BIOCHEMISTRY TOPICS
Gibbs free energy
The Gibbs free energy function, G. The second law recast.
The Gibbs free energy function, 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. The tendency of any chemical reaction to proceed to equilibrium is interpretable as a spontaneous process leading the system to the attainment of the minimum available value of a physicochemical potential energy function, generally referred to as free energy. In what follows, we'll see exactly how the Gibbs free energy function is defined, how it may be used to determine spontaneity or equivalently, thermodynamic favorability, for a process.
Chemical equilibrium for a reaction is characterized by its equilibrium constant, Keq. The value of Keq is determined by its free energy change under very specific conditions that are termed standard conditions, a quantity called the standard free energy change, ΔG°, for that reaction.
Inventing the Gibbs free energy function
In this section, we will develop the rationale for a new state function that is a combination of enthalpy and entropy multiplied by temperature. The ultimate usefulness will be that the function will provide a simplified criterion for spontaneity, evaluated for the system alone, and appropriate for the study of biochemistry.
The second law of thermodynamics
ΔSuniv = ΔSsys + ΔSsurr > 0
serves as our reliable criterion for spontaneity. The inequality holds for all irreversible - that is, surroundings. spontaneous processes, yet for many processes it is inconvenient to assess the entropy change of the One way to avoid this problem is only deal with isolated systems. Any process occurring in an isolated system must be spontaneous, and since q = 0, we must have ΔSsurr = 0. Therefore, for any irreversible process in an isolated system,
ΔSsys > 0
However, it is necessary to study systems that interact with the surroundings by exchange of energy. Another way we can recast the second law into a form that focuses on the state of the system alone is to instead restrict our considerations to constant temperature and constant pressure processes. If heat transfer occurs to or from the surroundings at constant temperature
ΔSsurr = −qsys /T
Furthermore, at constant pressure, q = qP = ΔHsys and thus we can write
ΔSsurr = −ΔHsys/T
Then the second law becomes
ΔSsys + ΔSsurr = ΔSsys − ΔHsys/T > 0
Since absolute temperature is always greater than zero, this expression can be multiplied by −T and rearranged as
ΔHsys − TΔSsys < 0
It is convenient at this point to introduce the Gibbs free energy function, G, which will allows us to determine spontaneity by looking only at the changes in the free energy of the system. G is a state function, defined by the relation G = H – TS, and for processes occurring at constant temperature and pressure, ΔG = ΔH − TΔS, and the criterion for spontaneity becomes ΔGsys < 0. Fortunately for biologists and biochemists, enzyme-catalyzed reactions or virtually any imaginable cellular process occur at constant T, P.
The change in Gibbs free energy, ΔG, for any process which occurs at constant temperature is given by the equation ΔG = ΔH − TΔS. In what follows, we develop some examples that illustrate these important concepts. The left-side expression above is the change in the Gibbs free energy function we introduced last time for constant temperature and pressure.
The ΔG for any process is also a measure of the maximum available energy (i.e. "free" energy) that can be harnessed by the system to produce nonexpansion work.
Summary: For a system at constant T, P:
- ΔG = ΔH − TΔS < 0 ↔ process is spontaneous
- At equilibrium, ΔG = 0.
- Equivalently, at equilibrium, G is at a minimum.
Related topics pages: