Acids, Bases, and pH

THE pH SCALE

In the previous section, we learned that the K_w expression for water is

and that pure water, being neutral, has

By convention, acidic solutions are those where the [H₃O⁺] is greater than the [OH^–], and basic solutions are those where the [OH^–] is greater than the [H₃O⁺]. In other words:

Note: even in acidic solutions, OH^– is present, and in basic solutions H₃O⁺ is also present.

We have learned that in aqueous solutions the actual concentration of [H₃O⁺] is often very small. For instance, in pure water, which is neutral, the [H₃O⁺] is 10^–7 M. Since living cells keep their acid concentrations close to neutral, working with these small physiological [H₃O⁺] values as exponents can be very cumbersome. To circumvent this problem, a logarithmic measure of the [H₃O⁺] (or [H⁺] for short) was devised by a Danish scientist in 1909. He called this measure pH, short for the power of hydrogen. The relationship of pH to the concentration of H⁺ ions is given by the following equation:

If pure water has an [H⁺] concentration of 10^–7 M, then neutral water has a pH of –log (10^–7), or 7. This value was designated the middle of the pH scale. The pH scale ranges from 0 to 14, reflecting [H⁺] from 1 M (pH = 0) to 10^–14 M (pH = 14). Note how much easier it is to manipulate pH values from 0 to 14 than to deal with variations in H⁺ concentrations from 1 M to 0.00000000000001 M. Keep in mind that since the “log” function removes the exponents from the [H⁺] expression, a one point change in the pH is equivalent to a tenfold change in the [H⁺]!

Also keep in mind that in nonaqueous solution, it is possible to have a [H⁺] that lies outside the range of the pH scale. However, such values of H⁺ are not found in biological systems, and are not physiologically relevant.