Equilibrium Constants Comparison (Kc, Kp, Ksp, Ka, Kb, Kw) Cheat Sheet

A printable reference covering Kc, Kp, Ksp, Ka, Kb, Kw, reaction quotients, acid-base equilibria, and solubility products for grades 11-12.

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Equilibrium constants describe how far a reversible chemical process goes toward products under a given set of conditions. This cheat sheet compares $K_c$ , $K_p$ , $K_{sp}$ , $K_a$ , $K_b$ , and $K_w$ so students can choose the correct expression quickly. It is useful for solving equilibrium, gas reaction, solubility, acid-base, and pH problems in chemistry. Clear comparisons help prevent mixing up similar constants that are used in different contexts. The main idea is that each equilibrium constant is a ratio of product activities to reactant activities at equilibrium, with each term raised to its coefficient. Pure solids and pure liquids are left out of equilibrium expressions. For gases, $K_p$ uses partial pressures, while $K_c$ uses molar concentrations and connects through $K_p=K_c(RT)^{\Delta n}$ . Acid-base constants connect through $K_aK_b=K_w$ , which is especially important for conjugate acid-base pairs.

Key Facts

For $aA+bB\rightleftharpoons cC+dD$ , the concentration equilibrium constant is $K_c=\frac{[C]^c[D]^d}{[A]^a[B]^b}$ .
For gas equilibria, the pressure equilibrium constant is $K_p=\frac{(P_C)^c(P_D)^d}{(P_A)^a(P_B)^b}$ using equilibrium partial pressures.
The relationship between gas constants is $K_p=K_c(RT)^{\Delta n}$ , where $\Delta n=\text{moles of gaseous products}-\text{moles of gaseous reactants}$ .
For a sparingly soluble salt $M_aX_b(s)\rightleftharpoons aM^{b+}+bX^{a-}$ , the solubility product is $K_{sp}=[M^{b+}]^a[X^{a-}]^b$ .
For a weak acid $HA+H_2O\rightleftharpoons H_3O^++A^-$ , the acid dissociation constant is $K_a=\frac{[H_3O^+][A^-]}{[HA]}$ .
For a weak base $B+H_2O\rightleftharpoons BH^++OH^-$ , the base dissociation constant is $K_b=\frac{[BH^+][OH^-]}{[B]}$ .
At $25^\circ\text{C}$ , water has $K_w=[H_3O^+][OH^-]=1.0\times10^{-14}$ .
For a conjugate acid-base pair at $25^\circ\text{C}$ , $K_aK_b=K_w=1.0\times10^{-14}$ .

Vocabulary

Equilibrium constant: A value that compares products to reactants at equilibrium for a specific reaction at a fixed temperature.
Reaction quotient: A ratio written like the equilibrium expression, called $Q$ , that uses current concentrations or pressures before equilibrium is confirmed.
Partial pressure: The pressure contributed by one gas in a mixture, used in $K_p$ expressions for gas-phase equilibria.
Solubility product: The constant $K_{sp}$ that describes the equilibrium between a slightly soluble ionic solid and its dissolved ions.
Acid dissociation constant: The constant $K_a$ that measures how much a weak acid ionizes in water.
Ion product of water: The constant $K_w=[H_3O^+][OH^-]$ that links hydronium and hydroxide concentrations in water.

Common Mistakes to Avoid

Including pure solids or pure liquids in the expression is wrong because their activities are treated as constant and are not written in $K_c$ , $K_p$ , $K_{sp}$ , $K_a$ , or $K_b$ expressions.
Using initial concentrations in $K$ is wrong because equilibrium constants must use equilibrium concentrations or pressures, while initial or current values belong in $Q$ .
Forgetting coefficients as exponents is wrong because a balanced equation such as $2NO_2\rightleftharpoons N_2O_4$ gives $K_c=\frac{[N_2O_4]}{[NO_2]^2}$ , not $\frac{[N_2O_4]}{[NO_2]}$ .
Using $K_p=K_c(RT)^{\Delta n}$ with the wrong $\Delta n$ is wrong because $\Delta n$ counts only gaseous moles, not solids, liquids, or aqueous species.
Assuming $K_a$ and $K_b$ are equal for a conjugate pair is wrong because they satisfy $K_aK_b=K_w$ , so a stronger acid has a weaker conjugate base.

Practice Questions

1 For $N_2(g)+3H_2(g)\rightleftharpoons2NH_3(g)$ , write the expressions for $K_c$ and $K_p$ , then find $\Delta n$ for the relationship $K_p=K_c(RT)^{\Delta n}$ .
2 At equilibrium for $H_2(g)+I_2(g)\rightleftharpoons2HI(g)$ , $[H_2]=0.20\,\text{M}$ , $[I_2]=0.30\,\text{M}$ , and $[HI]=1.20\,\text{M}$ . Calculate $K_c$ .
3 A weak acid has $K_a=1.8\times10^{-5}$ at $25^\circ\text{C}$ . Use $K_aK_b=K_w$ to calculate $K_b$ for its conjugate base.
4 Explain why $CaCO_3(s)$ is not included in the $K_{sp}$ expression for $CaCO_3(s)\rightleftharpoons Ca^{2+}(aq)+CO_3^{2-}(aq)$ , but the ion concentrations are included.

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