# 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.

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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 7 th Edition, page 335

LecturePLUS Timberlake5 Ionization of Water Occasionally, in water, a H + is transferred between H 2 O 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: H 3 O + and OH - H 2 O + H 2 O H 3 O + + OH - hydronium hydroxide ion ion 1 x 10 -7 M H3O+H3O+ OH -

7 Ion Product of Water K w K w = [ H 3 O + ] [ 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 10 0 1 x 10 -14 14 NaOH, 0.1 M Household bleach Household ammonia Lime water Milk of magnesia Borax Baking soda Egg white, seawater Human blood, tears Milk Saliva Rain Black coffee Banana Tomatoes Wine Cola, vinegar Lemon juice Gastric juice More basic More acidic pH [H 1+ ] [OH 1- ] pOH 7 1 x 10 -7 1 x 10 -7 7

Acid – Base Concentrations pH = 3 pH = 7 pH = 11 OH - H3O+H3O+ H3O+H3O+ H3O+H3O+ [H 3 O + ] = [OH - ] [H 3 O + ] > [OH - ] [H 3 O + ] < [OH - ] acidic solution neutral solution basic solution concentration (moles/L) 10 -14 10 -7 10 -1 Timberlake, Chemistry 7 th 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 H 3 O + and OH -. H 2 O + H 2 O º H 3 O + + OH - K w =[H 3 O + ][OH - ] K w - ion product of water K w = 1.0 x 10 -14 at 25 o C This equilibrium constant is very important because it applies to all aqueous solutions - acids, bases, salts, and non-electrolytes - not just to pure water.

O H H O H H O Self ionization reaction of water: + O H H H H + + -

pH and pOH pH = - log[H 3 O + ][H 3 O + ] = 10 -pH pOH = - log[OH - ][OH - ] = 10 -pOH pK w = pH + pOH = 14.00 neutral solution: [H 3 O + ] = [OH - ] = 10 –7 M pH = 7.0 acidic solution: [H 3 O + ] > 10 -7 M pH < 7.0 basic solution: [H 3 O + ] 7.0

LecturePLUS Timberlake14 Learning Check pH A. The [H 3 O + ] of tomato juice is 1 x 10 -4 M. What is the pH of the solution? 1) - 42)43)8 B. The [OH - ] of an ammonia solution is 1 x 10 -3 M. What is the pH of the solution? 1) 32)113)-11

LecturePLUS Timberlake15 Solution pH4 A. pH = - log [ 1 x 10 -4 ] = -(- 4) = 4 B. [H 3 O + ] = 1 x 10 -11 pH = - log [ 1 x 10 - 11 ] = -(- 11) = 11

LecturePLUS Timberlake16 Learning Check pH5 The pH of a soap is 10. What is the [H 3 O + ] of the soap solution? 1) 1 x 10 - 4 M 2) 1 x 10 10 M 3) 1 x 10 - 10 M

LecturePLUS Timberlake17 Solution pH5 The pH of a soap is 10. What is the [H 3 O + ] of the soap solution? [H 3 O + ] = 1 x 10 -pH M = 1 x 10 -10 M

18 pH on the Calculator [H 3 O + ] is 4.5 x 10 -6 M pH = -log(4.5 x10 -6 ) = 5.35

LecturePLUS Timberlake19 Learning Check pH6 A soap solution has a [H 3 O + ] = 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 [H 3 O + ] = 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 HNO 3 is prepared. Calculate the pH of the solution. (b) A 0.005 mol L–1 solution of H 2 SO 4 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?

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