Writing Equilibrium Constant Expressions: K_c, K_p and Heterogeneous Systems

For aA + bB ⇌ cC + dD the products go in the numerator and the reactants in the denominator, each raised to the power of its coefficient. The coefficients become exponents, never multipliers.

For N₂ + 3 H₂ ⇌ 2 NH₃, K_c = [NH₃]²/([N₂][H₂]³). The exponent three belongs to the whole concentration term [H₂], not to the subscript inside H₂. Use coefficients from the balanced equation and include dissolved ions as well as gases. For AgCl(s) ⇌ Ag⁺(aq) + Cl⁻(aq), the solid is omitted but both ions remain.

The thermodynamic K is dimensionless and uses activities: ideal gas activity is approximately P/P°, and dilute-solute activity approximately c/c°. Introductory K_c and K_p calculations often suppress those reference factors and use numerical molarities or pressures in specified units. Keep one convention throughout rather than mixing atm with bar or interpreting a dimensionless thermodynamic constant as carrying arbitrary units.

A pure solid or pure liquid has a fixed density, so its effective concentration does not change as the reaction runs. Anything that is constant is folded into K itself and disappears from the expression. Dilute aqueous solutions treat the water solvent the same way.

Water is omitted when it is a pure liquid or an effectively constant solvent in the dilute-solution approximation. Water vapor is a gas and must be included. A dissolved substance is not omitted just because it is a liquid in its pure state: ethanol concentration can matter in a solution equilibrium. The pure-phase rule refers to its actual role and phase in the written reaction.

For CaCO₃(s) ⇌ CaO(s) + CO₂(g), both solids drop out and the expression is simply K_c = [CO₂]. This is why the pressure of CO₂ above heated limestone in a sealed vessel is fixed by temperature while the required pure solid phases coexist; complete consumption of a phase changes the constraints.

For CaCO₃(s) ⇌ CaO(s) + CO₂(g), equilibrium fixes the CO₂ pressure at a given T only while the required solid phases coexist. If all CaCO₃ is consumed before that pressure is attained, the assumed heterogeneous equilibrium cannot be maintained. Adding more of an already present pure solid changes neither its activity nor K, but removing an entire phase can invalidate that equilibrium condition. More exposed surface can change the speed of equilibration without changing the equilibrium relation.

Substituting P = (n/V)RT into the expression gives a factor of RT for every net mole of gas produced. Dn counts moles of gaseous product minus moles of gaseous reactant. Use R = 0.08206 L atm/mol K with pressures in atm and T in kelvin.

The classroom ideal-gas conversion K_p = K_c(RT)^Δn uses Δn = Σνgas,products − Σνgas,reactants. Count gases only: solids, liquids and aqueous species do not enter Δn. For 2 NO₂(g) ⇌ N₂O₄(g), Δn = 1 − 2 = −1, so K_p = K_c/(RT). For H₂ + I₂ ⇌ 2 HI, Δn = 0 and the corresponding numerical constants agree under matching conventions. Use kelvin, and choose R for the pressure and concentration units supplied.