Law of Chemical Equilibrium — Revision Notes

⚡ 30-Second Revision

Law of Mass Action: — For $aA + bB \rightleftharpoons cC + dD$, Rate $\propto [Reactants]^{coeff}$.
Equilibrium Constant ($K_c$): — $K_c = \frac{[C]^c[D]^d}{[A]^a[B]^b}$ (at equilibrium, in molar concentrations).
Equilibrium Constant ($K_p$): — $K_p = \frac{P_C^c P_D^d}{P_A^a P_B^b}$ (at equilibrium, in partial pressures).
Relation between $K_p$ and $K_c$: — $K_p = K_c (RT)^{Delta n_g}$, where $\Delta n_g = (c+d) - (a+b)$ for gaseous species.
Reaction Quotient ($Q_c$): — $Q_c = \frac{[C]_t^c[D]_t^d}{[A]_t^a[B]_t^b}$ (at any time $t$).
Predicting Reaction Direction: — If $Q < K$, forward; if $Q > K$, reverse; if $Q = K$, equilibrium.
Heterogeneous Equilibria: — Pure solids and liquids are excluded from $K$ expressions.

2-Minute Revision

The Law of Chemical Equilibrium, or Law of Mass Action, quantifies the state of dynamic equilibrium in reversible reactions. At equilibrium, the rates of the forward and reverse reactions are equal, leading to constant (but not necessarily equal) concentrations of reactants and products.

The equilibrium constant, $K_c$ (for concentrations) or $K_p$ (for partial pressures), is a fixed ratio of product to reactant concentrations (or partial pressures), each raised to their stoichiometric coefficients, at a given temperature.

A large $K$ signifies a product-favored equilibrium, while a small $K$ indicates a reactant-favored one. For gaseous reactions, $K_p$ and $K_c$ are related by $K_p = K_c (RT)^{Delta n_g}$, where $Delta n_g$ is the change in moles of gaseous species.

The reaction quotient ($Q$) helps predict the direction of a reaction not at equilibrium: $Q < K$ means forward shift, $Q > K$ means reverse shift, and $Q = K$ means equilibrium. Remember to exclude pure solids and liquids from $K$ expressions for heterogeneous equilibria.

5-Minute Revision

The Law of Chemical Equilibrium is fundamental to understanding reversible reactions. It states that at equilibrium, the ratio of the product of concentrations (or partial pressures) of products to reactants, each raised to their stoichiometric coefficients, is a constant at a given temperature.

This constant is the equilibrium constant, $K_c$ (for molar concentrations) or $K_p$ (for partial pressures). For a general reaction $aA + bB \rightleftharpoons cC + dD$, $K_c = \frac{[C]^c[D]^d}{[A]^a[B]^b}$.

Key Points:

1
Dynamic Nature: — Equilibrium is dynamic; forward and reverse reactions continue at equal rates.
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Temperature Dependence: — $K$ is constant at a given temperature and changes only with temperature.
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Magnitude of K: — Large $K (>10^3)$ means products are favored; small $K (<10^{-3})$ means reactants are favored.
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$K_p$ and $K_c$ Relation: — For gaseous reactions, $K_p = K_c (RT)^{Delta n_g}$, where $Delta n_g = \sum n_{products, gas} - \sum n_{reactants, gas}$. Remember $R = 0.0821,\text{L atm mol}^{-1}\text{K}^{-1}$ and $T$ in Kelvin.
5
Reaction Quotient ($Q$): — Calculated like $K$ but with non-equilibrium concentrations. It predicts reaction direction:

* If $Q < K$: Reaction proceeds forward. * If $Q > K$: Reaction proceeds reverse. * If $Q = K$: System is at equilibrium.

1
Heterogeneous Equilibria: — Pure solids and liquids are excluded from $K$ expressions because their concentrations are constant. For example, for $CaCO_3(s) \rightleftharpoons CaO(s) + CO_2(g)$, $K_p = P_{CO_2}$.

Worked Example: For $N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g)$, if $K_c = 0.10,\text{M}^{-2}$ at $700,\text{K}$. Calculate $K_p$.

$Delta n_g = 2 - (1+3) = -2$.
$K_p = K_c (RT)^{Delta n_g} = 0.10 \times (0.0821 \times 700)^{-2} = 0.10 \times (57.47)^{-2} = 0.10 \times 0.000303 = 3.03 \times 10^{-5},\text{atm}^{-2}$.

Prelims Revision Notes

Definition: — Chemical equilibrium is a dynamic state where forward reaction rate ($R_f$) equals reverse reaction rate ($R_r$). Macroscopic properties (concentrations, pressure) remain constant.
Law of Mass Action: — For $aA + bB \rightleftharpoons cC + dD$, $R_f = k_f[A]^a[B]^b$ and $R_r = k_r[C]^c[D]^d$.
Equilibrium Constant ($K_c$): — $K_c = \frac{k_f}{k_r} = \frac{[C]^c[D]^d}{[A]^a[B]^b}$. Units are $(\text{mol/L})^{Delta n}$.
Equilibrium Constant ($K_p$): — $K_p = \frac{P_C^c P_D^d}{P_A^a P_B^b}$. Units are $(\text{atm})^{Delta n_g}$.
Relationship $K_p$ and $K_c$: — $K_p = K_c (RT)^{Delta n_g}$.

- $\Delta n_g = \sum n_{gaseous,products} - \sum n_{gaseous,reactants}$. - $R = 0.0821,\text{L atm mol}^{-1}\text{K}^{-1}$ (if pressure in atm, volume in L). - $T$ must be in Kelvin. - If $\Delta n_g = 0$, then $K_p = K_c$.

**Significance of $K$:**

- $K > 10^3$: Products favored (reaction goes almost to completion). - $K < 10^{-3}$: Reactants favored (reaction proceeds to a small extent). - $10^{-3} \le K \le 10^3$: Significant amounts of both present.

Reaction Quotient ($Q$): — Same form as $K$ but uses non-equilibrium concentrations/pressures.

- $Q < K$: Net reaction proceeds forward. - $Q > K$: Net reaction proceeds reverse. - $Q = K$: System is at equilibrium.

Heterogeneous Equilibria: — Pure solids and pure liquids are excluded from the $K$ expression because their concentrations are constant. Example: For $C(s) + O_2(g) \rightleftharpoons CO_2(g)$, $K_c = \frac{[CO_2]}{[O_2]}$ and $K_p = \frac{P_{CO_2}}{P_{O_2}}$.
Factors Affecting $K$: — Only temperature. $K$ is independent of initial concentrations, pressure, or catalyst.
Catalyst: — A catalyst speeds up both forward and reverse reactions equally, helping equilibrium to be achieved faster, but it does not change the value of $K$ or the equilibrium composition.

Vyyuha Quick Recall

King Queen Really Think Diamonds Nice Gems: $K_p = K_c (RT)^{Delta n_g}$