The hydronium ion concentration tells us if a solution is acidic, basic, or neutral. Not only are these concentrations very small, but there is a wide range of concentrations. It is more convenient to use pH to determine if a solution is acidic, basic, or neutral. The pH is defined as the negative base 10 logarithm of the hydronium ion concentration in molarity.

pH = -log[H₃O⁺]

The hydronium ion concentration is determined by taking the antilog of the -pH.

[H₃O⁺] = 10^-pH

The pOH is in terms of OH^– ion concentration and is

pOH = -log[OH^–]

and the OH^– ion concentration can be determined by taking the antilog of the -pOH.

[OH^–] = 10^-pOH

If a solution is 1.3 x 10^-6 M hydronium ion the pH = -log[1.3 x 10^-6] = 5.89. Notice, there are three significant figures for the pH. The number of digits to the right of the decimal place in the pH is equal to the number of significant figures in the hydronium ion concentration. So, if we have a hydronium ion concentration of 1.25 x 10^-3, the pH would be 2.903 because the hydronium ion concentration has 3 significant figures.

We will derive another important equation here that relates pH and pOH.

K_w = [H₃O⁺][OH^–] = 1.0 x 10^-14

Take the log base 10 of both sides of the equation.

log{[H₃O⁺][OH^–]} = log(1.0 x 10^-14

From the properties of logarithms

log[H₃O⁺] + log[OH^–] = log(1.0 x 10^-14)

Multiply through by a -1

-log[H₃O⁺] – log[OH^–] = -log(1.0 x 10^-14)

pH + pOH = 14.00

Please make sure you know the following equations:

Below is a table that gives the hydronium ion concentrations and the corresponding pH, pOH, and hydroxide ion concentrations. Note, the pH or pOH can be equal to zero or can have negative values.

If the pH < 7.00, the solution is acidic.

If the pH = 7.00, the solution is neutral.

If the pH > 7.00, the solution is basic.

The pH of a solution can be measured in the lab with a pH meter. Electrodes are placed into the solution, and a voltage is generated between the electrodes and the meter gives the reading in pH units. A less precise method of the determination of pH is with the use of acid-base indicators. These indicators change color within a small range of pH.

The acid form of an indicator can be represented by HIn, and the base form as In^–. The equilibrium is:

HIn (aq) + H₂O (l) ⇄ In^– (aq) + H₃O⁺ (aq)   \(\displaystyle K_a\;=\;\frac{[\mathrm {H_3O^+][In^-}]}{\mathrm {HIn}}\)

If a base, OH, is added to an acidic solution of phenolphthalein, the OH^– ion will react with the H₃O⁺ ion. This will shift the equilibrium to the right to replace the H₃O⁺ ion according to Le Chatelier’s principle, and the HIn will be converted to its pink base form In^–. Phenolpthalein, is an indicator that is colorless in acidic solution and pink in basic solution. It will begin to turn pink at a pH of 8.00 and the color change is complete at a pH of 9.70. In the table below are some indicators and the pH range for the color change.

The oxides of the alkaline earth metals, Group 2A, are stronger bases than the hydroxides. The oxide ion, O^2-, does not exist in aqueous solution, but it does pick up a proton from water to form hydroxide ion. Hydroxide ion is the strongest base in aqueous solution.

O^2- (aq) + H₂O (l) → 2 OH^– (aq)

If SrO₂ is dissolved in water, it will produce 2 OH^– ions per unit of SrO₂.

Please watch the following video

Determination of pH, pOH, Hydronium and hydroxide ion concentrations

Exercises

Exercise 1. What is the hydronium ion concentration, hydroxide ion concentration, the pH, and pOH of a solution that is 0.020 M HNO₃?

Check Solution to Exercise 1

Exercise 2. An aqueous solution has a pOH of 13.52. What is the hydronium ion concentration? What is the pH of the solution?

Check Solution to Exercise 2

Exercise 3. What is the pH and pOH of a solution that is prepared by dissolving 0.86 g HCl in water to give 250. mL of solution?

Check Solution to Exercise 3

Exercise 4. Calculate the hydronium ion concentration, the hydroxide ion concentration, the pH, and the pOH by diluting 45.0 mL of 0.68 M Ba(OH)₂ to a volume of 250.0 mL?

Check Solution to Exercise 4

Exercise 5. How many grams of CaO should be dissolved in water to make 1.50 L of a solution with a pH of 11.20?

Check Solution to Exercise 5

Back to Acids and Bases: Aqueous Equilibria
Back to Study Guides for General Chemistry 2