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.

G^o_sys 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.G^o_sys cannot be measured directly. The more negative the value for G^o_sys, 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.

G^o_sys = H^o_sys– TS^o_sys

The sign of G^o_sysis T-independent when H^o_sysand S^o_syshave opposite signs. The sign of G^o_sysis T-dependent when H^o_sysand S^o_syshave the same signs.

When the reaction is spontaneous and the H^o_sys and S^o_sys have the same sign, G^o_sys=0

T = H^o_sys/S^o_sys

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 = [P_products]/[P_reactants]

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 = work_max is done by the system. For a non-spontaneous process, G= work_min 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.

G_rxn= nG_products mG_reactants

G values have properties like H values since both are state functions. G_f⁰ of an element in its standard state is zero.