Reading Notes
for Chapter 16
These are Dr. Bodwin's reading notes for Chapter 16 of "Chemistry
2e" from OpenStax.
I am using a local .pdf copy that was downloaded in May 2020.
Chapter
Summary:
We've looked at quite a few rules and trends, but how do we know if a
chemical reaction actually happens?
Equilibrium gave us some clues when we looked at reaction quotients and
decided if a reaction had to shift toward products or reactants, but
equilibrium doesn't tell us the whole story. Back when we looked at Kinetics, we said that
much of chemistry could be divided into two "big picture" areas:
kinetics and thermodynamics. Now it's time for thermodynamics!
Thermodynamics is the study of energy change in chemical processes and
together with kinetics it tells us just about everything we need to
know about chemical systems.
Thermochemistry
vs. Thermodynamics:
Don't forget what you already know! Way back in Chapter 5, we looked at
Thermochemistry, the
study of the heat associated
with chemical reactions. We called this heat enthalpy and it was a good
introduction to thermodynamic quantities. The enthalpy change of a
chemical process tells us whether the process is endothermic or
exothermic, whether it absorbs heat or liberates heat. As we saw in a
number of examples, both endothermic and exothermic reactions can occur
spontaneously... that seems a little odd, because one might think that
and endothermic process which
requires heat would not happen
without some "help". There must be something else going on.
Thermochemistry review - if you're unsure about any of these topics, go
back and give them a read:
Heat capacity
Specific Heat
State Functions
Reaction Coordinate Diagrams
Enthalpy Change for a Reaction
Endothermic vs Exothermic
We also talked about some thermichemistry concepts in Chapter 10 when we looked
at phase changes and heating/cooling curves. Review that material as
well... it will make thermodynamics make a little more sense.
Spontaneous
vs Non-spontaneous Processes:
We know heat must have an influence
on the spontaneity of a chemical process, but it's not the only thing.
Ultimately, spontaneous processes are those which spread out energy
(and matter).
Your textbook makes a very important point that deserves to be repeated
- the thermodynamic spontaneity of a reaction is not a measure of the speed (or
rate) of a reaction. A spontaneous process can be fast or slow.
Kinetics and thermodynamics are separate.
Entropy:
Your textbook develops entropy in a rigorous mathematical way that
walks though some of the important history of entropy. The short
definition: entropy is a discription of the dispersal or disorder of a
substance or the change in
the dispersal or disorder in a chemical process.
A sponaneous process is one which tends toward more dispersed energy,
one with increasing entropy.
Laws of
Thermodynamics:
What's a law in science? Laws are descriptions of repeated (and
repeatable) observations that are accepted to be true. They are not
explanations, they don't answer "why". The Ideal Gas Law is a
description of how pressure, volume, temperature, and amount of a gas
are related, but there is no "why"... that's what Kinetic Molecular
Theory is for.
A useful tool in all of thermodynamics is the idea of defining a
"system". Once we define a system, everything outside of that system is
the surroundings. We saw this in thermochemistry... in an exothermic
process, heat moves from the system to the surroundings. Our ability to
define a system is a very powerful tool!
The system plus
the surroundings defines the "universe". In many cases, the "universe"
(in a thermodynamic sense) is actually the Universe, but if we can
sufficiently insulate a smaller portion from any outside influence, we
can define a "universe" on a smaller scale. Either way, it's another
very useful way to model thermodynamics.
The mathematical transformations on p.876 of your textbook are very important. The entropy of the
universe is always increasing (this is one of the few places that we
can legitimately use the word "always"). The entropy of the universe is
the sum of the entropy of the system and the entropy of the
surroundings. Measuring a well-defined system might not be that hard,
but how do you measure the entropy of the surroundings when the
surroundings is the rest of the Universe?!?! We're saved by a seemingly
simple little relationship, qsurroundings = -qsystem. That's the power of defining the
system! Now we have a way to look at the entropy of the universe by looking at only properties of the system!
Calculating Free Energy:
One nice thing about thermodynamics is that the changes in
thermodynamic quantities (enthalpy, entropy) are calculated the same
way, the sum of the products minus the sum of the reactants, as shown
on p.873 for entropy. It's the same way you calculated entropy change
way back in Chapter 5.
There are two main ways to do these calculations. Your textbook does
the standard "sum of the products minus sum of the reactants" method.
It's a good method. It works. It's reliable.It's a nice method to memorize so that you can "plug and chug" through calculations.
