Chemical Equilibrium — Le Chatelier's Principle & Kc, Kp

Chemical equilibrium is the state of a reversible reaction where the forward and reverse reactions run at the same rate, so the overall composition stops changing. It does not mean the amounts on both sides are equal. The core tools are $Kc$, $Kp$, and Le Chatelier's principle: write the equilibrium expression to see which side is favored, and use Le Chatelier or compare $Q$ with $K$ to predict the direction of a change.

The Expressions And Their Symbols

For a reversible reaction

equilibrium means the forward rate equals the reverse rate, so the amounts stop changing with time. That is equal rates, not equal amounts: a system can sit at equilibrium with mostly reactants, mostly products, or an even mixture.

$Kc$ uses concentrations (usually $\mathrm{mol/L}$):

The exponents are the balancing coefficients, and only species whose concentrations can change meaningfully appear; pure solids and pure liquids are omitted because their activities are treated as constant. The size of $Kc$ gives a quick read: $Kc \gg 1$ favors products, $Kc \ll 1$ favors reactants, and $Kc$ near $1$ favors neither strongly.

$Kp$ uses partial pressures for gas-phase equilibria:

Why $Kc$ And $Kp$ Connect The Way They Do

For gas equilibria the two constants are related by

where

The reason for the $(RT)^{\Delta n_{\mathrm{gas}}}$ factor is the ideal-gas link between pressure and concentration, $P = (n/V)RT$. When the moles of gas change across the reaction, that conversion does not cancel, and the leftover powers of $RT$ are exactly $\Delta n_{\mathrm{gas}}$. If there are no gases, this relationship is not the tool to focus on.

Worked Example: $Kc$ For $N_2O_4(g) \rightleftharpoons 2NO_2(g)$

Suppose an equilibrium mixture at one temperature has

Then

Because $Kc < 1$, this equilibrium is reactant-favored at that temperature. The key step is noticing that the coefficient $2$ in front of $NO_2$ becomes an exponent. For the same reaction $\Delta n_{\mathrm{gas}} = 2 - 1 = 1$, so

which connects the concentration form to the pressure form.

Predicting Direction: Le Chatelier And Q Vs. K

Le Chatelier's principle answers "which way will it move?" If a system at equilibrium is disturbed, it shifts to partially oppose the disturbance. It does not give exact new amounts.

• Concentration: adding a reactant shifts toward products; adding a product shifts toward reactants; removing a species shifts toward replacing it. Applies only to species in the expression.
• Pressure/volume (gases): decreasing volume raises pressure and shifts toward the side with fewer moles of gas; increasing volume shifts toward more moles. Equal moles on both sides means no shift from volume alone.
• Temperature: treat heat as part of the reaction. Heat is a product for an exothermic forward reaction and a reactant for an endothermic one. Temperature is the one change that actually alters the value of $K$.
• Catalyst: reaches equilibrium faster but does not change the position.

For a more exact direction tool, plug current values into the expression to get the reaction quotient $Q$: if $Q < K$ the system shifts right, if $Q > K$ it shifts left, and if $Q = K$ it is at equilibrium.

Your Turn

Apply the same steps to

Write $Kc = \dfrac{[HI]^2}{[H_2][I_2]}$, then ask what happens if you add more $HI$ (shifts left, toward reactants) or compress the container. The compression question is a good check: the total moles of gas are equal on both sides, so the volume change alone causes no shift.

Common Equilibrium Mistakes

• Mixing up equal rates and equal amounts. At equilibrium rates are equal; concentrations need not be.
• Forgetting coefficients become exponents. $2NO_2$ gives $[NO_2]^2$ or $(P_{NO_2})^2$.
• Including pure solids or liquids in the expression. They are left out of standard introductory expressions.
• Using Le Chatelier as a calculator. It gives direction reliably, not exact final amounts.
• Assuming every change alters $K$. At fixed temperature, concentration, pressure, or volume changes shift the position but not $K$; only temperature changes $K$.

Chemical equilibrium appears in gas reactions, acid-base systems, solubility, complex-ion formation, and industrial reaction design, wherever a reaction runs both ways and the final composition depends on conditions. It also links kinetics (how fast a system changes) with the condition it settles into at a given temperature.