Dynamic Equilibrium and the Equilibrium Constant

A reversible reaction can go in both directions: reactants form products (the forward reaction) and products re-form reactants (the reverse reaction). We show this with a double arrow, $\rightleftharpoons$. At the start only the forward reaction runs quickly, because there is plenty of reactant and almost no product. As products build up, the reverse reaction speeds up, and as reactants are used up, the forward reaction slows down. Eventually the two rates become equal. From then on, every molecule of product formed is matched by one that turns back into reactant, so the concentrations stay constant even though both reactions continue. That is why it is called dynamic equilibrium.

• Closed system: no matter can enter or leave. An open beaker of a reaction that gives off a gas can never reach equilibrium because the product escapes.
• Constant macroscopic properties: colour, pressure and concentrations stop changing once equilibrium is reached.
• Can be approached from either side: starting with pure reactants or pure products at the same temperature gives the same value of K.
• Physical equilibria count too: water and its vapour in a sealed bottle, or a saturated salt solution in contact with undissolved crystals, are dynamic equilibria. Evaporation and condensation (or dissolving and crystallizing) keep happening at equal rates.

Experiments show that for a reaction at a given temperature, one particular ratio of equilibrium concentrations always comes out to the same number, no matter what amounts you started with. For the general reaction $a\text{A}+b\text{B}\rightleftharpoons c\text{C}+d\text{D}$, that ratio is the equilibrium constant. Each concentration (in mol/L, written in square brackets) is raised to the power of its coefficient in the balanced equation, with products on top and reactants on the bottom.

• Leave out pure solids and pure liquids. Their concentration does not change as the reaction proceeds, so they are already built into the value of K. For ${\text{CaCO}}_3(s)\rightleftharpoons \text{CaO}(s)+{\text{CO}}_2(g)$, the expression is simply $K_{eq}=[{\text{CO}}_2]$.
• Water as the solvent in an aqueous reaction is also left out, for the same reason. Gases and aqueous species are always included.
• A homogeneous equilibrium has every species in the same phase (for example, all gases). A heterogeneous equilibrium involves more than one phase, which is when the solid/liquid rule matters.
• K is usually written without units, and its value changes only when the temperature changes.
• Reversing an equation gives $K_{reverse}=\frac{1}{K}$. Multiplying every coefficient by $n$ raises K to the power $n$.

For reactions of gases, chemists often use partial pressures instead of concentrations. The expression looks the same, with each pressure raised to its coefficient: for ${\text{N}}_2{\text{O}}_4(g)\rightleftharpoons 2{\text{NO}}_2(g)$, $K_p=\frac{{(P_{{\text{NO}}_2})}^2}{P_{{\text{N}}_2{\text{O}}_4}}$. Because pressure and concentration of a gas are proportional at constant temperature ($P=\frac{n}{V}RT$), $K_p$ and $K_c$ are related by $K_p=K_c{(RT)}^{\Delta n}$, where $\Delta n$ is moles of gaseous products minus moles of gaseous reactants. When $\Delta n=0$ the two constants are equal. The value of R must match the pressure unit you use.

Usually you do not know every equilibrium concentration. An ICE table (Initial, Change, Equilibrium) organizes what you do know. Write the balanced equation across the top, fill in initial concentrations, then express the change for each species using one unknown, $x$, scaled by the coefficients: if ${\text{H}}_2$ changes by $-x$, then $\text{HI}$, with coefficient 2, changes by $+2x$. The equilibrium row is simply Initial + Change. Always convert moles to mol/L first.