Reversible Reactions and Dynamic Equilibrium
Most introductory chemistry describes reactions as going "to completion" — all reactants convert to products. But many reactions are reversible: once products form, they can react with each other to regenerate reactants. We write reversible reactions with a double arrow (⇌) rather than a single arrow (→).
Consider the reaction between hydrogen and iodine: H₂(g) + I₂(g) ⇌ 2HI(g)
Initially, only H₂ and I₂ are present, so only the forward reaction occurs. As HI accumulates, the reverse reaction (HI decomposing back to H₂ and I₂) begins. Eventually, the rate of the forward reaction equals the rate of the reverse reaction. At this point, concentrations stop changing — the system has reached chemical equilibrium.
Crucially, equilibrium is dynamic, not static. The reactions haven't stopped; they continue at equal rates in both directions. The apparent "stillness" is a balance of competing processes.
The Equilibrium Constant (K)
At equilibrium, the ratio of product concentrations to reactant concentrations (each raised to the power of its stoichiometric coefficient) has a fixed value called the equilibrium constant K.
For a general reaction: aA + bB ⇌ cC + dD
K = [C]^c [D]^d / [A]^a [B]^b
All concentrations are measured in mol/L (for Kc) or partial pressures in atm (for Kp, used with gases). Pure solids and pure liquids are excluded from the expression because their concentrations don't change.
Interpreting K Values
- K >> 1 (e.g., K = 10⁸): Products are strongly favored at equilibrium — the reaction "goes to completion" for practical purposes
- K << 1 (e.g., K = 10⁻⁸): Reactants are strongly favored — very little product forms
- K ≈ 1: Significant amounts of both reactants and products exist at equilibrium
Example: For H₂ + I₂ ⇌ 2HI at 425°C, K = 55.3. Products are somewhat favored but both reactants and products are present in measurable amounts.
The Reaction Quotient (Q)
The reaction quotient Q has the same mathematical form as K, but uses concentrations that are not necessarily at equilibrium:
Q = [C]^c [D]^d / [A]^a [B]^b (at any point in time)
Comparing Q to K tells you which direction the reaction will proceed: - Q < K: Not enough products relative to equilibrium → reaction proceeds forward - Q > K: Too many products relative to equilibrium → reaction proceeds reverse - Q = K: At equilibrium — no net change
Le Chatelier's Principle
Le Chatelier's Principle (1884) states: if a system at equilibrium is subjected to a stress, the system will shift in the direction that partially relieves that stress.
"Stress" includes changes in concentration, pressure, temperature, or volume.
Effect of Changing Concentration
If you add more of a reactant, the system shifts forward (toward products) to consume the added reactant. If you remove a product (e.g., by precipitating it or removing a gas), the system also shifts forward.
Industrial application: In the Haber process (N₂ + 3H₂ ⇌ 2NH₃), ammonia is continuously removed from the reaction chamber, driving the equilibrium forward and maximizing yield.
Effect of Pressure and Volume (Gases Only)
Increasing pressure (by decreasing volume) favors the side with fewer moles of gas.
For N₂ + 3H₂ ⇌ 2NH₃: - Left side: 1 + 3 = 4 moles of gas - Right side: 2 moles of gas
Increasing pressure favors the right side (fewer gas molecules). This is why the Haber process operates at 150–300 atm.
If a reaction has equal moles of gas on both sides (e.g., H₂ + I₂ ⇌ 2HI: 2 moles on each side), pressure has no effect on equilibrium position.
Effect of Temperature
Temperature changes actually change the value of K — unlike concentration and pressure changes, which only shift the equilibrium position.
For an exothermic reaction (ΔH < 0): heat is a "product." Increasing temperature shifts equilibrium backward, decreasing K. Decreasing temperature shifts it forward, increasing K.
For an endothermic reaction (ΔH > 0): heat is a "reactant." Increasing temperature shifts equilibrium forward, increasing K.
Example: For N₂ + 3H₂ ⇌ 2NH₃, ΔH = −92 kJ/mol (exothermic). High temperature decreases yield of NH₃. However, at low temperatures the reaction is too slow. The industrial compromise is ~400–500°C with an iron catalyst.
Effect of a Catalyst
A catalyst increases the rates of both forward and reverse reactions equally. It allows equilibrium to be reached faster but does not change the equilibrium position or the value of K.
Calculating Equilibrium Concentrations: The ICE Table
The ICE table (Initial, Change, Equilibrium) is the systematic tool for calculating equilibrium concentrations.
Problem: 1.00 mol each of H₂ and I₂ are placed in a 1.00 L flask at 425°C where K = 55.3. What are the equilibrium concentrations?
Initial concentrations: [H₂] = 1.00 M, [I₂] = 1.00 M, [HI] = 0
Change: Let x mol/L of H₂ and I₂ react, producing 2x mol/L of HI.
| H₂ | I₂ | 2HI | |
|---|---|---|---|
| I | 1.00 | 1.00 | 0 |
| C | −x | −x | +2x |
| E | 1.00−x | 1.00−x | 2x |
K expression: K = [HI]² / ([H₂][I₂]) = (2x)² / (1.00−x)² = 55.3
Taking the square root: 2x / (1.00−x) = 7.434
2x = 7.434 − 7.434x → 9.434x = 7.434 → x = 0.788
Equilibrium concentrations: [H₂] = [I₂] = 0.212 M, [HI] = 1.576 M
Solubility Equilibrium and Ksp
Solubility equilibrium is a special case where the equilibrium exists between a slightly soluble ionic solid and its dissolved ions. The equilibrium constant is called the solubility product (Ksp):
CaF₂(s) ⇌ Ca²⁺(aq) + 2F⁻(aq), Ksp = [Ca²⁺][F⁻]² = 3.9 × 10⁻¹¹
Le Chatelier's principle applies here too: adding Ca²⁺ (from CaCl₂, for example) shifts the equilibrium left, causing more CaF₂ to precipitate (common ion effect).
Real-World Significance
The Haber process for ammonia synthesis is the single most consequential industrial application of equilibrium chemistry — it produces fertilizers that feed roughly 3.5 billion people. The reaction conditions (400°C, 150–300 atm, iron catalyst) represent the optimal balance between thermodynamics (lower temperature favors products) and kinetics (higher temperature needed for acceptable rate).
Hemoglobin's binding of oxygen is an equilibrium process — the protein shifts between oxygen-bound and oxygen-free forms depending on local oxygen concentration. In the lungs (high O₂), hemoglobin loads oxygen; in tissues (low O₂), it releases oxygen. Le Chatelier's principle in action, in your blood.