| Chem 109 |
General Chemistry |
Summer 2002 |
| Lecture Notes::22 July |
© R. Paselk 2002 |
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Acids and Bases
What are acids and bases? There are three major definitions.
We will look at two (the third, Lewis definition, is not needed
for our study).
- Arrhenius Definition:
- Acids release protons (H+) into water.
- Bases release hydroxide ions (OH-) into water.
- This is very limited - it only deals with acids and bases
in water, and many substances which chemists and others think
of as bases (such as ammonia) don't fit the definition. Thus
we will focus on the Brønsted-Lowry definition (Brønsted
definition in abbreviation):
- Brønsted Definition:
- Acids are proton donors.
- Bases are proton acceptors.
- Note that there is no restriction as to solvent, and many
substances besides hydroxide ion can contribute basicity.
- Although I will signify protons in water as H+,
you should realize that naked protons do not exist in water -
they are always hydrated. At a minimum we see the hydronium ion,
H3O+. But hydronium ion is in fact also
generally thought to be hydrated, so you will sometimes see hydrogen
ion represented as H5O2+, H7O3+,
etc.
- A consequence of the Brønsted definition is that all
acids and bases are related to one or more conjugate bases
or acids. That is, when an acid dissociates to give a proton,
it also generates a conjugate base which can react with (accept)
a proton in the reverse reaction. For example, in the case of
water:
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H2O |
Æ |
H+ |
+ |
OH- |
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acid |
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conj. base |
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H+ |
+ |
OH- |
Æ |
H2O |
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base |
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conj. acid |
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| H3O+ |
¨ |
H+ |
+ |
H2O |
Æ |
OH- |
+ |
H+ |
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conj. acid
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acid
base
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conj.
base |
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Strong vs. Weak Acids & Bases
These terms have nothing to do with concentration, rather they
refer to the degree of dissociation of an acid or base:
- A Strong Acid is 100% dissociated at all concentrations
up to 1M. Common strong acids include:
- Nitric acid (HNO3)
- Hydrochloric acid (HCl)
- Sulfuric acid (H2SO4) for the first
dissociation only: H2SO4 ´
HSO4- + H+. The second dissociation
is weak, that is it hardly dissociates at 1M.
- A Weak Acid is only partly dissociated at 1M. The
degree of dissociation varies widely, from a few percent to an
infinitesimal degree. Common weak acids include:
- Acetic acid (HC2H3O2 or
CH3CO2H, etc.)
- Formic acid (HCO2H)
- Hydrofluoric acid (HF)
- Most acids of biological origin such as amino acids, fatty
acids, metabolites, nucleic acids etc.
- A Strong Base is 100% dissociated at all concentrations
up to 1M. Common strong bases include:
- Sodium hydroxide (NaOH)
- Potassium hydroxide (KOH)
- A Weak Base only partly reacts at 1M. The degree of
dissociation varies widely, from a few percent to an infinitesimal
degree. Common weak acids include:
- Ammonia (NH3)
- Aluminum hydroxide (Al(OH)3)
- Magnesium hydroxide (Mg(OH)2)
The pH Scale
The concentration of hydronium ion in water is extremely influential
on all kinds of chemistry. The range of hydronium ion concentration
in water is also vast, with extremes of about 10M to about 10-15M,
and commonly ranging from 1M - 10-14M. Imagine plotting
[H3O+] vs. volume of acid added to a base
solution in a titration. If you had one cm on the graph paper
= 10-14M, then you would need a piece of paper 109
km long (greater than the distance from the Sun to Jupiter) to
plot this titration! Obviously a more convenient measure is needed.
This is easily accomplished by looking instead at the logarithm
of [H+] and defining a new term,
pH = -log[H+]
Turns out that the concentration of hydrogen ion in water is
related to the concentration of hydroxide ion due to the equilibrium
dissociation of water:
H2O ´ H+
+ OH-, so
K = [H+][OH-] / [H2O]
But the concentration of water remains essentially
the same in dilute solution,
so by convention we define the dissociation constant
or ion product for water:
Kw= [H+][OH-] = 1.0
x 10-14 @ 25 °C
Let's look at some general characteristics of pH.
- Range: pH = -1 to pH = 15 (10M -10-15M)
- for 1 M HCl, pH = 0
- for 1 M NaOH, pH = 14
- At midrange [H+] = [OH-] = 10-7M.
