20.1. Entropy http://www.ck12.org
What Is Entropy?
At its most basic level,entropy(S) is a measure of probability. States that have a high probability of occurring by
random chance have a high entropy value, and states that are unlikely to occur by random chance have a low entropy
value. There is a natural tendency for things to increase in entropy over time. An equivalent statement is that nature
will spontaneously move toward the states that have the highest probability of existing.
Entropy can also be thought of as the number of possible arrangements that lead to a certain state. The more ways
that a given state can be achieved, the greater the probability of finding that state, and the higher its entropy value.
For example, think about the objects in your bedroom. Imagine every item being randomly placed at some location
within the room. Now imagine this happening again and again. How many of the resulting arrangements would lead
you to classify your room as "messy?" How many would qualify as a "clean" room? In this hypothetical example,
every state has an equal possibility of happening, but because there are so many more ways to arrange items to make
a messy room than a clean room, the "messy" state would have a higher entropy value than the "clean" state.
There are many examples in the chemical world of changes in entropy. Phase transitions are one obvious example.
When a substance makes a transition from the liquid state to the gaseous state, the particles have many more possible
arrangements, because they are no longer confined to a specified volume in which they are close to each other; gas
particles can move freely throughout their container. Vaporization represents an increase in entropy. In the opposite
direction, a liquid loses entropy when it freezes to a solid. Because solids have very ordered structures, there are
fewer possible arrangements of particles that would result in the properties associated with a solid.
The Second Law of Thermodynamics
Recall that, according to the first law of thermodynamics, the total amount of energy in the universe is conserved for
any given process. Entropy is not conserved; in fact, it is always increasing. Nature is constantly moving from less
probable states to more probable ones. Thesecond law of thermodynamicsstates that the entropy of the universe
will increase for any spontaneous process.
To determine whether a given process is spontaneous, it is often helpful to break down the total entropy change as
follows:
∆Suniv=∆Ssys+∆Ssurrwhere∆Ssysand∆Ssurrrepresent the changes in entropy that occur in the system and in the surroundings, respec-
tively.
To predict whether a given reaction will be spontaneous, we need to know the sign of∆Suniv. If∆Sunivis positive,
the entropy of the universe increases, and the reaction is spontaneous in the direction that it is written. If∆Sunivis
negative, the reaction is spontaneous in the reverse direction. If∆Sunivis equal to zero, the system is at equilibrium.
To predict whether a reaction is spontaneous, we need to determine the entropy changes in the system and in the
surroundings.
Entropy of a System (∆Ssys)
Let’s consider the change of state for one mole of water from liquid to gas:
H 2 O(l)→H 2 O(g)In this case, the water is the system, and the surrounding are everything else. How does the entropy of the water
change in this process? As we saw earlier, the vaporization process leads to an increase in entropy, because there