Sign in to save

Bookmark this page so you can find it later.

Sign in to save

Bookmark this page so you can find it later.

Equilibrium constants describe how far a reversible chemical process goes toward products under a given set of conditions. This cheat sheet compares KcK_c, KpK_p, KspK_{sp}, KaK_a, KbK_b, and KwK_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, KpK_p uses partial pressures, while KcK_c uses molar concentrations and connects through Kp=Kc(RT)ΔnK_p=K_c(RT)^{\Delta n}.

Acid-base constants connect through KaKb=KwK_aK_b=K_w, which is especially important for conjugate acid-base pairs.

Key Facts

  • For aA+bBcC+dDaA+bB\rightleftharpoons cC+dD, the concentration equilibrium constant is Kc=[C]c[D]d[A]a[B]bK_c=\frac{[C]^c[D]^d}{[A]^a[B]^b}.
  • For gas equilibria, the pressure equilibrium constant is Kp=(PC)c(PD)d(PA)a(PB)bK_p=\frac{(P_C)^c(P_D)^d}{(P_A)^a(P_B)^b} using equilibrium partial pressures.
  • The relationship between gas constants is Kp=Kc(RT)ΔnK_p=K_c(RT)^{\Delta n}, where Δn=moles of gaseous productsmoles of gaseous reactants\Delta n=\text{moles of gaseous products}-\text{moles of gaseous reactants}.
  • For a sparingly soluble salt MaXb(s)aMb++bXaM_aX_b(s)\rightleftharpoons aM^{b+}+bX^{a-}, the solubility product is Ksp=[Mb+]a[Xa]bK_{sp}=[M^{b+}]^a[X^{a-}]^b.
  • For a weak acid HA+H2OH3O++AHA+H_2O\rightleftharpoons H_3O^++A^-, the acid dissociation constant is Ka=[H3O+][A][HA]K_a=\frac{[H_3O^+][A^-]}{[HA]}.
  • For a weak base B+H2OBH++OHB+H_2O\rightleftharpoons BH^++OH^-, the base dissociation constant is Kb=[BH+][OH][B]K_b=\frac{[BH^+][OH^-]}{[B]}.
  • At 25C25^\circ\text{C}, water has Kw=[H3O+][OH]=1.0×1014K_w=[H_3O^+][OH^-]=1.0\times10^{-14}.
  • For a conjugate acid-base pair at 25C25^\circ\text{C}, KaKb=Kw=1.0×1014K_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 QQ, that uses current concentrations or pressures before equilibrium is confirmed.
Partial pressure
The pressure contributed by one gas in a mixture, used in KpK_p expressions for gas-phase equilibria.
Solubility product
The constant KspK_{sp} that describes the equilibrium between a slightly soluble ionic solid and its dissolved ions.
Acid dissociation constant
The constant KaK_a that measures how much a weak acid ionizes in water.
Ion product of water
The constant Kw=[H3O+][OH]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 KcK_c, KpK_p, KspK_{sp}, KaK_a, or KbK_b expressions.
  • Using initial concentrations in KK is wrong because equilibrium constants must use equilibrium concentrations or pressures, while initial or current values belong in QQ.
  • Forgetting coefficients as exponents is wrong because a balanced equation such as 2NO2N2O42NO_2\rightleftharpoons N_2O_4 gives Kc=[N2O4][NO2]2K_c=\frac{[N_2O_4]}{[NO_2]^2}, not [N2O4][NO2]\frac{[N_2O_4]}{[NO_2]}.
  • Using Kp=Kc(RT)ΔnK_p=K_c(RT)^{\Delta n} with the wrong Δn\Delta n is wrong because Δn\Delta n counts only gaseous moles, not solids, liquids, or aqueous species.
  • Assuming KaK_a and KbK_b are equal for a conjugate pair is wrong because they satisfy KaKb=KwK_aK_b=K_w, so a stronger acid has a weaker conjugate base.

Practice Questions

  1. 1 For N2(g)+3H2(g)2NH3(g)N_2(g)+3H_2(g)\rightleftharpoons2NH_3(g), write the expressions for KcK_c and KpK_p, then find Δn\Delta n for the relationship Kp=Kc(RT)ΔnK_p=K_c(RT)^{\Delta n}.
  2. 2 At equilibrium for H2(g)+I2(g)2HI(g)H_2(g)+I_2(g)\rightleftharpoons2HI(g), [H2]=0.20M[H_2]=0.20\,\text{M}, [I2]=0.30M[I_2]=0.30\,\text{M}, and [HI]=1.20M[HI]=1.20\,\text{M}. Calculate KcK_c.
  3. 3 A weak acid has Ka=1.8×105K_a=1.8\times10^{-5} at 25C25^\circ\text{C}. Use KaKb=KwK_aK_b=K_w to calculate KbK_b for its conjugate base.
  4. 4 Explain why CaCO3(s)CaCO_3(s) is not included in the KspK_{sp} expression for CaCO3(s)Ca2+(aq)+CO32(aq)CaCO_3(s)\rightleftharpoons Ca^{2+}(aq)+CO_3^{2-}(aq), but the ion concentrations are included.

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

A useful first step is to identify what is changing in the reaction. Use a general equilibrium constant for reactions in solution. Use Kp when the important species are gases and pressure data are given.

Use Ksp when a solid may dissolve or form as a precipitate. Use Ka or Kb when a weak acid or weak base reacts with water. Kw matters whenever hydronium and hydroxide concentrations are linked.

The reaction quotient, called Q, uses the same layout as the equilibrium constant but uses current values. If Q is smaller than K, the reaction moves toward products.

If Q is larger than K, it moves toward reactants. This comparison predicts direction before equilibrium is reached.

Gas problems need careful attention because partial pressure is not the same as total pressure. A gas has a partial pressure based on its fraction of the total gas mixture. Changes in volume can shift a gas equilibrium when the two sides contain different numbers of gas particles.

Adding an inert gas has different effects depending on whether volume or pressure is held constant. Temperature is especially important because every equilibrium constant changes when temperature changes. Heating does not always increase a constant.

The result depends on whether the forward reaction absorbs heat or releases heat. A value of K measured at one temperature should not be used automatically at another temperature.

Solubility questions often test the difference between Ksp and actual solubility. A small Ksp usually means a salt dissolves only slightly, but it does not directly give the same molar solubility for every salt. The ion ratio matters.

For example, a salt that makes two fluoride ions for each metal ion needs a different setup from a salt that makes equal amounts of two ions. Before a precipitate forms, calculate the ionic product and compare it with Ksp. A value above Ksp means precipitation occurs.

A common ion can reduce solubility strongly. Acidity can increase the solubility of salts containing basic ions because those ions react with hydronium.

Acid and base constants describe strength, not how much acid or base was originally added. A larger Ka means a weak acid transfers protons more readily. A larger Kb means a weak base reacts with water more readily.

Students often use pKa and pKb because logarithmic values are easier to compare. A lower pKa means a stronger acid. Conjugate pairs move in opposite directions.

A strong acid has a very weak conjugate base. In buffer calculations, the key idea is that a weak acid and its conjugate base resist sudden pH change by consuming added hydroxide or hydronium.

Keep track of temperature for Kw, since the familiar value of one times ten to the negative fourteen applies only near twenty five degrees Celsius. Always write the balanced reaction first, then decide which species belong in the calculation.