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, Kw. Although Kw
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.
Kw = [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 Kw. As long as we know
one, we know the other.
For pure water at 25°C, Kw = 1x10-14. If the
temperature changes, the value of Kw changes, but unless you
are given information to let you find or calculate a different Kw
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 = pKw = 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 Kw, 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 Ka and Kb.
Ka and Kb 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
Ka. "Strong" bases have a product-favored Kb.
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
Ka 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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