Free energy

The free energy, G, is a thermodynamic state function that we can use as an indicator of whether or not a process in a system will occur spontaneously. We can think of free energy G as a kind of potential energy which is the capacity to do useful work in a physicochemical system. We know that spontaneous processes are characterized by an accompanying decrease in potential energy, analogous to the decrease in gravitational potential energy occurring for a ball rolling downhill. In a physicochemical system that is not at equilibrium, we should expect a spontaneous change in the system, moving it toward equilibrium. We will see in this section that the tendency of any chemical reaction to proceed to equilibrium is interpretable as a spontaneous process leading the system to the attainment of a minimum of free energy, and that the actual equilibrium for a particular chemical reaction is determined by a quantity called the standard free energy change, ΔG°, for that reaction.

Gibbs free energy is a state function

We learned in our consideration of entropy that a spontaneous process is characterized by an increase in the total entropy (ΔS for both system and surroundings). This is a statement of the second law of thermodynamics. For physicochemical systems in general, and biochemical systems in particular, it would be convenient to have a state function defined for the system that would indicate whether or not a process is spontaneous. This would relieve us of the inconvenience of having to compute the entropy of the surroundings as well as that of the system in order to make this determination. Fortunately, there is such a state function, known as free energy, G (sometimes referred to as Gibbs free energy - hence the designation as G), which defined by a the equation G = H − TS that combines the state functions enthalpy, temperature, and entropy. (T is the temperature in K.) Since a linear combination of state functions is again a state function, we know that G is a state function. The Gibbs free energy function is appropriate for processes occurring at constant pressure. The change in free energy of a system for a process occurring at constant pressure and temperature is given as ΔG = ΔH − TΔS. This turns out to be convenient for biochemistry and biological systems since we nearly always deal with systems at constant pressure and temperature. The value of ΔG is that its sign - for just the system alone - tells us whether a process is spontaneous or not (i.e. ΔG < 0, for the system alone, is equivalent to ΔS (system) + ΔS (surroundings) > 0 ). A spontaneous process correponds to a decrease in the free energy of the system.

The sign of ΔG is the criterion for spontaneity of a reaction

Free energy and equilibrium

If a spontaneous process is one that is accompanied by a decrease in free energy, then when free energy reaches a minimum, no further decrease is possible, and the system must be at equilibrium. This can be illustrated for a simple chemical reaction.