Equilibrium Constant & $Q_c$
Master the dynamics of reversible reactions. Understand how to mathematically manipulate $K_c$, predict the exact direction of a reaction using $Q_c$, and evaluate the extent of product formation.
Module Focus
Chemical equilibrium is dynamic. A common trap for students is believing that reactions stop at equilibrium or that a catalyst shifts the equilibrium position. In this module, we will strictly focus on the mathematical properties of the Equilibrium Constant ($K$), how to use the Reaction Quotient ($Q$) as a compass, and the factors that actually dictate the extent of a reaction.
1. The Equilibrium Constant ($K_c$ and $K_p$)
For a general reversible reaction at equilibrium: $aA + bB \rightleftharpoons cC + dD$, the law of mass action defines the equilibrium constant in terms of concentration ($K_c$) or partial pressures ($K_p$).
Concentrations must be at equilibrium. Pure solids and pure liquids are assigned an active mass of 1.
Applicable only for reactions involving gases. Solids/liquids are ignored.
2. Characteristics & Manipulation of $K$ (Highly Tested)
The value of the equilibrium constant $K$ is independent of initial concentrations, pressure, volume, and the presence of a catalyst. It depends ONLY on Temperature. However, changing the stoichiometric representation of the reaction mathematically alters $K$.
Rules for Manipulating $K$
| Manipulation | Reaction Change | New Equilibrium Constant |
|---|---|---|
| Reversing the reaction | Products become reactants | $\frac{1}{K}$ |
| Multiplying by '$n$' | Stoichiometry scaled by $n$ | $K^n$ |
| Dividing by '$n$' | Stoichiometry scaled by $1/n$ | $K^{1/n}$ or $\sqrt[n]{K}$ |
| Adding two reactions | Rxn 1 + Rxn 2 = Net Rxn | $K_1 \times K_2$ |
A catalyst increases the rate of both the forward and backward reactions equally by lowering the activation energy.
Fact: A catalyst helps the system achieve equilibrium faster, but it DOES NOT alter the state of equilibrium, nor does it change the value of $K_c$ or $K_p$.
3. Predicting the Direction: Reaction Quotient ($Q_c$)
The Reaction Quotient ($Q_c$) has the exact same mathematical formula as $K_c$, but the concentrations used are at any given moment, not necessarily at equilibrium. Comparing $Q_c$ to $K_c$ acts as a compass to predict which way the reaction will shift to reach equilibrium.
The ratio of products to reactants is too low.
The system is perfectly balanced.
The ratio of products to reactants is too high.
4. Predicting the Extent of Reaction
The numerical value of the equilibrium constant indicates the extent to which the reactants are converted into products before equilibrium is reached.
-
$\mathbf{K > 10^3}$
Products Strongly Favored: The forward reaction proceeds almost to completion. Very little reactant remains at equilibrium.
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$\mathbf{K < 10^{-3}}$
Reactants Strongly Favored: The reaction rarely proceeds in the forward direction. Very little product is formed.
-
$10^{-3} \mathbf{\le K \le} 10^3$
Balanced Mixture: Appreciable concentrations of both reactants and products are present at equilibrium.
NEET Grand Test: Equilibrium Constants
15 High-Order Thinking Questions testing $K_c$ manipulation, $Q_c$ compass, and catalyst traps.
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