Due to the large range of proton concentration values ([H^{+}]) in
aqueous solution (typically from
10^{-15}
to 10 M), a logarithmic scale of acidity makes the most sense to put the
values into manageable numbers. The pH
scale of acidity
defines pH as the negative common logarithm of the concentration of
H^{+}: pH = - log
[H^{+}].

Before proceeding with our discussion on pH, let's review some properties of
Logarithms (affectionately called "logs"). A common
logarithm is a function that computes what exponent would be on 10 to obtain
the input number.
For example, the logarithm of 100 (written "log 100") is 2 because
10^{2} = 100. Likewise, log 1,000,000 = 6. To add logs, multiply their
arguments: log 100 + log
1000 =
log (100 x 1000)
= log (100,000) = 5. To subtract logs, divide their arguments: log 100 -
log 1000 = log
(100/1000) = log (0.1) = - 1. Given those simple rules, you can now
manipulate
logs well enough
to do any problem involving logs in acid-base chemistry. For this
section of chemistry,
you will get to know and love the log key on your calculator almost as much as
you did in kinetics.

The pH scale in water is centered around 7, which is called
neutral
pH. This value is not
randomly selected, but rather it comes from the fact that the [H^{+}] in
pure
water
is 10^{-7}
(recall that *K*
_{w} = 10^{-14}). An acidic solution
has a pH value less than 7
because [H^{+}] is greater than that of pure water. A basic
solution has a pH greater than 7 because there is a lower [H^{+}] than
that of pure water
(and consequently a larger [OH^{-}]).

Chemists use a pOH scale analogous to the pH acidity scale to gage hydroxide
ion concentrations of aqueous solutions. pOH is defined
as the negative
common logarithm of the concentration of OH^{-}: pOH = - log [OH^{-
}]. In
the pOH scale, 7 is neutral, less than 7 is basic, and greater than 7 is
acidic.
A useful relationship (which you should be able to derive using the definition
of *K*
_{w}) is
that pH + pOH = 14.
This formula will allow you to readily convert between values of pH and
pOH. A
comparison of the
pH and pOH scales is provided in . Note that because
*K*
_{w} is
constant, the product of [H^{+}] and [OH^{-}] is always
equal to
10^{-14}.

Figure %: A comparison of the pH and pOH scales of acidity

As you have probably guessed by now, the prefix "p" in front of a symbol means
"take the negative
log". We have defined pH and pOH as values to describe the acidic or basic
strength of solutions. Now we can talk about p*K*
_{a} (- log
*K*
_{a}) and
p*K*
_{b}
(- log *K*
_{b}) as measures of acidity and basicity, respectively,
for standard acids and bases. An
acid with a
p*K*
_{a} less than zero is called a strong acid because it
almost
completely dissociates
in water, giving an aqueous solution a relatively low pH. Acids with
p*K*
_{a}'s greater than
zero are called weak acids because they only partially dissociate in water,
to make solutions with
larger pH's than those strong acids produce at the same concentration.
Similarly, bases
with
p*K*
_{b}'s
less than zero are strong bases and bases with p*K*
_{b}'s
greater
than
zero are called
weak bases.

Now that we have the tools to be able to describe the acidity and
basicity
of compounds with
known p*K*
_{a}'s, let's analyze trends in acidity and basicity to
reach an intuitive
understanding of those trends.

First, let's consider the acidity of the halogen acids--HF, HCl, HBr, and HI-- collectively abbreviated HX as shown in , where X represents the halogen. From the data in the figure below, you can see that the major factor affecting the acidity of halogen acids is the strength of the H-X bond. Intuitively, a larger electronegativity difference should lead to a stronger acid due to the polarization of electrons away from hydrogen. However, the trend in bond strength is enough to overrule that competing trend in electronegativity. The smaller the halogen, the closer in size it is to the proton and the greater the orbital overlap; so HF is most the strongly bonded and weakly acidic of the halogen acids.

Figure %: Factors affecting the strengths of halogen acids

Generalizing that result, we can say that when the an H-A bond is strong, the
acid is weak.
Experimental confirmation of this postulate comes from the oxyacid series of
compounds. An
oxyacid is a molecule of the form AO_{n}(OH)_{m}, where A is a
non-metal.
Pauling and Ricci derived the following approximate equation for oxyacid
acidity
from experimental
observations:

p*K*
_{a} = 8 - 9f + 4n

The variable f is the formal charge on A when all oxygens are singly bound to A. The variable n represents the number of O atoms bound to A that are not bound to an H. A general trend, summarized in the Pauling-Ricci rule above, is that the more electron withdrawing (more electropositive) the non- metal center, the stronger the acid due to a weakening of the O-H bond.

In summary, we note the following trend regarding acidity: hydrogens are more
weakly
bound to more
electronegative groups, and this produces stronger acids. By using the
relationship *K*
_{w} = *K*
_{a} * *K*
_{b},
you
should be able to figure out that we need only to discuss the acidity of
compounds to describe
basicity. From the above discussion, we can deduce that bases with
weaker
conjugate acids are
more basic than those with stronger conjugate acids. Therefore, bases that
form
stronger bonds to H
will have larger *K*
_{b}'s and are stronger bases.

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