Reading Notes for Chapter 14

These are Dr. Bodwin's reading notes for Chapter 14 of "Chemistry 2e" from OpenStax. I am using a local .pdf copy that was downloaded in May 2020.

Chapter Summary:

Acids and bases have a number of "special" behaviors and definitions, but the key to understanding acids and bases is to realize that they are just equilibria applied to a specific set of substances under some restricted conditions. Because acid-base chemistry is the basis of much of what we call life, this chemistry has been studied in a variety of ways under a variety of conditions and can be described and understood from a number of different perspectives.

Definitions:

As we've seen with a few different topics, acids and bases have a couple different "levels" of definition.

Definition:	An acid is:	A base is:
Arrhenius	An H⁺ donor or A substance which when dissolved in water causes the H⁺ (or H₃O⁺) concentration to increase	An OH^- donor or A substance which when dissolved in water causes the OH^- concentration to increase
Bronsted-Lowry	An H⁺ donor	An H⁺ acceptor
Lewis	An electron (pair) acceptor	An electron (pair) donor

Acids are all about H⁺, but when H⁺ is dissolved in water (a polar molecule), it tends to associate with a water molecule to form H₃O⁺. This terminology will likely flip back and forth pretty freely, especially if you look at different resources. For our purposes, we can probably think about H⁺, H⁺(aq), H₃O⁺, and H₃O⁺(aq) as all describing the same thing.

The Arrhenius definitions are the most restrictive, so although those definitions are included here, we will focus on the Bronsted-Lowry definitions for most of our discussion. Once we understand acids and bases a little better with the Bronsted-Lowry (B-L) definitions, the Lewis definitions are actually the most general and broadly useful.

NOTE: State labels are always important and informative, but state labels are especially inportant when looking at acid-base reactions. Many of the conditions and simplifying assumptions we make with acids and bases are absolutely dependent upon the state of the reactants and products, so it is critical to include state labels.

Conjugate Pairs:

Whenever we're looking at an acid-base reaction (B-L), we can always identify conjugate pairs. A conjugate pair is two chemical species that differ only by a single H⁺. The half of the pair that has the H⁺ is the conjugate acid, and the half of the pair that is missing the H⁺ is the conjugate base. Practice identifying conjugate acid/conjugate base pairs in acid-base reactions. For an acid in water, we can look at the reaction:

HA(aq) + H₂O(l) <=> H₃O⁺(aq) + A^-(aq)

In this reaction, HA(aq) is a (conjugate) acid, and its conjugate base is A^-(aq).
In this reaction, H₂O(l) is a (conjugate) base, and its conjugate acid is H₃O⁺(aq).
Similarly, for a base in water, we can look at the reaction:

B(aq) + H₂O(l) <=> OH^-(aq) + HB⁺(aq)

In this reaction, B(aq) is a (conjugate) base, and its conjugate acid is HB⁺(aq).
In this reaction, H₂O(l) is a (conjugate) acid, and its conjugate base is OH^-(aq).

Autoionization of Water:

Looking at the 2 reactions above, a question hopefully popped into your head... Is water an acid or is water a base? The answer is: BOTH! Although we don't often explicitly state it, the definitions of acids and bases are relative definitions: an acid donates H⁺ only if there's a something to accept that H⁺; similarly, bases are only bases when they're reacting with acids.
In the case of water, it has H⁺ to donate to become OH^-, but it can also accept an H⁺ to form H₃O⁺. Water reacts with itself by the autoionization reaction:

H₂O(l) + H₂O(l) <=> H₃O⁺(aq) + OH^-(aq)

This is one of the properties of water that make it the foundation of life on earth. Because water can act as both acid and base, the strength of other acids and bases are moderated when they are dissolved in water.
Autoionization of water is a special equilibrium, and as such it gets its own "letter" for the equilibrium constant, K_w. Although K_w refers to a specific chemical reaction and a specific equilibrium constant, remember that it is still an equilibrium and follows all the same rules and behaviours as any other equilibrium. Don't make it something completely new and unique.

