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

Hint: The Gibbs free energy is the change in the criterion when the temperature and pressure are considered as the independent variables. It is represented by the equation $dG = - SdT + VdP$. This equation represents the change in Gibbs free energy for a closed system and the Gibbs Helmholtz equation is derived by this equation only.

Complete answer:
The Gibbs Helmholtz equation is a type of thermodynamic equation which is used for determining the changes in the Gibbs energy of a system as a function of the temperature. The equation was named after Hermann von Helmholtz and Josiah Williard Gibbs.
The equation is given as follows:
${\left( {\dfrac{{\partial \left( {\dfrac{G}{T}} \right)}}{{\partial T}}} \right)_P} = - \dfrac{H}{{{T^2}}}$
Where, H is the enthalpy, G is the Gibbs free energy and T is the absolute temperature of the system and all the values are considered at constant pressure P. According to this equation, the change in $\dfrac{G}{T}$ ratio at a constant pressure results in an infinitesimally small change in the factor $\dfrac{H}{{{T^2}}}$.
The applications of Gibbs Helmholtz equation are as follows:
It can be used to determine the overall enthalpy of a reaction and its variation with temperature from the given value of Gibbs free energy at constant pressure.
It can be used to determine the value of Gibbs free energy for a reaction at a temperature other than 298 K.
It can be used to determine the effect of change in temperature on equilibrium constant.
It can be used to determine the spontaneity of a reaction.

Note:
Remember that for a spontaneous reaction i.e., a reaction which favours the formation of the products, the value of change in Gibbs free energy must always be negative. It is one of the most important criteria to determine spontaneity of a reaction. If the value is negative, then the reaction is said to be a non-spontaneous reaction.