pH is one of the most commonly made measurements in water testing, but one of the least understood. Here is an attempt at an explanation:
In order to understand the pH scale, we have to discuss the ideas of moles and of logarithms.
Moles: When chemists talk about the amount of a substance, they often like to use the unit of moles, rather than grams. A mole of a substance is, simply, the number of grams of that substance equal to its molecular weight. A mole of water, weighs about 18 grams, because water has a molecular weight of about 18. A mole of calcium carbonate, CaCO3, weighs about 100 grams; a mole of methyl alcohol, CH3OH, 32 grams, etc. The advantage for chemists of using moles is that an equal number of moles of any substance contains the same number of molecules, so it is easier to calculate the amounts of substances which react with one another.
In a liter of pure water at room temperature the number of moles
of hydrogen ions is about 0.0000001. (For hydrogen, with an atomic weight
of 1, this is also about equal to the number of grams of hydrogen ions.)
In scientific notation, this is written as 1 x 10-7, where the
superscript,
-7, is known as a power, an exponent, or a logarithm. (All three
terms mean the same thing. The seven indicates the number of places to
the right of the decimal point that the "one" is located.) It turns out,
when measuring hydrogen ion concentration electrochemically, that the electrical
potential (voltage) generated at the measuring electrode is directly
related not to the H+ concentration, but to the logarithm of
the H+ concentration. This makes it more convenient to refer
to the H+ concentration in terms of its logarithm. And since
H+ concentrations in water solutions are almost always less
than one mole per liter, the exponent is almost always going to be negative,
because that is the way scientific notation expresses numbers less than
one. So, the negative of the logarithm of the hydrogen ion concentration
in a solution is given a special name. It is called the
pH, which
stands for the potential of the hydrogen ion.
Of course, in the pure water, the concentration of hydroxide ions is
also 1 x 10-7 moles per liter, since each water molecule that
dissociates produces one ion of each type. The water is said to be neutral.
It has a pH of 7 and also a pOH of 7, where the term pOH refers
to the negative logarithm of the hydroxide ion concentration. There are
substances which, when dissolved in water, will upset that balance, and
produce an excess of either H+ or OH-. They may contain
those ions and release them (dissociate) when they dissolve, or they may
react with the water (hydrolyze) and produce them that way. Those substances
which increase the concentration of H+ are called acids; those which
decrease it (and increase the OH- ) are bases or alkalis.
For instance, if a strong acid solution increases the H+ concentration
to 0.1 moles per liter (1 x 10-1), which has a million times
as many H+ ions as a neutral solution, then the pH is equal
to 1. Similarly, if a strong base solution contains 0.1 moles per liter
of OH- ions, it has a pOH of 1. According to the laws of chemical
equilibrium, the pH and the pOH always add up to 14 (at about room temperature),
so the solution with the pOH of 1 has a pH of 13. Most solutions have a
pH between 0 and 14, and 7 is the neutral point. pH's below 7 are increasingly
acidic as the number decreases; pH's above 7 are increasingly alkaline.
And since the scale is logarithmic, each unit change in pH represents 10
times as many ions in solution.
A strong acid or base is one which dissociates completely when
it dissolves in water. The amount of it in solution can be estimated from
the pH. Most acids and bases, however, are weak; they dissociate
or hydrolyze only partially. Many solutions also contain mixtures of several
acidic or basic substances. In these cases, it is difficult to estimate
the total amount of acid or base by measuring the pH, so this must be done
by titration. As every high school chemistry student knows, acids react
with bases to form water and salts. Therefore, an acid is titrated using
a standard base, and visa versa. In water and wastewater analysis,
the amount of acid needed to titrate a solution to a particular pH is a
measure of the acid neutralizing capacity of that solution, and is referred
to as the solution's alkalinity. In natural waters, the pH is most
often controlled by the concentrations of carbonate, bicarbonate, and carbon
dioxide, since these are products of respiration and fermentation. Because
of this, alkalinity is usually measured in terms of the amount of acid
needed to reach the pH of a pure solution of one or another of these substances.
Similarly, acidity is defined as base neutralizing capacity,
and is measured by titration against a standard base.
(While a chemist might prefer to measure these quantities in moles
per liter, engineers seem more comfortable with standard weight units.
So acidity and alkalinity are usually expressed in units of milligrams
per liter of calcium carbonate. Calcium carbonate, or limestone,
is a weakly alkaline material, 50 grams of which react with one mole of
hydrogen ions.)
To see some examples of titration curves which illustrate the principles discussed below, click here for browsers running Javascript 1.1 or later-- or here for a non-Javascript version.
