Standard Gibbs Energy Change and Equilibrium Constant

Gibbs free energy can be defined as the potential that measures the process obtained from a thermodynamic system at constant pressure and temperature. 

As in mechanics, potential energy is defined as the capacity to do work similarly in Thermodynamics. Gibbs energy is a capacity of a system to do non-mechanical work, and Delta G measures the non-mechanical work done.

         G = H−TS

Here G = Gibbs free energy

         H = enthalpy 

         T = temperature 

         S = Entropy 

The Gibbs free energy is the maximum amount of non-expansion work done by a closed system; this maximum can be obtained only by a completely reversible thermodynamic process. In a reversible reaction, Where the initial state is wholly turned to A final state, the Gibbs free energy is equal to the work exchange by the system with the surrounding minus the work of the forces. Gibb’s free energy reduces once the chemical reaction reaches its equilibrium.

Standard Gibbs free energy(ΔGo)  can be defined as the quantity that gives the Gibbs free energy at Standard experimental conditions.

The standard conditions are

• Gases:  at 1 atm partial pressure
•  pure liquids:  liquid under 1 atm pressure
•  solute:  concentration of 1 M
•  Solids: a pure solid under the pressure of 1 atm. 

The standard Gibbs free energy of change of a particular compound is its change in Gibbs free energy of one mole at a standard temperature and pressure.

As most of the reactions don’t occur at an ideal condition, a simple formula is used to determine Gibb’s free energy change.

ΔG°(reaction) = ΣGƒ°(products) − ΣGƒ°(reactants)

To calculate the standard Gibbs free energy of any particular compound, we still need to know the standard enthalpy, standard entropy and the temperature of the species which are reacting with each other to form the product. Then the formula can be deduced as

ΔGƒ° = ΔHƒ° − TΔSƒ°,

The traditional values of Entropy and enthalpy, are calculated for every particular compound at the standard temperature 298 K and the standard pressure of 1 atm. These values are available in a tabulated form, including the standard Gibbs free energy calculated by Substituting the respective values.

A clear note should be taken that the standard Gibbs free energy of formation of any element is 0 as there is no change of enthalpy or entropy.

Change in entropy and enthalpy have a particular sign convention according to the reactions taking place, and this plays an essential role in determining the standard Gibbs free energy.

So < 0 or -ve: Change in entropy is negative when disorderliness in a reaction decreases.

So > 0 or +ve: Change in entropy is positive when disorderliness in a reaction increases.

Ho < 0 or -ve : Exothermic reaction. 

Ho > 0  or +ve : Endothermic reaction.

Ho is negative, and So is positive Gois therefore negative, and any reaction that has a negative Go is a spontaneous reaction.

WhenHo is positive So and negative, Go is therefore positive and is a non-spontaneous reaction.

When Go is positive, it is an endergonic reaction.

When Go is negative, it is an exergonic reaction. 

It is seen that the reaction favoured by both enthalpy and entropy is mostly the favoured reaction. There is no need to calculate whether this type of reaction should proceed for others or know the same goes when the reaction is not favoured by both enthalpy and entropy.

The sign of Go tells the direction in which direction the equilibrium has to shift in a reaction, And the magnitude of Go tells us how far the reaction is going to take place. That is, the larger the Go value, the further the reaction should move to reach equilibrium.

Effect of Temperature on the Standard Free Energy of a Reaction

The equation used to calculate the standard free energy of a reaction clearly states that temperature is one of the main components to be known to calculate free energy.

So, according to the equation, when the temperature rises, the entropy also increases. Therefore, if the entropy is less or the temperature is less, ultimately it will lead to an unfavourable reaction or a non-spontaneous reaction. 

The Relationship Between Standard Gibbs Free energy and Equilibrium Constant 

When a reaction does not take place in a standard state due to a change in the ratio of the concentration of the product to the reactant, we have to calculate the system free energy in a non-standard state.

The main difference between standard Gibbs free energy and free energy is that for any given reaction, there is only one Go value at a given standard temperature and an infinite number of values are possible for G.

To understand the relationship between standard Gibbs free energy and equilibrium constant we are taking a graph that is plotted between  G and the logarithm to the base e of the reaction quotient for the reaction of formation of ammonia.

N2(g) + 3 H2(g) 2 NH3(g)

  As the left side of the x-axis shows negative smaller values on the right side show a positive small available, and in the y-axis, the above show the positive values, and below shows the negative value.

 When the value of G  is negative and smaller, it shows that the reaction has to move further to reach equilibrium because the concentration of the reactants is more than the products to reach the state of equilibrium, it must shift right, when the value of G is larger and negative. The reaction shows that the concentration of product is more than the reactants to reach the state of equilibrium, it must shift left.

Points of intersection on the x-axis and y-axis play an important role.

 the point at which the straight line crosses the x-axis, the reaction quotient for the system is equal to 1. At this point, the value of at this point is equal to the standard Gibbs free energy of a reaction.

When Qp = 1: G = Go,

The Point at which the straight line crosses the y-axis explains that the system for whichG is equal to zero because there are no driving forces behind the reaction, and it is said that at this point, the reaction is at equilibrium.

When  Qp = Kp:  G = 0,

The relationship between Gibbs free energy of a reaction at any moment in time and standard Gibbs free energy of reaction as the following

G = Go + RT ln Q

Here, R = ideal gas constant 8.214 J/mol K

T = temperature in K

Q = the reaction quotient of that moment in time

When is G equal to zero we know that the reaction is at equilibrium so Q = K.

Then the equation is, 0 = Go + RT ln K

Hence the relationship between change in standard Gibbs free energy and equilibrium constant is 

 Go = – RT ln K

The above  Equation allows us to calculate the change in standard free energy and the equilibrium constant when one of the values is given and vice versa.

The equilibrium constant can be expressed in two ways one is Kc and Kp, Kp represents partial pressures of the reactants and products, and Kc is based on the concentration.

Equilibrium constants are not always constant values because they change with temperature. With the change in temperature, the equilibrium constant changes. 

Conclusion

Standard Gibbs free energy plays an important role in most biochemical processes in living beings. As we know, every reaction is complete only when it reaches its equilibrium state in a biochemical process and is defined by the formulas given for the change in standard Gibbs free energy.

In this article, we discuss the Gibbs free energy, standard Gibbs free energy, and how standard Gibbs free energy is related to the equilibrium constant.