K_w = [H₃O⁺]_eq[OH^-]_eq

This means that for water or any reasonable dilute aqueous solution, we can always relate the concentration of hydronium ions to the concentration of hydroxide ions by K_w. As long as we know one, we know the other.
For pure water at 25°C, K_w = 1x10^-14. If the temperature changes, the value of K_w changes, but unless you are given information to let you find or calculate a different K_w value, use 10^-14.
For pure water, [H₃O⁺]_eq = [OH^-]_eq = 10^-7. {Go ahead and set up an equilibrium table to prove that to yourself...}

pH and pOH:

Because the concentrations of hydronium ion and hydroxide ion are very small numbers, it's convenient to express them in a different way... that's where "pH" and "pOH" come in. In fact, we use "p" similarly in a number of situations to express small numbers where "pX" means "-logX".
The pH of pure water is 7. Add an acid and pH goes down, add a base and pH goes up.
The pOH of pure water is 7. Add an acid and pOH goes up, add a base and pOH fores down.
pH + pOH = pK_w = 14

NOTE: Why do we focus on "pH" instead of "pOH" in so many cases? Well, it's an interesting case of a technology race. Because pH and pOH really are equivalent concepts in aqueous solutions, either of them is equally "good" at describing the solution. Long ago, there were two teams working on ways to measure this problem. One of them focussed on trying to measure pH, the other was trying to measure pOH. The pH team won the "race", so today we use pH.

Between pH/pOH and K_w, if you are given either pH, pOH, [H₃O⁺], or [OH^-], you should be able to calculate the other 3

Acid and Base Strength:

"Strong" acids and bases are shown in your textbook Figure 14.6. These are one of the things you should memorize. If an acid or base is not on this list, you can assume it is weak, unless there is specific information that would lead you to believe otherwise. {more on that in the next section...}
It is important to distinguish between the "strength" of an acid or base and the "acidity or basicity" of a solution. "Strength" indicates how completely an acid or base dissociates; "acidity" or "basicity" describes how acidic or basic a solution is. We can make a solution of HCl(aq) {a "strong" acid} that has very low acidity by adding a drop or two of HCl(aq) to a bucket full of water. Similarly, we can make a reasonably acidic solution using acetic acid, a "weak" acid.
Many acids can donate H+ multiple times, such as H₂SO₄, H₂CO₃, or H₃PO₄. These are called polyprotic acids. The "strength" of these acids decreases with each deprotonation - HSO₄^-1 is a weaker acid than H₂SO₄, although they can both function as acids.

Acid-Base Equilibrium:

As we saw above, acids and bases react with water in an equilibrium. These are also special cases with special conditions, so they are given the specific equilibrium constants K_a and K_b.
K_a and K_b refer to specific reactions, but they are still equilibrium constants and follow all the same rules as any other equilibrium constant.
"Strong" acids are those which have a product-favored K_a. "Strong" bases have a product-favored K_b.
The strength of a conjugate acid and a conjugate base pair is inversely related - a stronger conjugate acid will have a weaker conjugate base and vice versa.
Acid and base equilibrium problems make a LOT of use of those simplifying assumptions, especially the "small equilibrium constant" assumption. Again, you can always try the assumptions, but check them to make sure they're valid.

Titrations and Titration Curves:

"Titration" is a specific type of stoichiometry problem. Yet again, this is not a new concept, it's just a specific application of something we already know how to do. Follow the same steps.

WARNING - Do not use "C₁V₁=C₂V₂" to do a titration problem. C₁V₁=C₂V₂ is used for dilutions and only for dilutions. If you use C₁V₁=C₂V₂ for a titration problem that I am grading, you will receive zero points for the problem regardless of any other work that is shown. C₁V₁=C₂V₂ is a sloppy, lazy shortcut that is inconsistent with actually learning how to calculate a titration correctly. If you choose to use it, you will earn zero points. Don't do it.
OK, now that I have your attention... C₁V₁=C₂V₂ is one of those formulas that sometimes will accidentally give you the correct answer, or will give you the correct answer only if a number of conditions and assumptions are made and met. Treating titrations like stoichiometry problems (which they are) will work every time, no accident. Use the appropriate tool for the job you're trying to do. If you have a hammer and a screwdriver, don't use the hammer to pound in a screw. Yes, if the screw has small threads and the wood is soft and the joint doesn't really have to hold together all that well, you could probably pound in the screw with a hammer and it would be good enough for a while. But why not just use the screwdriver? When you're finished with Gen Chem and you want to find shortcuts, go for it. When they work, they're great, they save time and effort. When they don't work, you end up wasting time, money, and resources that can (in some cases) cost you your job or someone's life.

