Free Energy

The capacity of a system to do work, or use force to move an object, is its free energy. This is often expressed as Gibbs free energy, named after the American scientist Josiah Willard Gibbs, known for his work in thermodynamics in the late 1800s. Gibbs free energy (G) is the amount of work that can be done by a system, and it is expressed as $G=H-TS$, where H is enthalpy in kilojoules (which is the total internal energy of the system plus the product of the pressure and volume), T is temperature, and S is entropy.

For any chemical reaction, the change in Gibbs free energy ($\Delta G$) can be calculated. Assuming that temperature is standard (25°C, which is 298.15 K), the change in Gibbs free energy is $\Delta G=\Delta H-T\Delta S$, with T = 298.15 K. Importantly, if $\Delta G$ is less than 0, then the reaction is spontaneous; it does not need energy input to proceed. If $\Delta G$ is greater than 0, then the reaction is nonspontaneous and requires energy input to proceed.

Not all reactions proceed at 298 K. Therefore, the temperature at which a reaction proceeds affects whether the reaction is spontaneous. For the reaction between nitrogen gas and hydrogen gas occurring at a temperature of 550 K, the Gibbs free energy change is: This reaction has a $\Delta{G}$ greater than 0, so it is not spontaneous. Standard molar free energy change ($\Delta G_{f}^\circ$), given in kL/mol, is the energy change for a reaction at standard temperature and pressure that produces one mole of a substance from its constituent elements. Standard molar free energy change has been calculated for most compounds. It can be used to understand the relationship between free energy ($\Delta{G}$) for a reaction and the equilibrium constant (K_eq) for that reaction as a function of temperature. It can also be used to determine whether or not a reaction is at equilibrium, in which the forward and reverse reactions are equal. K_eq is the ratio of the concentration of products and reactants of a chemical reaction at equilibrium and indicates whether the reaction favors products or reactants. The relationship between $\Delta{G}$ and K_eq is given as R is the ideal gas constant, 8.314 J/mol⋅K, which relates the kinetic energy of molecules to temperature per mole, and T is temperature.