What equilibrium means
Many reactions are reversible. Equilibrium is reached when the forward and reverse rates are equal, so the concentrations stop changing. Nothing has stopped happening; the changes are simply balanced. For a general reaction a A + b B ⇌ c C + d D, the equilibrium constant is K = [C]^c [D]^d / ([A]^a [B]^b), using molar concentrations for Kc (or partial pressures for Kp). Pure solids and pure liquids are left out. K depends only on temperature. A large K (well above 1) means products dominate; a small K means reactants dominate.
Manipulating K
- Reverse the reaction: K becomes 1/K.
- Multiply the coefficients by n: K is raised to the power n.
- Add two reactions: multiply their K values.
- Convert between Kp and Kc using Kp = Kc (RT)^Δn, where Δn is moles of gas products minus moles of gas reactants.
Reaction quotient
The reaction quotient Q has the same form as K but uses the current concentrations. Compare: if Q < K the reaction runs forward; if Q > K it runs in reverse; if Q = K it is at equilibrium.
Le Chatelier's principle
A system at equilibrium that is disturbed shifts to partly counteract the change. Adding a reactant shifts the reaction forward; removing a product does the same. Raising pressure by compressing a gas mixture favours the side with fewer gas moles. Raising temperature favours the endothermic direction, and this is the only disturbance that actually changes the value of K. A catalyst speeds up both directions equally, so it reaches equilibrium sooner but does not change K or the position.
Solubility equilibria
For a slightly soluble salt, the solubility product Ksp is the product of ion concentrations raised to their coefficients, such as Ksp = [M^2+][X^-]^2 for MX2.
Worked example
For N2O4(g) ⇌ 2 NO2(g), Kc = 0.0060 at a certain temperature. Initially [N2O4] = 0.200 M and there is no NO2. Find [NO2] at equilibrium.
- Let x be the N2O4 that reacts. Then [N2O4] = 0.200 − x and [NO2] = 2x.
- Kc = (2x)^2 / (0.200 − x) = 0.0060, so 4x^2 + 0.0060x − 0.00120 = 0.
- The quadratic formula gives x = [−0.0060 + sqrt(0.0060^2 + 4(4)(0.00120))] / 8 = 0.01659 M.
- [NO2] = 2x = 0.033 M, and [N2O4] = 0.183 M.
Check: 0.0332^2 / 0.1834 = 0.0060. Since x is about 8 percent of 0.200, the usual approximation of ignoring x would be too crude here, so the full quadratic was needed.