Calculating the Equilibrium Constant

For a general reaction $aA + bB \rightleftharpoons cC + dD$, the equilibrium expression for concentration ($K_c$) is written as: $K_c = \frac{[C]^c [D]^d}{[A]^a [B]^b}$ where square brackets denote molarity ($mol/L$).

For gaseous systems, the equilibrium constant can be expressed in terms of partial pressures ($K_p$): $K_p = \frac{(P_C)^c (P_D)^d}{(P_A)^a (P_B)^b}$ where $P$ represents the partial pressure of each gas, typically in atmospheres ($atm$).

In both expressions, the coefficients from the balanced chemical equation become the exponents for the respective species in the ratio.

Pure solids ($s$) and pure liquids ($l$) are never included in the equilibrium expression. Their concentrations are considered constant and are effectively incorporated into the value of $K$ itself.

Only species in the aqueous ($aq$) or gaseous ($g$) phases appear in the expression because their concentrations or pressures can vary significantly.

Although the individual concentrations or pressures used to calculate $K$ have units, the equilibrium constant itself is traditionally reported as a unitless value.

If $K > 1$, the equilibrium mixture contains a higher concentration of products than reactants. The reaction is said to "favor the products" or lie to the right.

If $K < 1$, the equilibrium mixture contains a higher concentration of reactants than products. The reaction is said to "favor the reactants" or lie to the left.

Extremely large values of $K$ (e.g., $> 10^{10}$) suggest the reaction goes essentially to completion, while extremely small values (e.g., $< 10^{-10}$) suggest the reaction barely proceeds at all.

Reversing a Reaction: If a chemical equation is reversed, the new equilibrium constant is the reciprocal of the original ($K_{new} = 1/K_{orig}$).

Scaling Coefficients: If the coefficients of a balanced equation are multiplied by a factor $n$, the equilibrium constant is raised to the power of that factor ($K_{new} = (K_{orig})^n$).

Adding Reactions: When two or more reactions are added together to get a net reaction, the equilibrium constant for the net reaction is the product of the individual constants ($K_{net} = K_1 \times K_2$).

These rules apply equally to $K_c$, $K_p$, and the reaction quotient $Q$.

Check State Symbols: Always look for $(s)$ or $(l)$ in the equation first and cross them out so you don't accidentally include them in your expression.

Notation Matters: Use square brackets $[ ]$ for $K_c$ (concentrations) and parentheses $(P)$ for $K_p$ (pressures). Mixing these notations can lead to lost points on formal assessments.

Temperature Check: If a problem provides $K$ at two different temperatures, remember that you cannot use the $K$ from one temperature to solve for concentrations at the other.

Sanity Check: If $K$ is very small, your equilibrium concentrations for products should be significantly smaller than your starting reactant concentrations.