- The second part is for the reaction at standard conditions. Again, that has
already been evaluated in Example 3.7, and is
S 2 326.7
KJ
- The third part is assumed to be zero:
S 3 0
KJ
The overall rxnSis the combination of the three:rxnS142.3 326.7 + 0
KJ
rxnS184.4
KJ
The effects of entropy are seen at a biological level, as well. The joining of
two single strands of RNA or DNA is accompanied by a small decrease in en-
thalpy (about 40 kJ/mol per base pair), as expected for hydrogen-bonding in-
teractions. There is also a nontrivial entropy change, about 90 J/molK per
base pair. Compare this value to the entropy of combustion in Example 3.9.
3.8 Summary
In this chapter, we have introduced a new state function: entropy. It will have
a unique impact on our study of thermodynamics. It is not an energy, like in-
ternal energy or enthalpy: it is a different kind of state function, a different
quantity. One way to think of it, as introduced by Boltzmann, is as a measure
of the number of states available to a system.
The definition of entropy ultimately brings us to an idea that we call the
second law of thermodynamics: that for an isolated system, any spontaneous
change occurs with a concurrent increase in the entropy of the system. The
mathematical definition of entropy, in terms of the change in heat for a re-
versible process, allows us to derive many mathematical expressions we can use
to calculate the entropy change for a physical or chemical process. The concept
of order brings us to what we call the third law of thermodynamics: that the
absolute entropy of a perfect crystal at absolute zero is exactly zero. We can
therefore speak of absolute entropies of materials at temperatures other than
0 K. Entropy becomes—and will remain—the only thermodynamics state
function for a system that we can know absolutely. (Contrast this with state
variableslike p,V,T, and n, whose values we can also know absolutely.)
We began this chapter with the question of spontaneity. Will a process oc-
cur by itself? If the system is isolated, we have an answer: it will if the entropy
increases. But most processes are not truly isolated. Many systems allow for en-
ergy to move in and out (that is, are closed, not isolated, systems). In order to
have a truly useful spontaneity test, we have to consider changes in energy as
well as changes in entropy. We will introduce such considerations in the next
chapter.
3.8 Summary 85