Kirchhoff’s Law for Reaction Enthalpy

Kirchhoff’s law corrects a reaction enthalpy from one temperature to another using the heat-capacity change. The relation is useful for Correct tabulated reaction enthalpies to experimental temperatures.. If ΔrH(298 K)=−100.0 kJ/mol and ΔrCp=+25.0 J·mol⁻¹·K⁻¹, then at 350 K ΔrH≈−98.70 kJ/mol. Check: a positive ΔrCp makes the enthalpy less negative as T rises. 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: ΔrH(T): reaction enthalpy at temperature T (J/mol); ΔrCp: difference in molar heat capacities, products minus reactants (J·mol⁻¹·K⁻¹); T: absolute temperature (K). Follow ΔrH in J/mol · ΔrCp in J·mol⁻¹·K⁻¹ · temperatures 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.

The simple integrated form assumes reaction heat capacity is constant over the interval. ΔrCp is the stoichiometric sum for products minus reactants. Phase transitions or significant heat-capacity variation require integration with appropriate data. 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: If ΔrH(298 K)=−100.0 kJ/mol and ΔrCp=+25.0 J·mol⁻¹·K⁻¹, then at 350 K ΔrH≈−98.70 kJ/mol. Check: a positive ΔrCp makes the enthalpy less negative as T rises. Check ΔrH in J/mol · ΔrCp in J·mol⁻¹·K⁻¹ · temperatures 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.

Kirchhoff’s Law for Reaction Enthalpy is related to Reaktionsenthalpie (Satz von Hess), Gibbs-Energie (Freie Enthalpie), Clausius–Clapeyron Equation for Vaporization, Gibbs–Helmholtz Equation, but answers a distinct question: Correct tabulated reaction enthalpies to experimental temperatures.. 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.