Gibbs Free Energy and Its Formula | Thermodynamic System | Energy Management

After reading this article you will learn about the gibbs free energy and its formula,which is a process-initiating work obtainable from an isothermal,isobaric thermodynamic system.

Gibbs free energy is the measures of “useful” or process-initiating work obtainable from an isothermal, isobaric thermodynamic system. It is the maximum amount of non-expansion work that can be extracted from a closed system; this maximum can be attained only in a completely reversible process. When a system changes from a well-defined initial state to a well-defined final state, the Gibbs free energy ∆G equals the work exchanged by the system with its surroundings. The free energy change (∆G) of a reaction determines its spontaneity. A reaction is spontaneous if ∆G is negative (if the free energy of the products is less than the free energy of the reactants).

For a reaction A + B <->C + D

Where ∆G= change in free energy, ∆G⁰ = standard free energy change (with 1 M reac­tants and products, at pH 7), R = gas constant, T = absolute temperature

At equilibrium, ∆G equals zero. Solving for ∆G⁰‘ yields the relationship at left.

K’_eq, the ratio [C][D]/[A][B] at equilibrium, is called the equilibrium constant.

The standard free energy change (∆G⁰‘) of a reaction may be positive and the actual free energy change (∆G) negative, depending on cellular concentrations of reactants and products. Many reactions for which ∆G⁰‘ is positive are spontaneous because other reactions cause depletion of products or maintenance of high substrate concentrations.

An equilibrium constant greater than one, (more products than reactants at equilibrium) indicates a spontaneous reaction (negative ∆G°’). Free energy changes of coupled reactions are additive.

Examples of different types of coupling:

Type 1:

Some enzyme-catalyzed reactions can be expressed in two coupled half-reactions, one spontaneous and the other non-spontaneous. The free energy changes of the half-reactions may be added, to yield the free energy of the coupled reaction.

For example, in the reaction catalyzed by the Glycolysis enzyme Hexokinase, the two half-reactions are:

ATP + H₂O <—> ADP + Pi

∆G⁰‘ = -31 kJoules/mol —> (1)

Pi + glucose <—> glucose-6-P+ H₂O

∆G°’ = +14 kJoules/mol —> (2)

Coupled reaction- (1) + (2)

ATP + glucose <—>ADP + glucose-6-P

∆G°’ = (-31 + 14) = -17 kJoules/mol

Type 2:

Two separate enzyme-catalyzed reactions occurring in the same cellular compart­ment, one spontaneous and the other non-spontaneous may be coupled by a common inter­mediate (reactant or product). For example, reactions involving pyrophosphates,

A + ATP <—> B + AMP + PP_i

∆G⁰‘ = +15 kJ/mol—> Enzyme 1

PP_i + H₂O <—> 2 P_i ∆G⁰‘ = -33 kJ/mol —> Enzyme 2

Overall reaction A + ATP+ H₂O <—> B + AMP + 2P_i ∆G⁰‘ = (+15-33) = -18 kJ/mol

Pyrophosphate (PP_i) is often the product of a reaction that needs a driving force. Its spontaneous hydrolysis, catalyzed by pyrophosphatase enzyme, drives the reaction for which PP_i is a product.

Type 3:

Active transport of ions through membrane is coupled to a chemical reaction, e.g., hydrolysis or synthesis of ATP, while the transports of an ion say A⁺ creates a potential dif­ference across the membrane.

The free energy change (electrochemical potential difference) associated with transport of an ion A⁺ across a membrane from side 1 to side 2 is represented as:

Where R = gas constant, T = temperature, Z = charge on the ion, F = Faraday constant, and ∆Ψ = voltage across the membrane.

Each of our cells has an electric potential associated with it. This potential, or voltage, helps to control the migration of ions across the cell membranes. A major example of electri­cal work is in the operation of the nerves. The nerves when get stimulated, they generate an electrical impulse called an action potential which can communicate information to the brain, or carry a signal from brain to a muscle to initiate its movement.

Since free energy changes are additive, the spontaneous direction for the coupled reac­tion will depend on the relative magnitudes of ∆G for the ion flux (∆G varies with the ion gradient and voltage) and ∆G for the chemical reaction (∆G⁰‘ is negative in the direction of ATP hydrolysis. The magnitude of ∆G also depends on the concentrations of ATP, ADP, and P_i).

Two examples of such coupling are:

a. Active Transport:

The membrane transport requires energy or ATP. The spontaneous ATP hydrolysis (negative ∆G) is coupled to (drives) ion flux against a gradient (positive ∆G).

b. ATP Synthesis:

It takes place in mitochondria, which is also known as the power house of the cell and where the synthesis of ATP occurs. The spontaneous H⁺ flux across a membrane (negative ∆G) is coupled to (drives) ATP synthesis (positive ∆G).