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, q_surroundings = -q_system. 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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