Key Concepts of Equilibrium Constants

Why This Matters

Equilibrium constants are the quantitative backbone of chemical equilibrium—they tell you how far a reaction goes, which direction it favors, and how it responds to change. In Honors Chemistry, you're being tested on your ability to write equilibrium expressions, predict reaction direction using Q vs. K, and calculate unknown concentrations. These skills connect directly to thermodynamics (through Gibbs free energy) and reaction kinetics, making equilibrium one of the most interconnected topics you'll encounter.

Understanding equilibrium constants means more than plugging numbers into formulas. You need to recognize why K changes with temperature, how to set up expressions for different reaction types, and what it means when Q doesn't equal K. Don't just memorize the equations—know what each concept tells you about molecular behavior and reaction spontaneity. Master these principles, and you'll be ready for any equilibrium problem the exam throws at you.

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Defining and Interpreting K

The equilibrium constant quantifies where a reaction "settles" when forward and reverse rates become equal. The magnitude of K reveals whether products or reactants dominate at equilibrium.

Definition of Equilibrium Constant (K)

• K expresses the ratio of product concentrations to reactant concentrations at equilibrium—each raised to the power of its stoichiometric coefficient
• Temperature-specific value means K only applies to one reaction at one temperature; change the temperature, change the K
• Large K (>>1) favors products while small K (<<1) favors reactants—this tells you which side of the equation dominates at equilibrium

Equilibrium Constant Expressions for Homogeneous and Heterogeneous Reactions

• Homogeneous equilibria involve all species in the same phase—every concentration term appears in the K expression
• Heterogeneous equilibria exclude pure solids and liquids from the expression—only gases and aqueous species have variable concentrations that affect equilibrium
• Derived from the balanced equation where coefficients become exponents: for $aA + bB \rightleftharpoons cC + dD$, write $K = \frac{[C]^c[D]^d}{[A]^a[B]^b}$

Units of Equilibrium Constants

• K is dimensionless when total moles of gaseous products equal total moles of gaseous reactants ($\Delta n = 0$)
• Units appear when $\Delta n \neq 0$—they depend on the concentration or pressure units used and the stoichiometry
• AP and standardized exams often treat K as unitless by convention, but understand why units technically arise

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Predicting Reaction Direction

The reaction quotient Q acts as a "snapshot" of where a reaction currently stands, while K represents the destination. Comparing Q to K tells you which way the reaction must shift.

Relationship Between K and Reaction Quotient (Q)

• Q uses the same expression as K but with current (non-equilibrium) concentrations—it's your diagnostic tool for any moment in the reaction
• Q < K means the reaction proceeds forward—there are too few products relative to equilibrium, so more must form
• Q > K means the reaction shifts backward—excess products will convert back to reactants until equilibrium is reached

Le Chatelier's Principle and Its Effect on Equilibrium

• Systems at equilibrium resist disturbance by shifting in the direction that counteracts the stress—this is the qualitative prediction tool
• Concentration changes shift equilibrium toward the side that consumes the added species or replenishes the removed species
• Pressure and temperature changes also cause shifts: increasing pressure favors the side with fewer gas moles; temperature changes actually alter K itself

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Types of Equilibrium Constants

Different reaction conditions call for different forms of K. Choosing between $K_c$ and $K_p$ depends on whether you're working with concentrations or pressures.

$K_c$ vs. $K_p$ (Concentration vs. Pressure-Based Constants)

• $K_c$ uses molar concentrations (M)—the standard choice for reactions in solution or when concentration data is provided
• $K_p$ uses partial pressures (atm or other pressure units)—essential for gas-phase equilibria when pressure data is given
• Connected by $K_p = K_c(RT)^{\Delta n}$ where $\Delta n$ = moles of gaseous products minus moles of gaseous reactants, $R = 0.0821 \frac{L \cdot atm}{mol \cdot K}$

Equilibrium Constants for Reversible Reactions

• Forward and reverse constants are reciprocals: if $K_f$ describes $A \rightleftharpoons B$, then $K_r = \frac{1}{K_f}$ for $B \rightleftharpoons A$
• Multiplying a reaction by a factor n raises K to that power: $K_{new} = K^n$
• Sequential reactions multiply: for $A \rightarrow B \rightarrow C$, the overall $K = K_1 \times K_2$

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Connecting Equilibrium to Thermodynamics

Equilibrium constants don't exist in isolation—they're directly linked to energy changes. The relationship between K and Gibbs free energy reveals whether a reaction is thermodynamically favored.

Relationship Between K and Gibbs Free Energy ($\Delta G$)

• At equilibrium, $\Delta G = 0$—the system has no driving force to shift in either direction
• Standard relationship: $\Delta G° = -RT\ln K$ connects the standard free energy change to the equilibrium constant at temperature T
• Negative $\Delta G°$ means K > 1 (products favored); positive $\Delta G°$ means K < 1 (reactants favored)

Temperature Dependence of Equilibrium Constants

• K changes with temperature because equilibrium is a thermodynamic property—this is the one factor that actually changes K's value
• Exothermic reactions ($\Delta H < 0$): increasing temperature decreases K because heat acts like a product
• Endothermic reactions ($\Delta H > 0$): increasing temperature increases K because heat acts like a reactant—the van 't Hoff equation quantifies this relationship

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Calculating Equilibrium Concentrations

Setting up and solving equilibrium problems requires systematic organization. The ICE table method transforms word problems into solvable algebra.

Calculation of Equilibrium Concentrations

• ICE tables organize data: Initial concentrations, Change during reaction (using stoichiometric ratios), and Equilibrium concentrations
• Substitute equilibrium expressions into the K equation and solve for the unknown variable (often called x)
• Stoichiometry is critical—coefficients from the balanced equation determine both the exponents in K and the ratios in your "Change" row

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Quick Reference Table

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Self-Check Questions

1. A reaction has $K = 4.5 \times 10^{-3}$ at 298 K. Without calculating, does this reaction favor products or reactants at equilibrium? What does this tell you about the sign of $\Delta G°$?

2. Compare and contrast $K_c$ and $K_p$: Under what conditions are they numerically equal, and when must you use the conversion equation?

3. For the reaction $2NO_2(g) \rightleftharpoons N_2O_4(g)$ with $\Delta H < 0$, predict how K changes when temperature increases. Which principle helps you answer this?

4. You calculate Q = 15 for a reaction with K = 8. Which direction will the reaction shift, and what will happen to the concentrations of products as equilibrium is established?

5. A heterogeneous equilibrium involves $CaCO_3(s) \rightleftharpoons CaO(s) + CO_2(g)$. Write the equilibrium expression and explain why adding more solid $CaCO_3$ doesn't shift the equilibrium position.