Burdge/Overby, Chemistry: Atoms First, 2e Ch14 | Page 9

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CHAPTE R 14? Entropy and Free Energy

Qualitatively Predicting the Sign of ????S°
sys
Equation 14.5 enables us to calculate ?S° for a process when the standard entropies of the prodrxn
ucts and reactants are known. However, sometimes it’s useful just to know the sign of ?S° .
rxn
Although multiple factors can influence the sign of ?S° , the outcome is often dominated by a
rxn
single factor, which can be used to make a qualitative prediction. Several processes that lead to an
increase in entropy are
• Melting
• Vaporization or sublimation
• Temperature increase
• Reaction resulting in a greater number of gas molecules

Number of molecules

When a solid is melted, the molecules have greater energy and are more mobile. They go from
being in fixed positions in the solid, to being free to move about in the liquid. As we saw in the
discussion of standard entropy, this leads to many more possible arrangements of the molecules
and, therefore, greater entropy. The same rationale holds for the vaporization or sublimation of a
substance. There is a dramatic increase in energy/mobility, and in the number of possible arrangements of a system’s molecules when the molecules go from a condensed phase to the gas phase.
Therefore, there is a much larger increase in the system’s entropy, relative to the solid-to-liquid
transition.
When the temperature of a system is increased, the energy of the system’s molecules
increases. To visualize this, recall from the discussion of kinetic molecular theory that increasing the temperature of a gas increases its average kinetic energy. This corresponds to an increase
in the average speed of the gas molecules and a spreading out of the range of molecular speeds.
[See Figure 11.4(a).] If we think of each of the possible molecular speeds within the range as a
discrete energy level, we can see that at higher temperatures, there is a greater number of possible
molecular speeds and, therefore, a greater number of energy states available to the molecules in
the system. With a greater number of available energy states, there is a greater number of possible
arrangements of molecules within those states and, therefore, a greater entropy.

Lower temperature

Higher temperature

Molecular speed
Range of possible molecular speeds at lower temperature
Range of possible molecular speeds at higher temperature

Multi 14.1
Animation: Factors that influence the
entropy of a system

bur11184_ch14_570-603.indd 578

Because the entropy of a substance in the gas phase is always significantly greater than its entropy
in either the liquid or solid phase, a reaction that results in an increase in the number of gas
molecules causes an increase in the system’s entropy. For reactions that do not involve gases,
an increase in the number of solid, liquid, or aqueous molecules also usually causes an entropy
increase.
By considering these factors, we can usually make a reasonably good prediction of the sign
of ?S° for a physical or chemical process, without having to look up the absolute entropy values
rxn
for the species involved. Figure 14.4 (pages 580–581) summarizes the factors that can be used to
compare entropies and illustrates several comparisons.
In addition to melting, vaporization/sublimation, temperature increase, and reactions that
increase the number of gas molecules, which can always be counted upon to result in an entropy
increase, the process of dissolving a substance often leads to an increase in entropy. In the case
of a molecular solute, such as sucrose (sugar), dissolving causes dispersal of the molecules (and
consequently, of the system’s energy) into a larger volume—resulting in an increase in entropy.
In the case of an ionic solute, the analysis is slightly more complicated. We saw in our discussion of solution formation [9 Section 13.2] that the dissolution of ammonium nitrate (NH4NO3)
is spontaneous, even though it is endothermic, because the system’s entropy increases when the

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