How Enthalpy, Entropy and Gibbs Free Energy are Interrelated ?

The following article will guide you about how enthalpy, entropy and Gibbs free energy are interrelated.

Enthalpy (H):

In a process carried out at constant volume (e.g., in a sealed tube), the heat content of a system is equal to internal energy (E), as no PV (pressure volume) work is done. But, in a constant pressure process, the system also expends energy in doing PV work.

There­fore, the total heat content of a system at constant pressure is equivalent to the internal energy (E) plus the PV (pressure volume product) energy. This is called as enthalpy and is represented by the symbol H. Thus, enthalpy may be defined by the equation,

H = E + PV

In simpler words, enthalpy is the total heat content of a system. It reflects the num­ber and kinds of chemical bonds in the reactants and products. Like internal energy, enthalpy is also a function of state and therefore, it is not pos­sible to quantify the absolute enthalpy. However, a change in enthalpy (∆H) accompany­ing a process can be measured accurately. Thus,

∆H = H_P – H_r

(where p = products; r = reactants)

The unit of ∆H is joules/mole (or calories/mole)

The reactions which are accompanied by release of heat energy are called as exother­mic reactions. In such cases, there is negative change in enthalpy (-∆H) from reactants to products. For example, in combustion of glucose to CO₂ + H₂O, large amount of heat is released. Therefore, this is an exothermic reaction with -∆H. melting of ice into liquid water and its subsequent vaporization into water vapours absorb considerable heat from the surroundings, therefore this is an endothermic reaction with + ∆H.

Entropy (S):

Entropy is a quantitative expression for the randomness or disorder in a system and is represented by the symbol S. Entropy has already been discussed in quite some detail while describing Second Law of Thermodynamics earlier. According to this law, ‘the entropy of the universe tends towards a maximum’.

Any change in entropy or disorder accompanying a process from start to finish, is represented by ∆S. When the products of a reaction are less complex or more disordered than the reactants, the reaction is said to proceed with gain in entropy (+∆S) or vice versa (-∆S). In all spontaneous reactions such as oxidation of glucose or melting of ice, the ∆S is positive.

Gibbs Free Energy (G):

Free energy is the component of the total energy of a system that is available to do work at constant temperature and pressure and is represented by the symbol G. It is called as Gibbs free energy in honour of Josiah Willard Gibbs (1839-1903), an American math­ematician and physical chemist who developed the theory of chemical thermodynamics in 1870s at Yale University and also the concept of free energy.

Since Gibbs free energy is also a thermodynamic quantity, it is not possible to quantify its absolute value. However, a change in Gibbs free energy (∆G) accompanying a process can be measured accurately. The unit of Gibbs free energy is joules/mole (or calories/ mole).

Gibbs free energy (G) can be defined by combining the enthalpy (H), entropy (S), along with the Kelvin temperature (T) as shown in the following equation,

G = H – TS

As with enthalpy (H) and entropy (S), we cannot quantify absolute free energy but only differences in free energy (i.e., ∆G), the above equation becomes,

∆G = ∆H – T∆S

∆G is the quantity that is used to describe whether a process is spontaneous or not. Processes with a negative free energy change (-∆G) are energetically feasible and are capable of occurring spontaneously.

Because the free energy of the products is less than those of reactants, reactions with negative ∆G (< 0) are also known as exergonic reactions or energy yielding reactions. Oxidation of glucose to CO₂ + H₂O, is an example of exergonic reaction which has negative free energy change (-∆G). Similarly, hydrolysis of ATP mol­ecules is an exergonic reaction.

On the other hand, processes with a positive free energy change (+∆G) are not ener­getically feasible and will not proceed without an input of energy. Reactions with a posi­tive ∆G (i.e., ∆G > 0) are known as endergonic reactions or energy consuming reactions. Conversion of glucose + Pi into glucose-6-phosphate accompanies with a positive free en­ergy change, and thus, is an endergonic reaction.

The syntheses of macromolecules such as proteins and nucleic acids from their simple monomeric components also require input of energy and are therefore, endergonic with +∆G. Synthesis of ATP during oxidative phos­phorylation whose apparent ∆G is as high as 67 kJ mol^-1, is also an endergonic process.

In biological systems, very often thermodynamically un-favourable energy requiring endergonic reactions couple them to other reactions that liberate free energy (exergonic re­actions), so that the overall process is exergonic.

The free energy change (∆G) of a chemical reaction is a function of its displacement from equilibrium. “The farther a reaction is poised away from equilibrium, the more free energy is available as the reaction proceeds towards equilibrium”. When a reaction is at equilibrium, ∆G is zero and no further work can be done.

The magnitude of free energy changes is mostly a function of the particular set of conditions for that reaction. Therefore, free energy changes in chemical reactions are compared under standard reaction conditions. The standard free energy change (∆G°’) represents free energy change of a reaction that occurs at pH 7 and 25°C under conditions when both reactants and products are at unit concentration i.e., 1M.

The actual free energy change (∆G) and standard free energy change (∆G°’) are two different quantities that will not necessarily match each other. The AG°’ is a constant that is characteristic for each specific reaction and is directly related to equilibrium constant (K_eq).