Variation of Reaction Enthalpy with Temperature (Kirchhoff's Law)

Kirchhoff's equation describes how reaction enthalpy varies with temperature at constant pressure. It states that the slope of enthalpy with respect to temperature equals the difference in heat capacities between products and reactants. This relationship allows scientists to predict enthalpy changes at different temperatures using standard enthalpy data and heat capacity values.

Both reactants and products have enthalpies that increase with temperature. However, the overall reaction enthalpy changes only when the enthalpy increases of reactants and products differ. This difference in how much each substance's enthalpy rises with temperature determines whether the reaction's overall enthalpy increases, decreases, or remains constant.

Heat capacity is the change in enthalpy divided by the change in temperature at constant pressure. The change in reaction enthalpy is proportional to the product of temperature change and the difference in heat capacities of products and reactants. Heat capacity values are calculated using stoichiometric coefficients, as each molecule possesses distinct heat capacities in its various states.

Kirchhoff's equation can be directly integrated for small temperature ranges, typically less than 100 Kelvin, assuming constant heat capacities. For larger temperature ranges, heat capacities vary significantly with temperature, complicating calculations. In these cases, temperature-dependent heat capacity values must be substituted into Kirchhoff's equation for accurate results.

At constant volume, a similar relation uses the temperature dependence of internal energy instead of enthalpy. Internal energy connects to enthalpy by adding the pressure-volume term, allowing reaction enthalpy to be evaluated under constant-volume conditions. This relationship extends Kirchhoff's law beyond constant-pressure scenarios.

The integrated form of Kirchhoff's equation is obtained by integrating between two given temperatures. It allows scientists to calculate reaction enthalpy at one temperature using known enthalpy data from another temperature. This form is particularly useful for predicting enthalpy changes across different thermal conditions in biochemical and chemical applications.

Heat capacity differences between products and reactants are calculated using a weighted sum that accounts for stoichiometric coefficients. Each molecule possesses distinct heat capacities in its various states, so the stoichiometric coefficients ensure accurate representation of how much of each substance participates in the reaction, directly affecting the overall enthalpy change calculation.