The other method is one that I tend to use more often, and is a little more conceptual and I describe it for enthalpy in Chapter 5. I'll repeat it here for entropy...
When you look up the standard entropy in a thermodynamic table, that
number represents the disorder that is "contained" in the substance. If
the substance is a reactant, then that entropy is lost
in the reaction you're looking at, so it can be represented as -(the
value from the table). If the substance is a product, then that entropy
is being gained by the
reaction you're looking at, so it can be represented by the number
taken directly from the table. Once you find all the individual
entropies for each reactant and product, add them up to get the entropy
of the reaction. A couple important points...
- The advantage to this method is that it doesn't matter what order
you add numbers together, you'll always get the same answer. If I can
avoid subtraction and division, I tend to do it.
- Another advantage is that this method makes us think about each
individual reactant or product and how their roles in the reaction
impact their contribution to the entropy of the reaction.
- Ultimately, this is just a math trick. Changing the sign of the
entropy value from the table for reactants and adding things up is
mathematically the same as subtracting reactants from products.
- Pick a method and stick to it!
Both methods work equally well and will give you the exact same answer
if used correctly. If you start to mix-and-match (like by changing sign
and subtracting...) things will go very bad very quickly. I don't really care which method you use.
If you prefer to memorize a formula, go for it and use the book method.
If that method doesn't really speak to you, try the second method. Both
get you to the correct answer, use the one that works for you.
Once you know {delta}H and {delta}S, you can use them to calculate {delta}G.
You can also calculate {delta}G directly from free enregy of formation
vlaues in a table of standard thermodynamic values. You use these the
same way you calculate {delta}H or {delta}S from tabulated values. If
you have no reason to calculate {delta}H and {delta}S, use this method
to calculate {delta}G. If you have to calculate {delta}S and {delta}H
anyway, use the other method. Both work.
NOTE: If you're ambitious and want to calculate {delta}G both
ways, you will likely notice that the two values are often slightly
different; you might get +67.15 from one method and +66.92 from the
other method. That's normal and is usually due to slightly different
rounding in the tabulated values. If you get +49.27 from one method and
-32.74 from the other method, double check your calculations... one of
them must be wrong.
Coupled Systems:
We can drive a non-spontaneous process by providing free energy from a
spontaneous process. This is exactly the same thing as the coupled
systems in Chapter 5 and 10.
Predicting Signs:
It's often helpful to predict the signs of {delta}S and {delta}G. Practice these with every probem that you do!
For {delta}S, consider these factors in this order:
- Phase change - Solids are the most ordered (least dispersed)
phase, gases are the least ordered (most dispersed) phase, liquids are
in between. Solutions have varying disorder (mostly depending upon the
states of matter of the solvent and solutes) that's somewhere in the
middle.
- Molecular complexity - if there are no differences in the phases of the reactants and products, a more complex molecule is usually
less ordered (more dispersed) than a less complex molecule due to
molecular flexibility and different equivalent orientations. This
includes atomic size... an iodide ion is more dispersed than a fluoride
ion. Don't make big predictions based upon subtle differences in what
you perceive as "molecular complexity".
- Number of pieces - if there are no differences in the phases of
reactants and products, and the molecule complexity seems similar,the side of the reaction with more "pieces" is less ordered (more dispersed) than the side of the reaction with fewer "pieces".
There's a really nice graphic in your textbook (Table 16.12 and 16.13) that can help predict the sign of {delta}G.
Non-standard Conditions:
When we are not at "standard conditions", we can still use {delta}G to
determine whether a reaction is spontaneous or non-spontaneous. Rather
than starting from scratch, we just add a "correction" to the standard
{delta}G as shown at the bottom of p.883 of your textbook. This
"correction" uses the reaction quotient, Q. At standard conditions, all
solution concentrations are 1 M, so if a system is at standard conditions, Q=1, and log(1)=0, so the correction term mathematically disappears.
Equilibrium:
We said that equilibrium was a thermodynamic quantity, so it makes
sense that it should be related to {delta}G. We often think of {delta}G
as the "driving force" of a reaction. When a reaction is at
equilibrium, the rate of the forward reaction is equal to the rate of
the reverse reaction - the reaction is not being "driven" in either
direction, so {delta}G=0. That gives us an expression that relates the
equilibrium constant to {delta}G. (p.884 of your textbook)
Thinking about our various descriptors, this relationship makes
sense... if a reaction is "spontaneous" as written, it should be
"product-favored" when it reaches equilibrium.
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