Relationship between Kp and Kc

This relation converts between dimensionless concentration-based and pressure-based equilibrium constants for an ideal-gas reaction. The relation is useful for Convert gas-equilibrium data between concentration and partial-pressure conventions.. For N₂(g)+3H₂(g)⇌2NH₃(g), Δn=−2. At 500 K, RTc°/p°=(8.314·500·1000)/100000=41.57, so Kp/Kc=41.57⁻²=5.79×10⁻⁴. Check: if Δn=0, the ratio is 1. The final check tests a balance, direction or magnitude relevant to this formula. First map each quantity to the actual experiment, then substitute values. The result describes the modelled relationship; it does not automatically establish every mechanism in the real sample.

The symbols mean: K_p: pressure-based equilibrium constant (dimensionless); K_c: concentration-based equilibrium constant (dimensionless); R: universal gas constant (J/(mol·K)); T: absolute temperature (K); c°: concentration standard, here 1000 mol/m³ (mol/m³); p°: pressure standard, here 100000 Pa (Pa); Δn_gas: sum of gaseous product ν minus reactant ν (dimensionless). Follow Kp and Kc dimensionless · R in J·mol⁻¹·K⁻¹ · c°=1000 mol/m³ · p°=100000 Pa · T in K. Concentrations, activities, volumes and times must use compatible scales. A logarithm needs a dimensionless argument, and a balance must include all contributing species. State temperature and standard state whenever they are part of the definition; otherwise the result may refer to a different chemical condition. An amount is not a mass without molar mass, and activity is not an unnormalised concentration. Say whether inputs were measured or taken from a reference.

Assume ideal gases and use the stated dimensionless standard states consistently. Δn counts gaseous product coefficients minus gaseous reactant coefficients; solids and liquids are excluded. Other standard-state conventions change the written conversion factor. Check this assumption for the actual sample, temperature and phase. Nonideality, mass transport or side reactions can make a precise calculation systematically wrong. Compare the balanced reaction and the activity or concentration scale with the model, then state the assumption that most affects the result. Near model boundaries, check activities and phase state rather than extending a dilute-solution approximation. Different conditions require a fresh model check.

Recalculate the example: For N₂(g)+3H₂(g)⇌2NH₃(g), Δn=−2. At 500 K, RTc°/p°=(8.314·500·1000)/100000=41.57, so Kp/Kc=41.57⁻²=5.79×10⁻⁴. Check: if Δn=0, the ratio is 1. Check Kp and Kc dimensionless · R in J·mol⁻¹·K⁻¹ · c°=1000 mol/m³ · p°=100000 Pa · T in K and substitute the value back into the relation. Also ask whether its sign, balance or magnitude is chemically plausible. If a check fails, inspect units, coefficients and reference values before blaming rounding. Substitution checks the algebra; comparing assumptions with the experiment checks whether the model is appropriate.

Relationship between Kp and Kc is related to Massenwirkungsgesetz (Gleichgewichtskonstante), Reaction Quotient, Ideales Gasgesetz, but answers a distinct question: Convert gas-equilibrium data between concentration and partial-pressure conventions.. Do not confuse it with a relation for a neighboring quantity or a different standard state. Name the target quantity and sample conditions first, then choose the equation containing that quantity. Similar-looking equations may use different stoichiometric bases or validity ranges. The linked entries may supply inputs for another step, but they do not replace this distinction. This keeps the interpretation auditable.