The Equilibrium Law and Stoichiometry
The equilibrium law describes how the equilibrium constant \(K_{\text{c}}\) is determined from reaction stoichiometry and equilibrium concentrations. The reaction quotient \(Q\) determines the direction of spontaneous shift toward equilibrium.
The Kc Expression
For a general homogeneous reaction:
Formulating Equilibrium Law Expressions
- Products on top, reactants on bottom: Concentrations are multiplied, never added.
- Coefficients become exponents: For \(2A + B \rightleftharpoons 3C\), \([A]^2\) and \([C]^3\).
- Reaction quotient \(Q\): If \(Q < K\), reaction shifts right; if \(Q > K\), reaction shifts left; if \(Q = K\), system is at equilibrium.
What Does Kc Tell Us?
| Value of Kc | Position of Equilibrium | Interpretation |
|---|---|---|
| \(K \gg 1\) | Far to the right | Products strongly favoured; reaction almost goes to completion |
| \(K \approx 1\) | Balanced | Significant amounts of both reactants and products |
| \(K \ll 1\) | Far to the left | Reactants strongly favoured; reaction hardly proceeds |
The Reaction Quotient Q
Q is calculated using the same expression as K, but with concentrations at any point in time (not necessarily at equilibrium).
Comparing Q and K
Worked Example: ICE Table
ICE Table Equilibrium Calculation
Problem: 0.100 mol of ethyl ethanoate is added to 0.100 mol of water (total volume = 1 dm³). At equilibrium, 0.0654 mol of water remains. Calculate Kc.
\(\text{CH}_3\text{COOC}_2\text{H}_5 + \text{H}_2\text{O} \rightleftharpoons \text{CH}_3\text{COOH} + \text{C}_2\text{H}_5\text{OH}\)
| Ester | H₂O | Acid | Alcohol | |
|---|---|---|---|---|
| I | 0.100 | 0.100 | 0 | 0 |
| C | −0.0346 | −0.0346 | +0.0346 | +0.0346 |
| E | 0.0654 | 0.0654 | 0.0346 | 0.0346 |
\(K_c = \frac{(0.0346)(0.0346)}{(0.0654)(0.0654)} = \frac{0.001197}{0.004277} = \textbf{0.280}\)
Approximations and Square Brackets in Kc Expressions
Always use square brackets [ ] denoting molar concentration. In ICE calculations where \(K < 10^{-3}\), you may assume \(x \ll [ ext{initial}]\), but always verify your approximation yields \(< 5\%\) error.
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