### Video Transcript

For which of the following
reactions will the entropy of the system decrease? A) CACO₃ solid reacting to form CaO
solid plus CO₂ gas. B) CO₂ solid reacting to form CO₂
gas. C) 4PCl₃ gas reacting to form P₄
gas plus 6Cl₂ gas. D) N₂ gas plus 3H₂ gas reacting to
form 2NH₃ gas. Or E) None of the other answers are
correct.

The entropy of a system has to do
with the number of microscopic configurations that are available to the system given
its properties, such as its current, its pressure, temperature, or energy. These microscopic configurations or
microscopic arrangements of our system are called microstates. If a system has more microstates,
that means it will have higher entropy. This definition of entropy is a
little abstract. So let’s take a look at some
examples.

Let’s compare two different
systems. In one, we have a substance that is
a solid. And in the other, we have a
substance that is a gas. Both of these systems have the same
number of particles. We want to determine which of these
systems will have a higher entropy. Which we know is related to the
number of microscopic configurations or arrangements of these particles. Whichever one has a greater number
of arrangements will have a greater entropy. For the substance that is a gas, we
can arrange the particles in the container pretty much however we want and the
system will still be a gas. Each of these different
arrangements or configurations that I’ve drawn are called microstates. I have drawn but a few for our
system of seven gas particles. But we could certainly imagine many
more.

For a real system of gas particles,
which would have about one mole of particles, that system would have about 10 to the
10 to the 23 microstates. Which is a mind bogglingly huge
number of microstates. We can arrange the particles of the
gas almost however we went to in a container. And that substance will still be a
gas. This means that a gas will have
many microstates. A solid, in comparison, will have
far fewer microstates because there’s fewer ways that we can arrange the particles
where that substance will still be a solid. After all, solids have to be stuck
together to be a solid, which isn’t true for a gas. Since, in general, gases have more
microstates available to them than solids do and since more microstates mean more
entropy, gases will have greater entropy than solids do.

We can use this information to
create a general rule of thumb to help us decide which substances will have more
entropy than others. The entropy of a gas will be the
greatest, followed by the entropy of an aqueous solution. Which will be greater than the
entropy of a liquid, leaving the entropy of the solid as the smallest. Now that we know, in general, what
substances will have greater entropy than others, let’s think of a process where we
have a change in entropy. Such as a change where we go from a
solid to a gas, like in answer choice B, the sublimation of CO₂.

The change in entropy for this
process would be the entropy of the gas minus the entropy of the solid. Since the entropy of a gas is
generally greater than the entropy of a solid, we would expect this process to have
a positive change in entropy. I do want to note one more time
that we’re using a rule of thumb here to guess the sign for the change in entropy
for our system. We can’t guarantee that every time
a system goes from a solid to a gas, it will have a positive change in entropy. This rule of thumb, however, is
really great for solving these types of problems and will get you in the right
ballpark most of the time.

Now that we understand a little bit
about entropy and how to determine if a reaction will have a positive or negative
change in entropy, let’s return to our question. This question is asking us to
determine which reaction will have a decrease in the entropy of the system. So we’re looking for a reaction
where the change in entropy will be negative. So let’s take a look at our first
answer choice. Here we have one mole of a solid
forming a mole of a solid and a mole of a gas. Since we’re forming a gas in the
products and we have no gaseous reactants, we would expect that this process would
have a positive change in entropy. Since gases, in general, have much
more entropy than solids do.

Since we’re looking for a reaction
where the entropy change for the system will be negative, answer choice A is not the
right answer. We used answer choice B as our
example. As we’ve already discussed, we
would expect this process to have a positive change in entropy because a gas has
more entropy than a solid does. In our third answer choice, all of
our products and reactants are gaseous. In our reactants, we have four
moles of gas. And in our products, we have seven
moles of gas. Since we have more moles of gas in
the products and gases have so much entropy, we would expect that the entropy change
for this process would be positive. Again, we’re looking for a decrease
in entropy. So answer choice C is not
correct.

In answer choice D, both our
products and our reactants, again, are all gaseous. But this time, we start off with
four moles of gas, and we form two moles of gas. Since the number of moles of gas is
decreasing, we would expect the entropy of this reaction to be negative. That means that answer choice D is
the answer we’re looking for. This reaction would have a decrease
in the entropy of the system.