The Foundations of Chemistry

are more highly ordered than in the gaseous state. Thus, the entropy of any substance

increases as the substance goes from solid to liquid to gas (Figure 15-11).

If the entropy of a system increases during a process, the spontaneity of the process is

favored but not required. The Second Law of Thermodynamics says that the entropy of

the universe(not the system) increases during a spontaneous process, that is,

Suniverse
Ssystem
Ssurroundings 0 (spontaneous process)

Of the two ideal gas samples in Figure 15-12, the more ordered arrangement (Figure

15-12a) has lower entropy than the randomly mixed arrangement with the same volume

(Figure 15-12b). Because these ideal gas samples mix without absorbing or releasing heat

and without a change in total volume, they do not interact with the surroundings, so the

entropy of the surroundings does not change. In this case

Suniverse
Ssystem

If we open the stopcock between the two bulbs in Figure 15-12a, we expect the gases to

mix spontaneously, with an increase in the disorder of the system, that is, 
Ssystemis posi-

tive.

unmixed gases88nmixed gases 
Suniverse
Ssystem 0

We do not expect the more homogeneous sample in Figure 15-12b to spontaneously

“unmix” to give the arrangement in Figure 15-12a (which would correspond to a decrease

in 
Ssystem).

mixed gases88nunmixed gases 
Suniverse
Ssystem 0

The ideas of entropy, order, and disorder are related to probability. The more ways an

event can happen, the more probable that event is. In Figure 15-12b each individual red

molecule is equally likely to be in either container, as is each individual blue molecule. As

a result, there are many ways in which the mixed arrangement of Figure 15-12b can occur,

so the probability of its occurrence is high, and so its entropy is high. In contrast, there

is only one way the unmixed arrangement in Figure 15-12a can occur. The resulting prob-

ability is extremely low, and the entropy of this arrangement is low.

The entropy of a system can decrease during a spontaneous process or increase during

a nonspontaneous process, depending on the accompanying 
Ssurr. If 
Ssysis negative

Figure 15-11 As a sample changes
from solid to liquid to gas, its
particles become increasingly less
ordered (more disordered), so its
entropy increases.

622 CHAPTER 15: Chemical Thermodynamics

Solid

Liquid Gas

Increasing disorder

Increasing entropy, S

(a) Stopcock closed

(b) Stopcock open

Figure 15-12 (a) A sample of gas
in which all molecules of one gas are
in one bulb and all molecules of the
other gas are in the other bulb. (b) A
sample of gas that contains the same
number of each kind of molecule
as in (a), but with the two kinds
randomly mixed in the two bulbs.
Sample (b) has greater disorder
(higher entropy), and is thus more
probable.