# Gibb’s energy change

Chemical Thermodynamics: Gibb’s energy change

The speed at which a reaction takes place is associated with its kinetics, however, the spontaneity of a reaction is an indication towards whether it is thermodynamically favored or not. A spontaneous process is those that occur under a specific set of conditions without any outside intervention. While non-spontaneous processes do not occur under a specific set of conditions. A non-spontaneous reaction will only take place when work is done on it.

A reversible process can be changed in either direction by an infinite small change in a variable and thereby produce maximum work. However, under real conditions, work is performed irreversibly; thus, maximum work is not obtained and some free energy is lost to the surroundings as heat. Likewise, a reaction at equilibrium cannot do work.

The Gibbs free energy is defined as the energy readily available to perform work. It will tell us if a reaction will occur or not but it can not tell how fast a reaction will occur.

Gosys is the change in free energy that will occur if the reactants in their standard states are converted to the products in their standard states.Gosys cannot be measured directly. The more negative the value for Gosys, the reaction will move to the right-hand side to achieve equilibrium because equilibrium is the lowest possible free energy position for a reaction.

The Gibbs free energy can be expressed in terms of enthalpy and entropy. It refers only to the system but it can be used to predict spontaneity.

Gosys = Hosys– TSosys

The sign of Gosysis T-independent when Hosysand Sosyshave opposite signs. The sign of Gosysis T-dependent when Hosysand Sosyshave the same signs.

When the reaction is spontaneous and the Hosys and Sosys have the same sign, Gosys=0

T = Hosys/Sosys

Figure 1: Predicting the sign of G

Spontaneity can change when the temperature changes. Temperature and spontaneity are not necessarily correlated.

Under standard conditions (1 M concentrations, 1 atm for gases), Q = 1 and ln Q = 0. Therefore:

G = G° + RT ln Q

• G = non-standard free energy
• G° = standard free energy (from tables)
• R = 8.314 J/K·mole
• T = temp in K
• Q = reaction quotient

At equilibrium, G = 0 and Q = K. The equation becomes:

0 = G° + RT ln K

or

G° = – RT ln K

R = Universal gas constant = 8.314 J/K mol

T = Temperature in Kelvin

K = Equilibrium constant = [Pproducts]/[Preactants]

The system is at equilibrium (no net movement) when,

G°= 0 (K = 1)

If the system is NOT at equilibrium, use q instead of K

## Relationship Between K and ΔG°

Figure 2: Relationship between K and G°

For a spontaneous process, G = workmax is done by the system. For a non-spontaneous process, G= workmin is done to the system for the process to occur.

Since free energy is a state function, it can be calculated from the table of standard values just as enthalpy and entropy changes.

Grxn= nGproducts mGreactants

G values have properties like H values since both are state functions. Gf0 of an element in its standard state is zero.