BioPHYSICAL chemistry

50 PARTI THERMODYNAMICS AND KINETICS

the system are exactly matched by corresponding oppo-

site changes in the entropy of the surroundings.

For a process that occurs at constant pressure, the heat

flow is equal to the change in enthalpy (eqn 3.6), and

the entropy change of the surroundings can be written

in terms of enthalpy:

(3.9)

Thus, if the process is exothermic,ΔHisnegati 9 e andΔSsur

ispositi 9 e, and the process is spontaneous.The entropy of

the surroundings increases when heat is released. This conclusion is

critical for understanding chemical equilibrium and will be used in the

formulation of the Gibbs energy, below.

If the change in the system is irreversible, the entropy change is not zero.

To determine the entropy change for an irreversible process, consider as an

example the isothermal expansion of an ideal gas against afixed pressure,

Pf(Figure 3.3). The value of fixed pressure is poised to be equal to the

final pressure of the gas after the expansion is completed. In this case,

the work performed is given by the product of the change in 9 olume,ΔV,

and the pressure, which is expressed using the ideal gas law:

(3.10)

Ideal gas law:

The work performed in this irreversible process is different from what

was determined for a reversible process (eqn 3.3):

(3.11)

For example, if the final volume is twice the initial volume, Vf= 2 Vi, then

the work is calculated to be −0.5nRTand −0.693nRTfor the irreversible

and reversible, respectively. Since these are isothermal ideal gases, q=−w

and the entropy change can be related to the work:

wnRT

V

V

f

i

=− ln

P

nRT

V

=

wPV

nRT

V

VnRT

V

f ffV

=−ΔΔ=− =−

Δ

Δ

Δ

S

H

sur T

=−

Δx

Pex  Pf

Irreversible

expansion

Vi

Vf

Figure 3.3
The irreversible
expansion for an
ideal gas with the
external pressure,
Pex, fixed to the
pressure, Pf.