The Gibbs-Helmholtz Equation
A Useful Expression in Thermodynamics
Temperature Dependence of Gibbs Free Energy
The Gibbs-Helmholtz equation is a widely used expression in thermodynamics that describes the temperature dependence of the Gibbs free energy (G). It establishes a relationship between G and other thermodynamic quantities, such as enthalpy (H) and temperature (T). The equation is particularly valuable in understanding how the spontaneity and equilibrium of chemical reactions vary with temperature.
The Gibbs-Helmholtz equation is mathematically represented as:
(∂G / ∂T)p = -H / T
where:
- G is the Gibbs free energy
- H is the enthalpy
- T is the temperature
- p is the pressure (assumed constant)
The Gibbs-Helmholtz equation highlights that the change in Gibbs free energy with temperature is directly proportional to the negative of the enthalpy divided by the temperature. This implies that the sign of the enthalpy change dictates the direction of the spontaneity of a reaction.
For example, if the enthalpy change is negative (exothermic reaction), the Gibbs free energy decreases with increasing temperature, indicating that the reaction becomes more spontaneous at higher temperatures. Conversely, if the enthalpy change is positive (endothermic reaction), the Gibbs free energy increases with temperature, making the reaction less spontaneous at higher temperatures.
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