If we think about a normal titration that we might do in lab, there's one reactant in a burette and the other reactant in a beaker or Erlenmeyer flask below the burette. How do we decide which is which? Well, that depends upon a few things:

The substance in the beaker is "being titrated". It is the substance you will be gathering the most information about.
The substance in the burette is the "titrant".
The titration will work best if the titrant is strong and monoprotic, for example, HCl(aq) or NaOH(aq).
The acid and the base should be approximately the same concentration. Within a factor of 2-3 is OK, within a factor of 10 is (generally) not.

That's about it. There are other little tweaks that make things work better in some situations, but as long as you stick to those guidelines your titration will probably be OK. And I call those "guidelines" because you can get away with violating them and still have a successful titration.
The purpose of most titrations is to find an equivalence point. An equivalence point is the point in a titration where the amount of acid and base are related by some stoichiometric relationship. If I am titrating 0.137mols of NaOH(aq) with HCl(aq), I will reach an equivalence point when I have added 0.137mols of HCl(aq). For polyprotic acids, there are multiple equivalence points.
The challenge in an acid-base titration is detecting the equivalence point. There are 2 main ways to do that:

Use a visual pH indicator - an indicator is a substance (usually an organic molecule of some sort) that has an intense color change at a specific, narrow pH range. The pH range at which an indicator changes color is called the endpoint. For a "good" titration, the endpoint of the indicator must coincide with an equivalence point in the chemical system being studied. Advantages: usually fairly quick, minimal equipment needs. Disadvantages: need to choose an indicator with an appropriate endpoint for the equivalence point that is being explored, minimal actual data to analyze, can be impossible to use for individuals who have challenges seeing color.
Use a pH meter to record a titration curve - a titration curve (such as the one shown in Figure 14.18 of your textbook) monitors the pH of a solution as titrant is added. At an equivalence point, the pH of the solution changes very rapidly with small additions of titrant; that is to say, the titration curve is most vertical at the equivalence points. {For the calculus folks, you can describe this with derivatives...} Advantages: produces a lot of information, little to no prior knowledge about the system is required. Disadvantages: a pH probe is required, usually takes significantly longer than an indicator titration, much too complex if only very simple information is needed.

If you are exploring the pH behaviour of a new substance or a complex mixture, recording a full titration curve will be much more useful. If you just need to know the concentration of a new supply of HCl(aq) or NaOH(aq) {or other "simple", well-known substance} then an indicator titration is good enough.
Your textbook has a number of nice titration curves for monoprotic titrations, but titration curves for polyprotic acids and bases are also interesting, perhaps even more interesting than monoprotics. I have a few posts on Chemistry In General about titrations and titration curves, check them out here:
https://chemistryingeneral.blogspot.com/search?q=titration

Buffers:

Buffers are: 1) approximately equimolar mixtures of a weak conjugate acid/weak conjugate base pair that; 2) resist changes in pH when small amounts of acid or base are added. Buffers are equilibria.
Think about a pH titration curve... where is there an approximately equimolar mixture of a conjugate acid/conjugate base pair that is resisting change in pH when acid or base is added? Asked another way: where is the titration curve the flattest?
Think about it.
No, really, think about it.
Seriously, stop reading and think about it!
Got it?
The titration curve is flattest between equivalence points. In fact, it is most flat exactly half way between equivalence points. This is sometimes called a half equivalence point. Now, that does not mean that you do a titration to make your buffer, but it's one of the extra bits of information that a titration curve can give us.
To make an effective buffer:
The concentration of conjugate acid and conjugate base should be within a factor of ~10 of each other.
The concentrations of BOTH the conjugate acid AND the conjugate base should be at least 100x the K_a of the acid.
For most buffer problems, we can use the Henderson-Hasselbalch Equation to help with the calculation. It's not magic, but it does take some practice.

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