For a strong acid, essentially all of the acid dissociates, so that the concentration of hydrogen ions (H+) is equal to the concentration of the acid. Therefore, the initial pH of the acid solution is equal to the negative logarithm of the concentration of the acid in moles per liter (by the definition of pH). When 90% of the acid has been neutralized (f= 0.9), the concentration of H+ is only one-tenth of its what it was originally-- so the pH will be one unit higher, since -log(0.1) = 1. When 99% has been neutralized (f= 0.99), the pH is 2 units higher, and so on. When f = 1, the pH should equal 7--- and any further addition will raise the pH to a value equal to [14 minus pOH], just as though it were being added to pure water. (Note that we have made the simplifying assumption here of ignoring the increase in the volume of the solution due to adding the base-- but this could easily be accounted for. We also assumed that the original acid concentration was a lot higher than 10-7 molar, so that we could ignore the H+ contributed by the dissociation of water.)
For a weak acid, an approximate formula can be derived for the pH of a solution of the pure acid which states that
pH = 1/2( pKa + pC )
For the hypothetical acid with the formula, HA, the reaction which occurs as the titration with strong base proceeds can be written as:
HA + OH- ===> A- + H2O
pH = pKa + log [(A-)/(HA)]
where (A-) means the molar concentration of A- and (HA) is the molar concentration of the remaining HA. Note that this formula can also be expressed as
pH = pKa + log [f/(1 - f<)]
When the concentration of the two species is equal, the ratio [(A-)/(HA)]
equals 1-- and since the logarithm of 1 equals zero, the pH is equal
to the pKa. At an earlier point in the titration, when,
say, one-tenth of of the acid had been neutralized, the pH would be equal
to pKa + log (0.1/0.9). This works out to about 0.95 pH units
below the pKa. When 90% of the titration is complete, the pH
should be about equal to pKa + log (0.9/0.1), or about 0.95
units above the pKa. So the pH change during the middle 80%
of the titration will vary less than one unit below or above the value
of the pKa. Likewise, you can easily show that between the 1%
and 99% points of the titration, the pH will vary between 2 units below
and two units above the pKa. (Note that the same assumptions
are made as for the strong acid case discussed above.)
For a monoprotic acid (also called a "monobasic" acid-- how's
that for a confusing term) at the end of the titration (f
= 1), there is another approximate formula for the pH:
pH = 7 +1/2( pKa - pC )
"Diprotic" (also called "dibasic") acids can be thought of of dissociating in two steps. For a generic dibasic acid H2Z, loss of one proton can be written as
H2Z <===> H+ + HZ- for which pKa is called pK1
HZ- <===> H+ + Z= for which pKa is called pK2
The pH range near the pKa value of a particular weak
acid is sometimes referred to as the buffer region.
As we have seen, the pH does not change much in this region when strong
acid or base is added-- even in amounts which are a significant fraction
of the amount of the weak acid/base mixture itself. This property is made
use of in chemical, biological and pharmaceutical work-- and in nature--
to keep solutions at a near-constant pH. To make a buffer solution, you
do not actually need to titrate a weak acid or base. For instance, to make
an acetic acid/acetate buffer you can purchase acetic acid and the salt,
sodium acetate, from a chemical supplier and make a solution containing
the proportions which will give the desired pH, based on the formula given
above. The buffer would be most efficient at a pH near the acid's pKa
value of 4.7.
In natural waters and in wastewater treatment plants, the water most
often relies on the carbonic acid/bicarbonate system for buffering
near neutral pH (pK = 6.3). The carbonic acid is formed when carbon dioxide
dissolves in water. It is a product of aerobic or anaerobic respiration
by microorganisms living in the water, and is also present in air; carbonates
are present is some minerals, such as limestone, with which the water may
come in contact.
In laboratories, phosphate buffers are often used in chemistry
or bacteriology to keep pH conditions constant. Phosphoric acid is a tribasic
acid, with pK's of 2.1, 7.2, and about 12.0. You can see that the middle
one, corresponding to a mixture of the ions H2PO4-
and HPO4=, would be very useful for making neutral
buffers. In wastewater analysis, phosphate buffers are used in the BOD
test, the DPD method for total chlorine residual and the colorimetric test
for cyanide, for diluting and rinsing in coliform bacterial testing, and
for calibrating pH meters.
As an example of the protective effect of buffer solutions, consider
the 0.01 M (moles per liter) carbonic acid/bicarbonate/carbonate
system shown in the last of the six titration curves.
If we take the case of this system at a pH of 7.0, the graph shows that
the value of f equals about
0.83. This means that of the total concentration of 0.01 moles per liter,
83% (0.0083 moles per liter) is in the form of bicarbonate (HCO3-)
-- so that 17% (0.0017 moles per liter) is iin the form of carbonic acid
(H2CO3).
[ The ratio, 0.0083 / 0.0017, equals 4.88-- the logarithm of which
is 0.69, or about 0.7. Add this to the pK1 of 6.3, according
to the formula above, and you get a pH of 7.0]
Now, let's say we add 0.001 moles of a strong acid to a liter of this
solution. [Remember that adding this amount of strong acid to pure water
will lower the pH from 7 down to a value of 3.] The reaction which would
occur,
HCO3- + H+ =====> H2CO3
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