Phun with the pH Scale

The acidity of a solution is related to the concentration of the hydronium ion in the solution: The more acidic the solution is, the higher the concentration. In other words, a solution in which the [H₃O⁺] equals 1.0 × 10^–2 is more acidic than a solution in which the [H₃O⁺] equals 1.0 × 10^–7.

Scientists developed the pH scale, a scale based on the [H₃O⁺], to more easily tell, at a glance, the relative acidity of a solution. The pH is defined as the negative logarithm (abbreviated as log) of [H₃O+]. Mathematically, it looks like this:

pH = – log [H₃O⁺]

In pure water, the [H₃O+] equals 1.0 × 10^–7, based on the water dissociation constant, Kw (see “Acting as either an acid or a base: Amphoteric water,” earlier in this chapter. Using this mathematical relationship, you can calculate the pH of pure water:

pH = – log [H₃O⁺]

pH = – log [1.0 × 10^–7]

pH = – [–7]

pH = 7

The pH of pure water is 7. Chemists call this point on the pH scale neutral. A solution is acidic if it has a larger [H₃O⁺] than water and a smaller pH value than 7. A basic solution has a smaller [H₃O⁺] than water and a larger pH value than 7. The pH scale really has no end. You can have a solution of pH that registers less than 0. (A 10 M HCl solution, for example, has a pH of –1.) However, the 0 to 14 range is a convenient range to use for weak acids and bases and for dilute solutions of strong acids and bases. Figure 1-1 shows the pH scale.  The [H₃O⁺] of a 2.0 M acetic acid solution is 6.0 × 10^–3. Looking at the pH scale, you see that this solution is acidic. Now calculate the pH of this solution:

pH = – log [H₃O⁺]

pH = – log [6.0 × 10^–3]

pH = – [–2.22]

pH = 2.22

The pOH is the negative logarithm of the [OH^–], and it can be useful in calculating the pH of a solution. You can calculate the pOH of a solution just like the pH by taking the negative log of the hydroxide ion concentration. If you use the Kw expression (which enables you to calculate the [H₃O⁺] if you have the [OH^–]; see the section “Acting as either an acid or base: Amphoteric water”) and take the negative log of both sides, you get 14 = pH + pOH. This equation makes it easy to go from pOH to pH.

Figure 1-1: The pH scale.

Just as you can you convert from [H₃O⁺] to pH, you can also go from pH to [H₃O⁺]. To do this, you use what’s called the antilog relationship, which is [H₃O⁺] = 10–pH Human blood, for example, has a pH of 7.3. Here’s how you calculate the [H₃O+] from the pH of blood:

[H₃O+] = 10^–pH

[H₃O+] = 10–7.3

[H₃O+] = 5.01 × 10^–8

You can use the same procedure to calculate the [OH–] from the pOH.