Along with the Gibbs free energy
, Helmholtz free energy
is a thermodynamic
measurement of the energy in a system. The Helmholtz free energy applies to a system being held a fixed temperature
T and volume V, and is a Legendre Dual
of the potential energy replacing entropy with temperature. In equilibrium
, a system will minimize its free energy. It is often used in chemistry
to determine if reaction is favorable or not, the more favorable the reaction, the more negative the free energy.
The fixed temperature T means that the system is not thermodynamically closed, since energy can come in and out of the system to regulate the temperature. This is the reason why we must look at free energy instead of just potential energy to determine if something is thermodynamically favorable.
In an unfortunate choice of symbols, Helmholtz free energy is denoted by F while enthalpy get the more logical H. Helmholtz free energy is defined as:
F = U + TS
Where U is the potential energy of the system, T is the temperature, and S in the entropy.
It is also often expressed in differential form (since the change in free energy is what determines if a reaction is favorable.)
deltaF = deltaU - T deltaS
For a chemical reaction, the change in potential energy is a result of bonds being formed, electrical attractions, etc. The change in entropy comes from the change in number of molecules, and their degrees of freedom. For example, two hydrogen atoms each have three degrees of freedom (x,y, and z movements.) A molecule of H2 has five degrees of freedom since it can spin on two axes, a reduction in entropy. Meaning deltaS is negative, and at a high enough temperature, delta F will become positive and molecular hydrogen will be unstable.
Normally, both numbers for a reaction can be found in a CRC. You'll need them both because it's possible for a reaction to be favorable at one temperature, and become unfavorable at a higher (-deltaU, +deltaS) or lower(+deltaU, -deltaS) temperature.