Concise Physical Chemistry

c05 JWBS043-Rogers September 13, 2010 11:25 Printer Name: Yet to Come

ENTROPY 73

but restoring the system entropy to its original state. Because of this necessity, some

of the heat drawn from the hot reservoir in an irreversible cycle isunavailableto do

work.

5.1.1 Heat Death and Time’s Arrow

Because there is always heat transferred to the surroundings in an irreversible cycle,

the entropy of the system plus the surroundings always increases. If we take the

universe as the surroundings, then since all real processes are irreversible we have

a consequence of the second law:The entropy of the universe tends to a maximum.

When the universe has reached its maximum entropy, no more irreversible change

will be possible. The driving force of change will be gone. This is called theheat

deathof the universe. In case you are worried, it is calculated to be in the far distant

future.

The entropy of the universe must be greater after an irreversible change has

occurred than it was before the change, so we have a thermodynamic definition of

the direction of time (which the first law doesn’t give). Time must go from before

the change to after the change; it cannot go in the reverse direction.^1 Entropy is

sometimes called “time’s arrow.”

5.1.2 The Reaction Coordinate

Prigogine has defined areaction coordinateξwhich progresses as a chemical reaction

takes place. Starting with pure reactant A, the reaction coordinate increases as product

B is produced:

A→B

At some point, the time derivative ofξbecomes zero and the reaction stops insofar as

macroscopic concentration measurements are concerned.^2 When the time derivative

of the reaction coordinate is zero, the system consisting ofnA+nBis at equilibrium.

Because there are no macroscopic concentration changes, the ratio of the mole num-

bers of reactant and productnB/nAis constant. It is called theequilibrium constant

Keq:

(

∂ξ

∂t

)

T,p

= 0

Keq=nB/nA

It would be appealing to think that the reaction coordinate is determined solely by

the energyUor enthalpyHof the system flowing from a high level to a low level,

(^1) Classical thermodynamics does not include QED.
(^2) There are microscopic exchanges between species A and B, but they are equal and opposite on average
so they do not bring about measurable concentration changes.