What is Gibbs Helmholtz equation? Explain with the help of applications.

The Gibbs-Helmholtz equation is a thermodynamic equation that relates the change in Gibbs free energy (∆G) of a system to the change in temperature (∆T) at constant pressure. It can be expressed as follows:

∆G = ∆H - T∆S

where:

∆G is the change in Gibbs free energy of the system,
∆H is the change in enthalpy of the system,
∆S is the change in entropy of the system,
T is the absolute temperature.
This equation provides valuable insights into the thermodynamic properties of a system, particularly in relation to its stability and spontaneity. Here are a couple of applications of the Gibbs-Helmholtz equation:

Stability and equilibrium: The Gibbs-Helmholtz equation is often used to determine the stability and equilibrium conditions of a chemical reaction or a phase transition. By examining the change in Gibbs free energy (∆G) with respect to temperature (∆T), it is possible to determine if a reaction or a process will be spontaneous or non-spontaneous at a given temperature. If ∆G is negative (∆G < 0), the reaction or process is spontaneous and the system tends towards equilibrium. If ∆G is positive (∆G > 0), the reaction or process is non-spontaneous and requires an input of energy to proceed. The Gibbs-Helmholtz equation allows us to analyze the temperature dependence of these processes.

Estimation of thermodynamic properties: The equation can also be rearranged to estimate thermodynamic properties such as the enthalpy (∆H) and entropy (∆S) changes of a system at different temperatures. By measuring the change in Gibbs free energy at two different temperatures and knowing the value of ∆H, ∆S can be calculated. This information is crucial for understanding the behavior of chemical reactions, phase transitions, and other thermodynamic processes.

Overall, the Gibbs-Helmholtz equation is a useful tool in thermodynamics for analyzing the stability, spontaneity, and temperature dependence of chemical reactions and processes. It provides a quantitative framework for understanding and predicting the behavior of systems under different conditions.