The pH Scale
As you know, water can act as either a proton donor (in the form of the hydronium ion, H3O+) or a proton acceptor (as OH-). In solution, a water molecule can even donate a proton to or accept a proton from another water molecule, and this process is called autoionization:
2H2O
H3O+ + OH-
Since this reaction takes place in equilibrium, we can write an equilibrium expression, Keq, for it:
Keq = [H3O+][OH-]
And since this expression refers specifically to the ionization of water, we can write the equilibrium expression as
Kw. At 25ºC, the value of
Kw, which is known as the
ion-product constant, is 1
10
-14. This means that the [H
3O
+] = [OH
-] and each is equal to 1
10
-7. When the concentrations of H
+ and OH
- are equal in a solution, the solution is said to be neutral. In acidic solutions, the concentration of H
+ is higher than that of OH
-, and in basic solutions, the concentration of OH
- is greater than that of H
+.
The pH of a solution is calculated as the negative logarithm in base 10 of the hydronium ion concentration—it is an expression of the molar concentration of H+ ions in solution:
pH = -log [H+] or -log [H3O+]
A solution like the equilibrium expression for water, which is neutral at standard temperature, would have a pH of
pH = -log [1
10-7] = -(-7.00) = 7.00
So as you can see, neutral solutions have a pH of 7. If the solution contains more hydronium ions than this neutral solution ([H
+] > 1
10
-7), the pH will be less than 7.00, and the solution will be acidic; if the solution contains more hydroxide ions than this neutral solution ([OH
-] > 1
10
-7), the pH will be greater than 7.00, and the solution will be basic.
Similarly, the pOH of a solution is calculated as the negative logarithm in base 10 of the hydroxide ion concentration:
pOH = -log [OH-]
and pH and pOH are related to each other by the equation
pH + pOH = 14
Since you won’t be allowed to have a calculator for the SAT II Chemistry test, you can use the following equation if you need to calculate the hydronium ion concentration of a solution:
[H3O+] = 10-pH
Now try a problem: What is the pH of a solution at 25ºC in which [OH
-] = 1.0
10
-5 M?
Explanation
The fact that this solution is at 25ºC tells us that we should use the
Kw relationships. If the [OH
-] = 1.0
10
-5 M, then pOH = 5. You know that 1.0
10
-5 is the same as plain old 10
-5. The log of 10
-5 is -5 (simply use the exponent when a number, any number, is written as 10
power, so the “negative” of the log is equal to -(-5), or simply 5. Now, if the pOH is 5, then the pH is 9 since pH + pOH = 14
