1. The pH Scale
The pH scale is a convenient way to represent solution acidity. The pH is a log scale based on 10, where
pH = -log[H+]
Thus for a solution where
[H+] = 1.0 x 10-7 M
pH = -log(1.0 x 10-7)
pH = -(-7.00) = 7.00

2. Significant figures for logarithms.
The rule is that the number of decimal places in the log is equal to the number of significant figures in the original number.
[H+] = 1.0 x 10-9 M
pH = 9.00
2 significant figures
2 decimal places

3. Since pH is a log scale based on 10, the pH changes by 1 for every power of 10 change in [H+].
For example, a solution of pH 3 has a H+ concentration 10 times that of a solution of pH 4 and 100 times that of a solution of pH 5.
Since pH is defined as –log[H+], the pH decreases as [H+] increases.

4. Consider the log form of Kw:
Kw = [H+][OH-]
log Kw = log[H+] + log[OH-]
-log Kw = -log[H+] – log[OH-]
Thus pKw = pH + pOH
Since pKw = 14.00
pH + pOH = 14.00

5. Calculating the pH of Strong Acid Solutions
When dealing with acid-base equilibria, the focus is on the solution components and their chemistry.
For example, what species are present in a 1.0 M solution of HCl?
Since HCl is a strong acid, we assume it is completely dissociated; thus, a 1.0 M solution of HCl exists as H+ and Cl- ions rather than HCl molecules.
Next we must consider which components are significant and which can be ignored.
In 1.0 M HCl, the major species are H+, Cl-, and H2O.
Since the solution is very acidic, OH- is present only in tiny amounts and can be ignored.

6. To illustrate, let’s calculate the pH of 1.0 M HCl.
List the major species involved: H+, Cl-, and H2O.
Since we want to calculate the pH, focus on those major species that furnish H+.
H+ from dissociation of HCl
H+ from autoionization of H2O.
H2O(l) ⇌ H+(aq) + OH-(aq)
From Le Chatelier’s Principle the H+ from the dissociated HCl will drive the position of this equilibrium to the left.
Thus the amount of H+ contributed by water is negligible and can be neglected.
Thus, the [H+] in the solution is 1.0 M.
The pH is then
pH = -log[H+] = -log(1.0) = 0

7. Calculating the pH of Weak Acid Solutions
Remember a weak acid is one for which the equilibrium lies far to the left.
Most of the acid originally placed in the solution is still present as HA at equilibrium.
That is, a weak acid dissociates only to a very small extent in aqueous solution.
Calculating the pH of a weak acid involves looking at the equilibrium occurring in aqueous solution.
We will also look at solving for the pH of weak acid mixtures.

8. Percent Dissociation
Note: Percent dissociation is also known as percent ionization.
It is often useful to specify the amount of weak acid that has dissociated to achieve equilibrium.
Percent dissociation is defined as:
For a given weak acid, the percent dissociation increases as the acid becomes more dilute.

9. For solutions of any weak acid HA, [H+] decreases as [HA]0 decreases, but the percent dissociation increases as [HA]0 decreases.
As an acid is diluted ([HA]0 decreases) the system must shift right to reach the new equilibrium position.
In other words as [HA]0 decreases Q is less than Ka and the system shifts right with more HA dissociating.