AP Chemistry: Dynamic Equilibrium and the Equilibrium Constant (Kc, Kp)

AP Chemistry – Dynamic Equilibrium and the Equilibrium Constant (Kc, Kp)

Dynamic Equilibrium and the Equilibrium Constant (Kc, Kp) – AP Chemistry Study Guide

What This Is

Dynamic equilibrium is the state where the rate of the forward reaction equals the rate of the reverse reaction, so the concentrations of reactants and products stay constant (but not necessarily equal). This concept is essential on the AP exam—it appears in multiple-choice questions, FRQs, and lab-based questions. A real-world example: carbonated soda. When you open a bottle, CO? escapes (forward reaction), but some CO? also dissolves back into the liquid (reverse reaction). At equilibrium, the rate of CO? escaping equals the rate of it dissolving, keeping the fizz level stable (until you open the bottle and disturb it!).

Key Terms & Concepts

• Dynamic Equilibrium: A state where the forward and reverse reaction rates are equal, and concentrations of reactants/products remain constant (but not necessarily equal).
• Equilibrium Constant (Kc): A ratio of product concentrations to reactant concentrations at equilibrium, each raised to the power of their coefficients.
• Formula: Kc = [C]?[D]? / [A]?[B]? (for aA + bB-cC + dD)
• Units: Usually omitted (dimensionless).
• Equilibrium Constant (Kp): Like Kc, but uses partial pressures (for gases) instead of concentrations.
• Formula: Kp = (P_C)?(P_D)? / (P_A)?(P_B)?
• Relationship to Kc: Kp = Kc(RT), where = (moles of gaseous products) – (moles of gaseous reactants).
• Reaction Quotient (Q): The same ratio as K, but calculated at any point in the reaction (not just equilibrium).
• Q < K: Reaction shifts right (toward products).
• Q > K: Reaction shifts left (toward reactants).
• Q = K: System is at equilibrium.
• Le Chatelier’s Principle: If a system at equilibrium is disturbed, it shifts to counteract the disturbance and re-establish equilibrium.
• Disturbances: Changes in concentration, pressure, volume, or temperature.
• Haber Process: Industrial production of ammonia (NH?) from N? and H?. High pressure and temperature are used to shift equilibrium toward NH? (real-world application of Le Chatelier’s Principle).
• ICE Table (Initial-Change-Equilibrium): A method to track concentration changes in a reaction.
• I: Initial concentrations (or pressures).
• C: Change in concentrations (use stoichiometry).
• E: Equilibrium concentrations.
• Homogeneous vs. Heterogeneous Equilibrium:
• Homogeneous: All reactants/products are in the same phase (e.g., all gases).
• Heterogeneous: Reactants/products are in different phases (e.g., solids/liquids excluded from K expressions).
• Solids & Liquids in K Expressions: Pure solids and liquids are omitted from Kc/Kp because their concentrations don’t change.
• Temperature & K: Only temperature changes alter K (not concentration or pressure). For endothermic reactions, K increases with temperature. For exothermic reactions, K decreases with temperature.

Step-by-Step / Process Flow

1. Writing Equilibrium Expressions (Kc or Kp)

1. Write the balanced equation (e.g., N?(g) + 3H?(g)-2NH?(g)).
2. Identify phases (only gases and aqueous solutions go in Kc; only gases in Kp).
3. Write Kc or Kp expression (products over reactants, raised to coefficients).
4. Kc = [NH?]² / ([N?][H?]³)
5. Kp = (P_NH?)² / (P_N? × (P_H?)³)
6. Omit solids/liquids (e.g., if H?O(l) is a reactant, it’s not in K).

2. Solving Equilibrium Problems (ICE Table)

1. Fill in the ICE table with initial concentrations/pressures.
2. Example: For N? + 3H?-2NH?, if [N?]? = 1.0 M, [H?]? = 3.0 M, [NH?]? = 0 M: | | N? | H? | NH? | |-------|-----|------|-----| | I | 1.0 | 3.0 | 0 | | C | -x | -3x | +2x | | E |1.0-x|3.0-3x| 2x |
3. Write the K expression (e.g., Kc = (2x)² / [(1.0-x)(3.0-3x)³]).
4. Solve for x (may require simplifying assumptions or quadratic formula).
5. Check assumptions (if x is <5% of initial concentration, assumption is valid).

