apply-chemical-equilibrium-analysis

Apply Chemical Equilibrium Analysis

Analyze and predict chemical equilibria by calculating equilibrium constants, determining reaction direction from Q vs K comparison, solving ICE table problems for equilibrium concentrations, and applying Le Chatelier's principle to predict system response to perturbations.

Why This Is Best Practice

Adopted by: Chemical equilibrium analysis is foundational to industrial process optimization (Haber-Bosch for ammonia, Contact process for sulfuric acid), pharmaceutical formulation stability, environmental chemistry (buffering, solubility), and biochemistry (enzyme kinetics, Henderson-Hasselbalch). IUPAC defines equilibrium constants and their thermodynamic basis; NIST maintains the authoritative database of thermodynamic data for equilibrium calculations. Impact: The Haber-Bosch process — which feeds ~50% of Earth's population — was optimized using equilibrium analysis. Fritz Haber's recognition that high pressure favors NH₃ formation (Le Chatelier) while high temperature increases rate (Arrhenius) led to the compromise conditions (200 atm, 450°C) used industrially. Pharmaceutical formulation relies on equilibrium analysis for pH stability, solubility prediction, and buffer design — failures cause drug precipitation, reduced bioavailability, and stability failures.

Steps

1. Write the balanced equilibrium expression

For any reaction: aA + bB ⇌ cC + dD

Equilibrium constant expression:

Kc = [C]^c [D]^d / [A]^a [B]^b

Rules:

• Include only species in solution or gas phase — pure solids and pure liquids omitted (activity = 1)
• For gas-phase equilibria: use partial pressures → Kp
• Relationship: Kp = Kc(RT)^Δn where Δn = moles gas products − moles gas reactants

2. Determine K from thermodynamic data

If K is not tabulated, calculate from standard Gibbs free energy:

ΔG°rxn = Σ ΔGf°(products) − Σ ΔGf°(reactants)
K = e^(−ΔG°rxn / RT)

Where R = 8.314 J/mol·K and T in Kelvin.

Or combine known equilibria:

Hess's law for K: if reaction = reaction 1 + reaction 2:
K = K₁ × K₂
If reaction is reversed: K_new = 1/K_old
If reaction is multiplied by n: K_new = K^n

3. Compare Q to K to predict reaction direction

Reaction quotient Q has the same form as K but uses initial concentrations:

Q < K: reaction proceeds forward (toward products)
Q > K: reaction proceeds reverse (toward reactants)
Q = K: system is at equilibrium

This is the first calculation to perform before setting up an ICE table — it confirms the direction of progress.

4. Solve for equilibrium concentrations using ICE tables

ICE = Initial, Change, Equilibrium

Species	A	B	C	D
Initial	[A]₀	[B]₀	[C]₀	[D]₀
Change	−ax	−bx	+cx	+dx
Equilibrium	[A]₀−ax	[B]₀−bx	[C]₀+cx	[D]₀+dx

Substitute equilibrium row into K expression; solve for x.

Simplification: if K is very small (<10⁻³) and initial concentrations are large, the 5% approximation applies:

Assume x << [A]₀: [A]₀ − ax ≈ [A]₀
Check: x/[A]₀ < 0.05 → approximation valid; if >0.05, solve quadratic exactly

5. Apply Le Chatelier's principle to shift equilibrium

Predict system response to perturbations:

• Increase concentration of reactant: equilibrium shifts right (toward products)
• Increase concentration of product: equilibrium shifts left (toward reactants)
• Increase pressure (gas-phase): shifts toward side with fewer moles of gas
• Increase temperature: shifts toward endothermic direction (increases K for endothermic; decreases K for exothermic)
• Add catalyst: does NOT shift equilibrium; only increases rate of reaching equilibrium

Note: temperature changes K value itself; other perturbations shift position but not K.

6. Apply to common equilibrium types

Acid-base (Ka, Kb):

pH = pKa + log([A⁻]/[HA])  (Henderson-Hasselbalch)
Buffer capacity maximum at pH = pKa ± 1

Solubility (Ksp):

For AB: Ksp = [A⁺][B⁻]
Common ion effect: adding A⁺ decreases solubility of AB (Q > Ksp → precipitation)

Complex formation (Kf):

Large Kf (>10⁶): nearly complete complexation at stoichiometric amounts

Common Mistakes

• Including pure liquids or solids in the K expression: Water (in aqueous solution) and solid precipitates have activity = 1 and are excluded from K.
• Confusing K and Q: K is the equilibrium constant (fixed at given T); Q is calculated from current concentrations and determines direction of progress.
• Not checking the 5% approximation: If x/[A]₀ > 5%, the simplification is invalid and the quadratic must be solved exactly.

When NOT to Use

• Systems far from equilibrium with fast kinetics: kinetics (not thermodynamics) determines the outcome — equilibrium analysis predicts final state but not whether it will be reached in a practical timeframe.