Chemical Equilibrium: Principles, Calculations, and Le Châtelier’s Principle

Chemical Equilibrium

Dynamic Equilibrium Basics

Chemical equilibrium occurs in reversible reactions when the rates of the forward and reverse reactions become equal. At this point, the concentrations of all reactants and products remain constant, although the reactions continue at the molecular level.

• Dynamic equilibrium: The state where the forward and reverse reaction rates are equal, and concentrations of all species remain unchanged over time.

• Equilibrium does not mean equal concentrations of reactants and products; it depends on the reaction's favorability.

• As a reaction proceeds, reactant concentrations decrease and product concentrations increase, causing the forward rate to decrease and the reverse rate to increase until equilibrium is reached.

Equilibrium Constant (K)

The equilibrium constant quantifies the ratio of product and reactant concentrations at equilibrium, as described by the law of mass action.

• For a general reaction: $aA + bB \rightleftharpoons cC + dD$

• The equilibrium constant expression is: $K_c = \frac{[C]^c[D]^d}{[A]^a[B]^b}$

• Magnitude of K:

  • $K \gg 1$: Product-favored (mostly products at equilibrium)

  • $K \ll 1$: Reactant-favored (mostly reactants at equilibrium)

  • $10^{-3} < K < 10^{3}$: Significant amounts of both reactants and products

• Kinetics connection: At equilibrium, $k_f[A] = k_r[B]$ for $A \rightleftharpoons B$, so $K_c = \frac{k_f}{k_r}$

Example: For $N_2 + 3H_2 \rightleftharpoons 2NH_3$, $K_c = \frac{[NH_3]^2}{[N_2][H_2]^3}$

Manipulating Chemical Equations and K

The value of the equilibrium constant changes in predictable ways when the chemical equation is manipulated.

• Reversing the equation: $K_{reverse} = \frac{1}{K_{forward}}$

• Multiplying the equation by n: $K_{new} = (K_{original})^n$

• Adding reactions: When reactions are added, their equilibrium constants are multiplied: $K_{overall} = K_1 \times K_2 \times \ldots$

Example:

• Given $2NOBr \rightleftharpoons 2NO + Br_2$, $K_1 = 0.014$

• $Br_2 + Cl_2 \rightleftharpoons 2BrCl$, $K_2 = 7.2$

• Net: $2NOBr + Cl_2 \rightleftharpoons 2NO + 2BrCl$, $K_3 = 0.014 \times 7.2 = 0.10$

Kc, Kp, and Heterogeneous Equilibria

Equilibrium constants can be expressed in terms of concentrations ($K_c$) or partial pressures ($K_p$), and special rules apply for reactions involving solids and liquids.

• $K_c$: Uses molar concentrations (M)

• $K_p$: Uses partial pressures (atm)

• Relationship: $K_p = K_c(RT)^{\Delta n}$, where $\Delta n$ = (moles of gaseous products) − (moles of gaseous reactants)

• If $\Delta n = 0$, then $K_p = K_c$

• Heterogeneous equilibria: Only include (aq) and (g) species in $K$; omit pure solids (s) and pure liquids (l)

Example: For $PbCl_2(s) \rightleftharpoons Pb^{2+}(aq) + 2Cl^-(aq)$, $K_c = [Pb^{2+}][Cl^-]^2$

• Key properties of K:

  • Always products over reactants, using equilibrium concentrations

  • Exponents are stoichiometric coefficients

  • Unitless (relative to 1 M, 1 atm)

  • Depends on reaction and temperature; catalysts do not affect K

ICE Tables and Calculating K or Equilibrium Concentrations

ICE tables (Initial, Change, Equilibrium) are systematic tools for solving equilibrium problems, either to find K or unknown concentrations.

• To find K from equilibrium data:

  1. Set up an ICE table with initial concentrations

  2. Use known equilibrium data for one species to determine its change

  3. Apply stoichiometry to find changes for other species

  4. Calculate equilibrium concentrations and substitute into the K expression

• To find equilibrium concentrations given K:

  1. Set up an ICE table with initial concentrations

  2. Use the reaction quotient Q to determine the direction of shift

  3. Represent changes as ±x times stoichiometric coefficients

  4. Write equilibrium expressions in terms of x and substitute into the K expression

  5. Solve for x (may require quadratic equation or approximation)

  6. Small x approximation: If $\frac{x}{[initial]} \times 100\% < 5\%$, ignoring x in the denominator is valid

Example: For $H_2 + I_2 \rightleftharpoons 2HI$, given initial [H2], [I2], and equilibrium [HI], use stoichiometry to find all equilibrium concentrations and calculate $K_c$.

Reaction Quotient (Q) and Direction of Shift

The reaction quotient Q has the same form as K but uses current (not necessarily equilibrium) concentrations or pressures. Comparing Q to K predicts the direction the reaction will shift to reach equilibrium.

• For $aA + bB \rightleftharpoons cC + dD$:

• $Q_c = \frac{[C]^c[D]^d}{[A]^a[B]^b}$ (using current concentrations)

• $Q_p$ uses partial pressures in the same way

• Comparing Q and K:

  • $Q > K$: Too much product; reaction shifts left (reverse) to form more reactant

  • $Q < K$: Too much reactant; reaction shifts right (forward) to form more product

  • $Q = K$: System is at equilibrium

Le Châtelier’s Principle

Le Châtelier’s Principle predicts how a system at equilibrium responds to disturbances in concentration, pressure/volume, or temperature. The system shifts to counteract the disturbance and restore equilibrium.

a) Concentration Changes

• Adding reactant: Shifts right (toward products) to consume some reactant

• Removing reactant: Shifts left (toward reactants) to replace it

• K remains unchanged (unless temperature changes)

b) Volume / Pressure Changes (Gases)

• Decrease volume (increase pressure): Shifts toward side with fewer moles of gas

• Increase volume (decrease pressure): Shifts toward side with more moles of gas

• Example: For $CO + 3H_2 \rightleftharpoons CH_4 + H_2O$, decreasing volume shifts right (from 4 to 2 moles of gas)

c) Temperature Changes

• Treat heat as a reactant (endothermic, $\Delta H > 0$) or product (exothermic, $\Delta H < 0$)

• Exothermic reactions ($\Delta H < 0$):

  • Increase T (add heat): Shifts left (away from heat), K decreases

  • Decrease T (remove heat): Shifts right, K increases

• Endothermic reactions ($\Delta H > 0$):

  • Increase T (add heat): Shifts right (toward heat), K increases

  • Decrease T (remove heat): Shifts left, K decreases

Summary Table: Effects on Equilibrium

Disturbance	System Response	Effect on K
Add reactant	Shifts right (forms more product)	No change
Remove reactant	Shifts left (forms more reactant)	No change
Decrease volume (gases)	Shifts to side with fewer gas moles	No change
Increase temperature (exothermic)	Shifts left (away from heat)	K decreases
Increase temperature (endothermic)	Shifts right (toward heat)	K increases

Additional info: The above notes expand on the original outline by providing definitions, stepwise procedures for ICE tables, and a summary table for Le Châtelier’s Principle. All equations are provided in LaTeX format as required for academic clarity.