1. Auto dissociation of Water Water molecules allow protons to be transferred between molecules & an equilibrium is established. HOH (l) + HOH (l) H 3 O + (aq) + OH - (aq) Overall: 2H 2 O (l) H 3 O + (aq) + OH - (aq) Keq = Kw = [H 3 O + ] [ OH - ] = 1.0 x 10 -14 at 25 0 C Anytime H 3 O + ions or OH - ions are present, this equilibrium is automatically established & this regulates the allowable concentrations of H 3 O + & OH -.

2. Thus, Kw = [H 3 O + ] [ OH - ] can be used to calculate [H 3 O + ] & [ OH - ] in acidic & basic solutions. In a neutral solution [H 3 O + ] [ OH - ] = 1 x 10 -7 M (i.e. pH=7) SAMPLE PROBLEMS: 1) In a certain container of H 2 O it was found that the [OH - ] was 1.0 x 10 -4. What is [H 3 O + ]? What is the pH?

3. 2) A 0.0001 M HCl (a strong acid) solution will have a pH of what? What would be [OH - ] be? 3) Ca(OH) 2 is a strong base. If a 0.000 05M solution dissociates in water, what will the pH be?

4. Easy (basic) Math Definition of pH [H 3 O + ] = 10 -pH M Ex) solution where [H 3 O + ] = 0.001 M (10 -3 M). Find the pH. [H 3 O + ] = 0.001 M or 1 x 10 -3 M so pH = 3 Ex) Find the pH of a 0.0001 M solution of HCl. We need to find the [H 3 O + ]. Since HCl is a strong acid, it completely dissociates. HCl + H 2 O  H 3 O + + Cl - Initial: 0001M 0 M so [H 3 O + ] = 0.0001 M = 1 x 10 -4 0 M.0001 M pH = 4

5. Log arithmetic Definition of pH pH – the pH of a solution is defined as the negative of the log of the hydronium ion concentration Ex) [H 3 O + ] = 3.25 x 10 -3 M, find the pH. Answer: pH = -log 3.25 x 10 -3 = Ex) [H 3 O + ] = 1.44 x 10 -10 M, find the pH. Answer: pH = -log 1.44 x 10 -10 =

6. Finding Concentrations from pH values Ex) pH = 2.80, find [H 3 O + ]. We must work in reverse (take the “antilog” of the negative pH). pH = 2.80 [H 3 O + ] = antilog -2.8 = Ex) pH = 11.4 [H 3 O + ] = antilog -11.4 =

7. Calculating pOH The pOH is the pH value of a solution using the concentration of the OH - ions. pH + pOH = 14 Ex) What is the pH of a 3.41 x 10 -4 M NaOH solution?