From grimoire
Calculates equilibrium constants, predicts reaction direction via Q vs K comparison, solves ICE table problems, and applies Le Chatelier's principle.
How this skill is triggered — by the user, by Claude, or both
Slash command
/grimoire:apply-chemical-equilibrium-analysisThe summary Claude sees in its skill listing — used to decide when to auto-load this skill
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.
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.
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.
For any reaction: aA + bB ⇌ cC + dD
Equilibrium constant expression:
Kc = [C]^c [D]^d / [A]^a [B]^b
Rules:
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
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.
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
Predict system response to perturbations:
Note: temperature changes K value itself; other perturbations shift position but not K.
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
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