pH Scale and Calculations

Chapter 14

pH Scale

• We use this scale to measure the strength of an acid or base.

• pH is defined as the –log[H+]

• pH can use the concentration of hydronium ions or hydrogen ions.

pH Scale

Acid Base

0

7

14

Zumdahl, Zumdahl, DeCoste, World of Chemistry 2002, page 515

pH of Common Substances

Timberlake, Chemistry 7th Edition, page 335

LecturePLUS Timberlake 5

Ionization of Water

Occasionally, in water, a H+ is transferred between H2O molecules

. . . . . . . .H:O: + :O:H H:O:H + + :O:H-

. . . . . . . . H H H

water molecules hydronium hydroxide ion (+) ion (-)

6

Pure Water is Neutral

Pure water contains small, but equal amounts of ions: H3O+ and OH-

H2O + H2O H3O+ + OH-

hydronium hydroxide

ion ion

1 x 10-7 M 1 x 10-7 MH3O+ OH-

7

Ion Product of Water Kw

Kw = [ H3O+ ] [ OH- ]

= [ 1 x 10-7 ][ 1 x 10-7 ]

= 1 x 10-14

pH of Common Substance

14 1 x 10-14 1 x 10-0 0 13 1 x 10-13 1 x 10-1 1 12 1 x 10-12 1 x 10-2 2 11 1 x 10-11 1 x 10-3 3 10 1 x 10-10 1 x 10-4 4 9 1 x 10-9 1 x 10-5 5 8 1 x 10-8 1 x 10-6 6

6 1 x 10-6 1 x 10-8 8 5 1 x 10-5 1 x 10-9 9 4 1 x 10-4 1 x 10-10 10 3 1 x 10-3 1 x 10-11 11 2 1 x 10-2 1 x 10-12 12 1 1 x 10-1 1 x 10-13 13 0 1 x 100 1 x 10-14 14

NaOH, 0.1 MHousehold bleachHousehold ammonia

Lime waterMilk of magnesia

Borax

Baking sodaEgg white, seawaterHuman blood, tearsMilkSalivaRain

Black coffeeBananaTomatoesWineCola, vinegarLemon juice

Gastric juice

Mor

e ba

sic

Mor

e ac

idic

pH [H1+] [OH1-] pOH

7 1 x 10-7 1 x 10-7 7

Acid – Base Concentrations

pH = 3

pH = 7

pH = 11

OH-

H3O+OH-

OH-H3O+

H3O+

[H3O+] = [OH-] [H3O+] > [OH-] [H3O+] < [OH-]

acidicsolution

neutralsolution

basicsolution

co

nc

en

trat

ion

(m

ole

s/L

)

10-14

10-7

10-1

Timberlake, Chemistry 7th Edition, page 332

pH

pH = -log [H+]

Kelter, Carr, Scott, Chemistry A World of Choices 1999, page 285

Self-Ionization Of Water

• Even the purest of water conducts electricity. This is due to the fact that water self-ionizes, that is, it creates a small amount of H3O+ and OH-.

H2O + H2O H3O+ + OH-

Kw = [H3O+][OH-]

• Kw - ion product of water

Kw = 1.0 x 10-14 at 25 oC

• This equilibrium constant is very important because it applies to all aqueous solutions - acids, bases, salts, and non-electrolytes - not just to pure water.

OH

H

OH

HO

Self ionization reaction of water:

+O

HH

H

OHOHOH2 32

C)25(at10][OH]O[HK -143w

[OH-]

Kw]O[H3

H

+

+-

pH and pOH

• pH = - log[H3O+] [H3O+] = 10-pH

pOH = - log[OH-] [OH-] = 10-pOH

• pKw = pH + pOH = 14.00

• neutral solution: [H3O+] = [OH-] = 10 –7 M pH = 7.0

acidic solution: [H3O+] > 10-7 M pH < 7.0

basic solution: [H3O+] < 10-7 M pH > 7.0

LecturePLUS Timberlake 14

Learning Check pH

A. The [H3O+] of tomato juice is 1 x 10-4 M.

What is the pH of the solution?

1) - 4 2) 4 3) 8

B. The [OH-] of an ammonia solution is

1 x 10-3 M. What is the pH of the solution?

1) 3 2) 11 3) -11

LecturePLUS Timberlake 15

Solution pH4

A. pH = - log [ 1 x 10-4] = -(- 4) = 4

B. [H3O+] = 1 x 10-11

pH = - log [ 1 x 10- 11] = -(- 11) = 11

LecturePLUS Timberlake 16

Learning Check pH5

The pH of a soap is 10. What is the [H3O+] of the soap

solution?

1) 1 x 10 - 4 M

2) 1 x 1010 M

3) 1 x 10 - 10 M

LecturePLUS Timberlake 17

Solution pH5

The pH of a soap is 10. What is the [H3O+]

of the soap solution?

[H3O+] = 1 x 10-pH M

= 1 x 10-10 M

18

pH on the Calculator

[H3O+] is 4.5 x 10-6 M

pH = -log(4.5 x10-6 )

= 5.35

LecturePLUS Timberlake 19

Learning Check pH6

A soap solution has a [H3O+] = 2 x 10-8 M. What is the pH of

the solution?

1) 8

2) 7.7

3) 6

20

Solution pH6

A soap solution has a [H3O+] = 2.0 x 10-

8 M. What is the pH of the solution?

B) = 7.7

Calculating pH from pOH

• The concentration of [OH–] in a cleaning product was found to be 10–3 mol L–1.

• Find the pH of the solution.

Practise

• (a) A 0.01 mol L–1 solution of HNO3 is prepared. Calculate the pH of the

• solution.

• (b) A 0.005 mol L–1 solution of H2SO4 is prepared. Assuming complete

• ionisation, calculate the pH of the solution.

Sample Problem: Calculating the pH of a dilution

• 50 mL of a solution of HCl of pH 2 is diluted so that the new pH is 5. What

• volume of water was added?