CHEM-GUIDE: Gibb's free energy and prediction for the feasibility of reaction

Free energy of a system is defined as the maximum amount of energy available to a system during a process that can be converted into useful work. In other words it is a measure of capacity of a system to do useful work. It is denoted by symbol G and is given by

G = H-TS

where H is the enthalpy of the system, S is its entropy and T is the absolute temperature.

Now, H = E + PV

G = E + PV- TS

Free energy change

The change in free energy may be expressed as

DG = DE + D(PV) - D(TS)

If the process is carried out at constant temperature and pressure, the terms D(PV) and D(TS) becomeD(PV) = PDV and D(TS) = TDS

DG = DE + PDV - TDS

But DE + PDV = DH

or DG = DH - TDS ….(1)

This equation is called Gibbs-Helmholtz equation and is very useful in predicting the spontaneity of a process.

Free energy change for predicting feasibility of a reaction

It has already been seen that the total entropy change, DS_t_o_t_a_l determines the spontaneity of a process. The total entropy change during a process is given by

DS_t_o_t_a_l = DS_s_y_s_t_e_m + DS_s_u_r_r_o_u_n_d_i_n_g_s ….(2)

If the reaction is carried out at constant temperature and pressure, heat involved is equal to enthalpy change,

q_s_y_s_t_e_m = DH_s_y_s_t_e_m

Now, if a reaction is conducted at constant temperature and pressure, and heat (q) is given out to the surroundings reversibly, then,

(q_p)_s_u_r_r_o_u_n_d_i_n_g_s = - q_s_y_s_t_e_m = - DH_s_y_s_t_e_m

The entropy change of the surroundings is:

(q_p)_s_u_r_r_o_u_n_d_i_n_g_s - DH_s_y_s_t_e_m ….(3)

DS_s_u_r_r_o_u_n_d_i_n_g_s = T = T

Substituting equation 3 in equation 2, we get

Multiplying both sides by T,

TDS_t_o_t_a_l = TDS_s_y_s_t_e_m - DH_s_y_s_t_e_m

- TDS_t_o_t_a_l = DH_s_y_s_t_e_m - TDS_s_y_s_t_e_m

From Equation1, D H - TDS = DG

DG_s_y_s_t_e_m = - TDS_t_o_t_a_l

It has been shown that for spontaneous chemical changes, DS_t_o_t_a_l is positive so that DG = -ve for spontaneous chemical changes.

Thus, the spontaneity of a chemical change can be predicted either by

(i) TDS system = +ve or

(ii) DG = -ve.

The use of Gibbs free energy change has the advantage because it refers to system only whereas in considering entropy criteria, the system as well as the surroundings are to be considered.

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Predicting spontaneity of a process in terms of DG

The free energy change, DG provides the overall criterion for the feasibility of a chemical process. It gives the balance of the two tendencies, DH and TDS as:

DG = DH - TDS

Even, if the reaction is not favored energetically (endothermic reaction), the driving force may be provided by a favorable change in entropy. It can be shown that only those processes are spontaneous or feasible in which free energy undergoes a decrease For e.g., DG is negative. By calculating DH and TDS and hence DG, it can be easily predicted whether reaction is spontaneous or not.

1) When energy and entropy factors are favorable, for instance, DH is negative and TDS is positive, thenDG must be negative.

For e.g., DG = (-) - (+) = -ve. Thus, DG is negative for a spontaneous process.

2) If both the tendencies oppose, for instance, DH is positive and TDS is negative, then DG is positive.

For e.g., DG = (+) - (-) = +ve. Thus, DG is positive for a non spontaneous process.

3) If both the tendencies are equal and opposite, for instance, if DH is positive (unfavorable) and TDS is also positive (favorable) or vice-versa and both are of equal magnitude, then DG becomes zero. At this stage, the process does not proceed in both direction and the reaction, is said to be in equilibrium state.

In short, it can be stated

i) if DG is negative, the process is spontaneous.

ii) if DG is zero, the process is in equilibrium state. There is no net reaction in either direction.

iii) if DG is positive, the process does not occur in the forward direction. It may, however, go in the reverse direction.

Thus, if a change is to be spontaneous in the forward direction, DG must be negative.

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Conditions for spontaneity of a process or DG to be negative

DG would be negative under the following conditions:

i) Both the energy and the entropy factors are favorable and may have any magnitude, For e.g., DH is negative and TDS is positive.

ii) When energy factor favors the change (DH = -ve), but entropy factor opposes the change (TDS = -ve), then the magnitude of DH should be more than that of TDS. DH(-ve) > TDS(-ve)

iii) When energy factor is not favoring (DH = +ve) but entropy factor favors the change (TDS = + ve), then the magnitude of TDS should be more than that of the energy factor TDS (+ve) > DH (+ve).