CHEMISTRY TEXTBOOK

If ∆H is the enthalpy change
accompanying a reaction (system) the
enthalpy change of the surroundings is -∆H.
With

∆Ssurr = - ∆H
T

(4.37)

Substituting above into Eq. (4.36),

∆Stotal = ∆S - ∆H
T

(4.38)

Thus ∆Stotal is expressed in terms of the
properties of the system only. Rearranging

T ∆Stotal = ∆H - T ∆S (4.39)

Substituting in Eq. (4.35)

∆G = - T ∆Stotal (4.40)

For a spontaneous reaction Stotal > 0 and
hence, ∆G < 0. At constant temperature and
pressure Gibbs energy of the system decreases
in a spontaneous process.

The second law leads to the conditions
of spontaneity which are summarised here.

i. ∆Stotal > 0 and ∆G < 0, the process is
spontaneous.

ii. ∆Stotal < 0 and ∆G > 0, the process is
nonspontaneous.

iii. ∆Stotal = 0 and ∆G = 0, the process is at
equilibrium.

4.11.7 Sponaneity and ∆H or ∆S

From ∆G = ∆H - T ∆S (at constant T
and P).

The temperature term determines relative
contributions of ∆H and ∆S to ∆G.

1. ∆H and ∆S are both negative then ∆G
   will be negative only when ∆H is more
   negative than T∆S. This is possible at low
   temperatures only.


2. ∆H amd ∆S both positive ∆G will be
   negative only if T∆S > ∆H. This is possible
   only at high temperatures.
   3. For ∆H negative and ∆S is positive it
   follows that ∆G is negative regardless of
   temperature.
   4. For ∆H positive and ∆S is negative then
   ∆G is positive regardless of temperature.
   Such reactions are nonspontaneous at all
   temperatures.
   4.11.8 Temperature of equilibrium
   For equilibrium
   ∆G = ∆H - T∆S gives

∴ T =

∆H

∆S^ (4.41)

T is the temperature at which the change

over from spontaneous to nonspontaneous

behavior occurs. ∆H and ∆S are assumed to

be independent of temperature in Eq. (4.41).

Introducing of temperature dependence of ∆H

or ∆S would not cause significant error for

the moderate temperature range.

4.11.9 Gibbs function and equilibrium

constant : Gibbs energy change for a chemical

reaction is given by

∆G = ∆G^0 + RT ln Q (4.42)

where ∆G^0 is standard Gibbs energy change

that is, the Gibbs energy change when the

reactants and products in a reaction are in their

standard states. Q is called reaction quotient Q

is analogus to that of the equilibrium constant.

and involves nonequilibrium concentrations or

partial pressures in case of gaseous reaction.

Consider

aA + bB cC + dD

∆G = ∆G^0 + RT ln Qc

= ∆G^0 + RT ln

[C]c[D]d

[A]a [B]b^ (4.43)

or ∆G = ∆G^0 + RT ln Qp

= ∆G^0 + RT ln

PCc×PDd

PAa× PBb^ (4.44)