3. Predicting Shifts (Le Chatelier’s Principle)

1. Identify the disturbance (e.g., adding reactant, increasing pressure, changing temperature).
2. Determine the direction of shift to counteract the disturbance.
3. Add reactant-shift right (toward products).
4. Increase pressure (decrease volume)-shift to side with fewer gas moles.
5. Increase temperature-shift in endothermic direction (treat heat as a reactant/product).
6. Predict new equilibrium position (but K only changes if temperature changes).

Common Mistakes

• Mistake: Including solids/liquids in K expressions. Correction: Only gases and aqueous solutions appear in Kc/Kp. Solids/liquids have constant concentrations and are omitted.

• Mistake: Confusing Kc and Kp units. Correction: Kc and Kp are unitless (technically, activities are used, but AP ignores this). Just write the ratio.

• Mistake: Assuming K changes with concentration/pressure. Correction: Only temperature changes K. Concentration/pressure shifts the equilibrium position but doesn’t alter K.

• Mistake: Forgetting to raise concentrations to their coefficients in K expressions. Correction: For 2NO?-N?O?, Kc = [N?O?] / [NO?]² (not [NO?]).

• Mistake: Misapplying the quadratic formula in ICE tables. Correction: If K is small (e.g., K < 10), assume x is negligible compared to initial concentrations (e.g., 1.0 - x-1.0).

AP Exam Insights

• FRQs often ask:
• To write K expressions for given reactions.
• To calculate equilibrium concentrations using ICE tables.
• To predict shifts using Le Chatelier’s Principle (especially with temperature changes).
• Multiple-choice traps:
• Kc vs. Kp: Know when to use each (Kp for gases, Kc for solutions).
• Q vs. K: If Q-K, the system isn’t at equilibrium—predict the shift.
• Temperature effects: Remember that K changes with temperature, unlike other disturbances.
• Lab-based questions: May ask about how to measure equilibrium (e.g., spectroscopy, pH) or how to disturb a system (e.g., adding a reactant).

Quick Check Questions

1. Multiple Choice

For the reaction: 2SO?(g) + O?(g)-2SO?(g) (Kc = 4.0 at 25°C), which change will increase the amount of SO? at equilibrium? (A) Adding a catalyst (B) Increasing the volume of the container (C) Adding more O? (D) Increasing the temperature (assuming the reaction is exothermic)

Answer: (C) Adding more O? Explanation: Adding O? shifts the equilibrium right (toward products) to consume the excess reactant. Catalysts (A) don’t affect equilibrium, increasing volume (B) shifts to the side with more gas moles (left), and increasing temperature (D) shifts left for exothermic reactions.

2. Short FRQ

The reaction CO(g) + H?O(g)-CO?(g) + H?(g) has Kc = 5.0 at 800 K. (a) Write the equilibrium expression for Kc. (b) If [CO] = 0.10 M, [H?O] = 0.10 M, [CO?] = 0.20 M, and [H?] = 0.20 M, is the system at equilibrium? If not, which way will it shift?

Answer: (a) Kc = [CO?][H?] / [CO][H?O] (b) Q = (0.20)(0.20) / (0.10)(0.10) = 4.0. Since Q < K (4.0 < 5.0), the system is not at equilibrium and will shift right to reach equilibrium.

Last-Minute Cram Sheet

1. Kc = [products]/[reactants] (coefficients as exponents).
2. Kp = (P_products)/(P_reactants) (only gases).
3. Kp = Kc(RT) ( = moles gas products – moles gas reactants).
4. Q < K-shift right; Q > K-shift left; Q = K-equilibrium.
5. Le Chatelier’s Principle: System shifts to counteract disturbances.
6. Solids/liquids are omitted from K expressions.
7. Only temperature changes K (not concentration/pressure).
8. Endothermic: K-with T; Exothermic: K-with T.
9. ICE tables: I = initial, C = change, E = equilibrium.
10. If K is small, assume x is negligible in ICE tables.