrium
Chemical equilibrium is a dynamic state where the forward and reverse reaction rates are equal, resulting in constant concentrations of reactants and products. This unit requires students to understand the equilibrium constant expression (Kc and Kp), how to calculate K from initial and equilibrium concentrations, and how to use the reaction quotient (Q) to predict the direction of reaction shift. Le Chatelier's Principle--that a system at equilibrium will shift to counteract any imposed change--is one of the most important concepts in chemistry. Students must apply it to changes in concentration, pressure (for gaseous systems), volume, temperature, and the addition of a catalyst. The relationship between delta G degrees and K (delta G degrees = -R T ln K) connects thermodynamics to equilibrium. The AP exam extensively tests equilibrium calculations, particularly ICE tables (Initial, Change, Equilibrium) for weak acid/base dissociation and solubility product (Ksp) problems. Understanding how to calculate Kp from Kc (Kp = Kc (R T)^delta n) and how to manipulate equilibrium constants for combined reactions is also critical. Students must also be comfortable with approximations such as assuming x is small relative to initial concentrations when K is very small.
Key Concepts
- Equilibrium Constant (K): K = [products]^coefficients / [reactants]^coefficients, with each concentration raised to its stoichiometric coefficient. Pure solids and liquids are omitted. K is temperature-dependent only.
- Reaction Quotient (Q): Calculated using initial concentrations in the same form as K. If Q < K, reaction proceeds forward. If Q > K, reaction proceeds reverse. If Q = K, system is at equilibrium.
- Le Chatelier's Principle: If a dynamic equilibrium is disturbed by changing conditions (concentration, pressure, temperature), the system adjusts to minimize the disturbance. Adding a catalyst speeds up both forward and reverse rates equally, so it does not shift equilibrium.
- ICE Tables: A systematic method for calculating equilibrium concentrations: set up Initial concentrations, determine Change in terms of x, and write Equilibrium expressions. Solve for x using K expression.
- Kp and Kc Relationship: Kp = Kc (R T)^delta n, where delta n = moles of gaseous products - moles of gaseous reactants. R = 0.0821 L atm/(mol K).
- Combining Equilibrium Constants: If a reaction is reversed, K' = 1/K. If multiplied by a factor n, K' = K^n. If two reactions are added, K_overall = K1 x K2.
Vocabulary
- Dynamic Equilibrium: A state in which the rate of the forward reaction equals the rate of the reverse reaction, so concentrations of reactants and products remain constant over time.
- Homogeneous Equilibrium: All reactants and products are in the same phase (typically all gases or all aqueous).
- Heterogeneous Equilibrium: Reactants and products are in different phases; pure solids and liquids are excluded from the equilibrium expression.
- Reaction Quotient (Q): A ratio of product concentrations to reactant concentrations at any point in time, used to determine the direction a reaction must proceed to reach equilibrium.
- Equilibrium Shift: A change in the concentrations of reactants and products as the system responds to a disturbance and re-establishes equilibrium.
- ICE Table: A structured method (Initial, Change, Equilibrium) used to calculate the concentrations of species at equilibrium given initial conditions and K.
Essential Formulas
- K = [products] / [reactants] (raised to stoichiometric coefficients)
- Q = same form as K but with initial concentrations
- Kp = Kc (R T)^delta n
- delta G degrees = -R T ln K
- R = 0.0821 L atm/(mol K) = 8.314 J/(mol K)
Common Mistakes
- Including Solids and Liquids in K: Pure solids and pure liquids have constant activity (approximately 1) and are omitted from equilibrium expressions.
- Using Initial Concentrations Instead of Equilibrium: K must be calculated using equilibrium concentrations, not initial concentrations.
- Confusing Kp and Kc: Use Kp when partial pressures are given; use Kc when molar concentrations are given. Convert between them using Kp = Kc (R T)^delta n.
- Adding Catalysts Shift Equilibrium: Catalysts speed up both forward and reverse reactions equally. They help the system reach equilibrium faster but do NOT change the equilibrium position or K.
AP Exam Strategies
- Set Up ICE Tables Clearly: Label rows I, C, E and columns for each reactant/product. Express change in terms of x using stoichiometric ratios.
- Use the 5% Rule: If K is small and the initial concentration is large, assume x is negligible compared to the initial concentration. Check that x / [initial] < 0.05.
- State Le Chatelier's Principle Explicitly: When predicting shifts, say "According to Le Chatelier's Principle, increasing [X] causes the system to shift toward products to consume the added X."
- Track Stoichiometry in Combined Reactions: When adding reactions, multiply K values. When reversing, take the reciprocal. When scaling by n, raise K to the nth power.
Real-World Applications
- Haber-Bosch Process Optimization: High pressure and moderate temperature are used to maximize ammonia yield according to Le Chatelier's principle, balancing thermodynamic favorability with kinetic rate.
- Blood pH Buffering: The bicarbonate buffer system (H2CO3 / HCO3-) maintains blood pH near 7.4 by shifting equilibrium to absorb or release H+.
- Kidney Stone Formation: Solubility product (Ksp) governs the precipitation of calcium oxalate and calcium phosphate in kidneys; hydration and dietary changes shift equilibrium toward dissolution.