The pH Scale
Acidity, or its opposite, alkalinity, is determined by measuring the concentration of
hydrogen ions in the liquid. In distilled water, there are 10-7 moles of hydrogen ions per
liter, which means one molecule out of each 5.6 billion is ionized. This number of ions in
the liquid makes it chemically neutral. As the concentration of hydrogen ions increases
from this value, the water becomes acidic; as it decreases, the water becomes alkaline, or
basic. While water is a solvent because it has the positive and negative charges in the
molecule separated from one another, neutral water does not “attack” other chemicals and
cause chemical change. Acids or bases do cause chemical changes. So it should be useful to
be able to characterize whether something is an acid or a base.
It is easy to see that the concentration is not a very useful way to characterize acidity or
alkalinity because of the smallness of the number. One part in 10 billion is hard to say
several times in succession.
Chemists have adopted an alternative way to speak about the neutrality (or lack thereof).
The power of the base (-7 is the power of the base, which is 10 in this case) is a relatively
“understandable” number. Chemists have chosen to use the negative of the logarithm to
the base 10 of the concentration; this is called the pH value (see Appendix 3).
Any number (N) may be expressed as a base number (b) to a power (p)
N = b p.
The logarithm to the base 10 of a number N is the power of 10 that will reproduce the
number N:
N = 10 (logarithm of N),
Energy, Ch. 14, extension 7 The pH scale
that is, the logarithm of N is the power of 10 that will reproduce N. We can use the pH
value to measure acidity or alkalinity.
Because the scale of pH is logarithmic, a pH value of 6 for a liquid, which is just 1 below
7, means that that liquid is ten times more acidic because it has 10 times the number of
hydrogen ions. A pH value of 5 would indicate that the liquid has 100 times more
hydrogen ions, and so is 100 (10 x 10) times more acidic. A liquid having a pH of 10 is
1000 (10 x 10 x 10) time less acidic (or 1000 times more basic).
Distilled water therefore has a pH of
pH water = - (log10 10-7 ) = 7.
Vinegar has 10-3 moles of ions per liter, and so has a pH of 3. Because the negative
logarithm is used, more acidity means a lower pH. Lemon juice is more acid than vinegar,
with a pH of about 2 (lower than that of vinegar). Figure E14.7.1 shows the pH scale and
indicates that, because of atmospheric carbon dioxide, unpolluted rain is a weak acid, with
a pH of 5.6.
Fig. E14.7.1 The pH scale.
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Energy, Ch. 14, extension 7 The pH scale
Since acids have extra hydrogen ions and bases have too few, mixing acids and bases can
“cancel out” the chemical effects, making something that is neither acidic nor basic, but is
neutral (or at least closer to neutral than the original acid and base.
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