The Equilibrium Constant, Kc

For a generalized reversible reaction: $aA + bB \rightleftharpoons cC + dD$

The $K_c$ expression is written as: $K_c = \frac{[C]^c [D]^d}{[A]^a [B]^b}$

In this formula, the square brackets $[ ]$ represent the equilibrium concentration of each species in $mol \cdot dm^{-3}$.

The stoichiometric coefficients ($a, b, c, d$) from the balanced chemical equation become the exponents for their respective concentrations in the expression.

In a heterogeneous equilibrium, the reactants and products are in different physical states (e.g., solids, liquids, and gases).

Pure solids and pure liquids are omitted from the $K_c$ expression because their concentrations (density divided by molar mass) remain effectively constant regardless of the amount present.

Only species in the aqueous (aq) or gaseous (g) phases are included in the calculation, as their concentrations can vary significantly during the reaction.

The numerical value of $K_c$ indicates the position of equilibrium and the extent to which a reaction proceeds toward products.

If $K_c \gg 1$ (e.g., $10^5$), the equilibrium lies far to the right, meaning the mixture consists almost entirely of products at equilibrium.

If $K_c \ll 1$ (e.g., $10^{-5}$), the equilibrium lies far to the left, meaning the reaction barely proceeds and the mixture is mostly reactants.

If $K_c \approx 1$, the concentrations of reactants and products are comparable at equilibrium.

The value of $K_c$ is constant at a specific temperature. If the temperature changes, the value of $K_c$ will change.

For an exothermic reaction, increasing the temperature decreases $K_c$ as the equilibrium shifts toward the reactants.

For an endothermic reaction, increasing the temperature increases $K_c$ as the equilibrium shifts toward the products.

Changes in concentration, pressure, or the addition of a catalyst do NOT change the value of $K_c$; they only affect the rate at which equilibrium is reached or the temporary position of the system.

Check the Units: Always derive the units for $K_c$ by substituting $(mol \cdot dm^{-3})$ into the expression and canceling terms. Units vary depending on the stoichiometry.

Equilibrium vs. Initial: Ensure you use concentrations at equilibrium, not initial concentrations. If only initial amounts are given, use an ICE table (Initial, Change, Equilibrium) to find the final values.

Balanced Equation: $K_c$ is specific to the balanced equation as written. If the coefficients are doubled, the $K_c$ value is squared; if the reaction is reversed, the new $K_c$ is the reciprocal ($1/K_c$).

Sanity Check: If a reaction is known to be highly favorable, your calculated $K_c$ should be a large number. If it is small, re-check your product/reactant placement.