The solution is said to be "neutral."
- This follows in aqueous solution from Kw = 1.0
x 10-14 = [H+] [OH-], thus if
[H+] = [OH-], then [H+] = (1.0
x 10-14)1/2= 1.0 x 10-7
- Low pH means acidic:
- For 1M strong acid, pH = 0.0 (log 1 = 0)
- For 0.1M strong acid, pH = 1.0
- For 10-7M H+, pH = 7
- High pH means basic:
- For 1M strong base, pH = 14 ([H+] = (1.0 x 10-14)
/ [OH-] = (1.0 x 10-14) / 1 = 1.0 x 10-14
and pH = -log(1.0 x 10-14) = 14.0.
- For 0.1 M OH-, (1.0 x 10-14) / 0.1
= 1.0 x 10-13 and pH = -log(1.0 x 10-13)
= 13.0.
- For 10-7M OH-, (1.0 x 10-14)
/ (10-7) = 1.0 x 10-7 and pH = -log(1.0
x 10-7) = 7
Examples:
- What is the pH of a solution of 0.015 M HCl?
- Strong acid, so [H+] = 0.015 M
- pH = - log [H+]
- pH = - log 0.015 = - (- 1.824)
- pH = 1.82
Note that the significant figures are correct, 1 is
the power of ten, only the figures to the right are significant.
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- What is the pH of a solution of 0.067 M NaOH
- Strong base, so [OH-] = 0.067 M
- Recall that [H+][OH-] = 1.0
x 10-14
- Substituting, [H+][0.067] = 1.0 x 10-14
- Rearranging, [H+] = (1.0 x 10-14)
/ 0.067 = 1.493 x 10-13
- pH = - log (1.493 x 10-13) = - (- 12.83)
- pH = 12.83
- Again note the significant figures - 12 corresponds
to the power of ten, only the figures to the right are significant.
Note that the "p" has the more general meaning of
"-log[]". Thus pOH is -log [OH-], pCa = -log
[Ca2+], etc.
pH of weak acid solutions
Weak acid dissociations involve equilibria. The equilibrium
constants have a specific symbol = Ka.
Example: What is the pH of a 0.10 M solution of acetic
acid. Ka = 1.8 x 10-5
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HOAc |
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H+ |
+ |
OAc- |
| Before reaction |
0.10 M |
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0 |
| @ Equilibrium |
- 0.10 M- x
- assume x << 1.8 x 10-5
- then HOAc = 0.10 M
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Ka = [H+][OAc-] /
[HOAc]
Substituting, Ka = (x)(x) / 0.10 = 1.8 x
10-5,
x2 = 1.8 x 10-6
x = 1.34 x 10-3M; assumption OK.
pH = - log (1.34 x 10-3) = 2.87
Notice the significant figures. For a log function
the number in front of the decimal is the exponent of ten,
thus pH = 2.87 is a 2 significant figure number!
Acid Equilibria
Buffer calculations: One of the
most frequent calls for calculating acid equilibria is calculations
involving buffers. What is a buffer?
- A buffer is a solution which resists changes in pH. Essentially
it consists of an acid and its salt (an acid and its conjugate
base) in solution together. Thus the solution has a proton donor
and a proton acceptor, so pH is stabilized.
- A buffer is simply an acid equilibrium system with significant
amounts of both the acid and its conjugate base.
With this in mind let's do some examples.
Example: Calculate the pH of a "buffer" (a
solution which resists changes in pH) made up by dissolving 0.0125
moles acetic acid (HOAc) and 0.0250 moles of sodium acetate (NaOAc)
in enough water to make 1.000 L of solution. Ka =
1.8 x 10-5
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HOAc |
´ |
H+ |
+ |
OAc- |
| Before reaction |
0.0125 moles/L |
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0.0250 moles/L |
| @ Equilibrium |
-
- (0.0125- x) M
- assume x is small,
- = 0.0125
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x |
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- (0.0250 - x) M
- assume x is small,
- = 0.0250
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Ka = [H+][OAc-] /
[HOAc]
Substituting, Ka = [H+](0.0250)
/ (0.0125) = 1.8 x 10-5
Rearranging, [H+] = (1.8 x 10-5)(0.0125)
/ (0.0250) = 0.90 x 10-5
x is within experimental error (0.000009 < ±0.0001),
so assumption OK
pH = 5.046
© R A Paselk
Last modified 22 July 2002
