Auto dissociation of WaterWater molecules allow protons to be transferred between molecules & an equilibrium is established.

HOH (l) + HOH(l) H3O+ (aq) + OH-

(aq)

Overall: 2H2O (l) H3O+ (aq) + OH-

(aq)

Keq = Kw = [H3O+ ] [OH-] = 1.0 x 10-14 at 250C

Anytime H3O+ ions or OH- ions are present, this

equilibrium is automatically established & this regulates the allowable concentrations of H3O+

& OH-.

Thus, Kw = [H3O+ ] [OH-] can be used to

calculate [H3O+ ] & [OH-] in acidic & basic

solutions. In a neutral solution [H3O+ ] [OH-] = 1

x 10-7 M (i.e. pH=7)

SAMPLE PROBLEMS:1) In a certain container of H2O it was found that the [OH-] was 1.0 x 10-4. What is [H3O+

]? What is the pH?

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?

Easy (basic) Math Definition of pH[H3O+] = 10-pH M

Ex) solution where [H3O+] = 0.001 M (10-3 M). Find the pH.

[H3O+] = 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 [H3O+].

Since HCl is a strong acid, it completely dissociates.HCl + H2O H3O+ + Cl-

Initial: 0001M 0 M so [H3O+] = 0.0001 M = 1 x 10-4

0 M .0001 M pH = 4

Log arithmetic Definition of pHpH – the pH of a solution is defined as the negative of the log of the hydronium ion concentration

Ex) [H3O+] = 3.25 x 10-3 M, find the pH.

Answer: pH = -log 3.25 x 10-3 =

Ex) [H3O+] = 1.44 x 10-10 M, find the pH.

Answer: pH = -log 1.44 x 10-10 =

Finding Concentrations from pH valuesEx) pH = 2.80, find [H3O+].

We must work in reverse (take the “antilog” of the negative pH).

pH = 2.80 [H3O+] = antilog -2.8 =

Ex) pH = 11.4 [H3O+] = antilog -11.4 =

Calculating pOHThe 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?