Topic 7: Equilibrium

Many reactions do not run to completion but settle into a dynamic balance where forward and reverse processes continue at equal rates. This unit shows how to describe that balance with equilibrium constants, predict the direction of change, and calculate concentrations using ICE tables. It also extends these ideas to dissolving salts through the solubility product.

Dynamic Equilibrium

A reversible reaction reaches equilibrium when the forward reaction rate equals the reverse reaction rate. Equilibrium is dynamic, not static: molecules keep reacting in both directions, but because the two rates are equal the macroscopic concentrations of reactants and products stay constant over time. We write reversible reactions with a double arrow, for example N2 + 3 H2 <=> 2 NH3. Equilibrium can be reached starting from pure reactants, pure products, or any mixture, and it requires a closed system at constant temperature so that nothing escapes or is added.

The Reaction Quotient Q vs the Constant K

For a general reaction a A + b B <=> c C + d D, the reaction quotient is Q = ([C]^c [D]^d) / ([A]^a [B]^b), using whatever concentrations exist at a given moment. The equilibrium constant K has the identical form but uses only the equilibrium concentrations. Comparing Q to K predicts which way the reaction will shift: if Q < K there are too few products, so the reaction proceeds forward (to the right); if Q > K there are too many products, so it proceeds in reverse (to the left); and if Q = K the system is already at equilibrium and no net change occurs. Pure solids and pure liquids are left out of both Q and K because their activities are constant.

Kc and Kp

When concentrations are measured in molarity the constant is written Kc; when reactant and product amounts are expressed as partial pressures of gases it is written Kp. For gas-phase equilibria the two are related by Kp = Kc (RT)^(delta n), where delta n is the moles of gaseous products minus moles of gaseous reactants, R is the gas constant, and T is the absolute temperature in kelvin. If delta n = 0 then Kp = Kc. Each equilibrium constant is dimensionless in the formal thermodynamic sense and depends only on temperature, so changing concentrations or pressures does not change the value of K, only the position of equilibrium.

Calculating K and Using ICE Tables

An ICE table organizes the Initial amounts, the Change, and the Equilibrium amounts for each species. Worked example: 1.00 mol of H2 and 1.00 mol of I2 are placed in a 1.00 L flask, so each starts at 1.00 M, for H2 + I2 <=> 2 HI. Let the change in H2 be -x; then I2 also changes by -x and HI changes by +2x. At equilibrium [H2] = 1.00 - x, [I2] = 1.00 - x, and [HI] = 2x. Suppose [HI] is measured as 1.56 M, so 2x = 1.56 and x = 0.78. Then [H2] = [I2] = 0.22 M. Therefore Kc = (1.56)^2 / ((0.22)(0.22)) = 2.43 / 0.0484, which is about 50. ICE tables can also run in reverse: given K, write equilibrium terms with x, substitute into the K expression, and solve for x (often with the quadratic formula or, when K is very small, the simplifying approximation that x is negligible).

The Magnitude of K

The size of K tells you where equilibrium lies. A large K (much greater than 1) means products dominate at equilibrium, so the reaction strongly favors the forward direction. A small K (much less than 1) means reactants dominate and very little product forms. A K near 1 means appreciable amounts of both reactants and products coexist. Magnitude says nothing about how fast equilibrium is reached, since that is governed by kinetics, not by K. Note that reversing a reaction inverts K (K reverse = 1 / K forward), and multiplying a reaction by a factor n raises K to the power n.

Le Chatelier's Principle

Le Chatelier's principle states that when a system at equilibrium is disturbed, it shifts in the direction that partially counteracts the disturbance. Adding a reactant or removing a product shifts the equilibrium toward products; removing a reactant or adding a product shifts it toward reactants. Increasing pressure by decreasing volume shifts a gaseous equilibrium toward the side with fewer moles of gas. Changing temperature actually changes the value of K: for an endothermic reaction (heat is a reactant) raising temperature increases K and favors products, while for an exothermic reaction (heat is a product) raising temperature decreases K and favors reactants. A catalyst speeds both directions equally and does not shift the position of equilibrium.

The Solubility Product Ksp

For a sparingly soluble salt, the dissolving equilibrium is described by a solubility product. For example, AgCl(s) <=> Ag+(aq) + Cl-(aq) gives Ksp = [Ag+][Cl-]. The solid does not appear in the expression because it is a pure solid. Molar solubility, s, is the number of moles of salt that dissolve per liter. For AgCl, s = [Ag+] = [Cl-], so Ksp = s^2. For a salt that produces different numbers of ions, such as CaF2(s) <=> Ca2+ + 2 F-, the stoichiometry carries through: [Ca2+] = s and [F-] = 2s, giving Ksp = (s)(2s)^2 = 4 s^3. A smaller Ksp generally means a less soluble salt, though comparing solubilities across salts is only valid when they release the same number of ions.

The Common-Ion Effect and pH Effects on Solubility

The common-ion effect describes how the solubility of a salt drops when a soluble compound supplying one of its ions is added. For instance, adding NaCl to a saturated AgCl solution raises [Cl-], so by Le Chatelier the equilibrium shifts back toward solid AgCl and less silver chloride dissolves; Ksp itself stays the same. The pH of the solution also affects solubility when the dissolved salt contains a basic or acidic ion. Salts of weak-acid anions, such as hydroxides, carbonates, and fluorides, dissolve more readily in acidic solution because added H+ reacts with the anion (for example F- + H+ -> HF), removing it from solution and pulling the dissolution equilibrium forward. Salts whose anion is the conjugate base of a strong acid, such as chlorides and nitrates, show little pH dependence.