1. Self Ionisation of Water Water undergoes Self Ionisation H 2 O (l) ⇄ H + (aq) +OH - (aq) or H 2 O (l) + H 2 O (l) ⇄ H 3 O + (aq) +OH - (aq) The concentration of H + ions and OH- ions is extremely small. Because the equilibrium lies very much on the left hand side.

2. Glossary Ionisation Ionic Product pH Logarithm Kw Indicator pH scale Strong/weak acids Strong/Weak bases pH Curve End-Point Dissociation Constant

3. Ionic Product of Water H 2 O (l) ⇄ H + (aq) +OH - (aq) Kc = In the above expression, the value of [H 2 O] may be taken as having a constant value because the degree of ionisation is so small. Kc = Kc [H 2 O] = [H + ] [OH - ] Both Kc and [H 2 O] are constant values so Kw = Kc [H 2 O] = [H + ] [OH - ] Kw = [H + ] [OH - ] is the ionic product of water

4. Kw is temperature dependent T (°C)K w (mol 2 /litre 2 ) 00.114 x 10 -14 100.293 x 10 -14 200.681 x 10 -14 251.008 x 10 -14 301.471 x 10 -14 402.916 x 10 -14 505.476 x 10 -14 Kw of pure water decreases as the temperature increases

5. Acid–Base Concentrations in Solutions

6. OH - H+H+ H+H+ H+H+ [H + ] = [OH - ] [H + ] > [OH - ] [H + ] < [OH - ] acidic solution neutral solution basic solution concentration (moles/L) 10 -14 10 -7 10 -1

7. pH Scale Soren Sorensen (1868 - 1939) The pH scale was invented by the Danish chemist Soren Sorensen to measure the acidity of beer in a brewery. The pH scale measured the concentration of hydrogen ions in solution. The more hydrogen ions, the stronger the acid.

8. The pH Scale NeutralWeak Alkali Strong Alkali Weak Acid Strong Acid 7891011121334562141 78910111213345621419101112345621

9. pH Scale The quantity of hydrogen ions in solution can affect the color of certain dyes found in nature. These dyes can be used as indicators to test for acids and alkalis. An indicator such as litmus (obtained from lichen) is red in acid. If base is slowly added, the litmus will turn blue when the acid has been neutralized, at about 6-7 on the pH scale. Other indicators will change color at different pH’s. A combination of indicators is used to make a universal indicator.

10. Measuring pH Universal Indicator Paper Universal Indicator Solution pH meter

11. Measuring pH pH can be measured in several ways Usually it is measured with a coloured acid-base indicator or a pH meter Coloured indicators are a crude measure of pH, but are useful in certain applications pH meters are more accurate, but they must be calibrated prior to use with a solution of known pH

12. Limitations of pH Scale The pH scale ranges from 0 to 14 Values outside this range are possible but do not tend to be accurate because even strong acids and bases do not dissociate completely in highly concentrated solutions. pH is confined to dilute aqueous solutions

13. pH At 25 0 C Kw = 1 x 10 -14 mol 2 /litre 2 [H + ] x [OH - ] = 1 x 10 -14 mol 2 /litre 2 This equilibrium constant is very important because it applies to all aqueous solutions - acids, bases, salts, and non-electrolytes - not just to pure water.

14. pH For H 2 O (l) ⇄ H + (aq) + OH - (aq) → [H + ] = [OH - ] [H + ] x [OH - ] = 1 x 10 -14 = [1 x 10 -7 ] x [1 x 10 -7 ] [H + ] of water is at 25 0 C is 1 x 10 -7 mol/litre Replacing [H + ] with pH to indicate acidity of solutions pH 7 replaces [H + ] of 1 x 10 -7 mol/litre where pH = - Log 10 [H + ]

15. pH is temperature dependent T (°C) pH 0 7.12 10 7.06 20 7.02 25 7 30 6.99 40 6.97 pH of pure water decreases as the temperature increases A word of warning! If the pH falls as temperature increases, does this mean that water becomes more acidic at higher temperatures? NO! Remember a solution is acidic if there is an excess of hydrogen ions over hydroxide ions. In the case of pure water, there are always the same number of hydrogen ions and hydroxide ions. This means that the water is always neutral - even if its pH change

16. Students should be able to: define pH describe the use of the pH scale as a measure of the degree of acidity/alkalinity discuss the limitations of the pH scale explain self-ionisation of water write an expression for K w

17. Acid – Base Concentrations and pH pH = 3 pH = 7 pH = 11 OH - H+H+ H+H+ H+H+ [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

18. pH describes both [H + ] and [OH - ] 0Acidic [H + ] = 10 0 [OH - ] =10 -14 pH = 0 pOH = 14 7 Neutral [H + ] = 10 -7 [OH - ] =10 -7 pH = 7 pOH = 7 14 Basic [H + ] = 10 -14 [OH - ] = 10 0 pH = 14 pOH = 0

19. pH pH = -log 10 [H + ] 14

21. pH of Common Substances Acidic Neutral Basic

22. 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 + ] [OH - ] pOH 7 1 x 10 -7 1 x 10 -7 7

23. Calculations and practice pH = – log 10 [H + ] You will need to memorize the following: pOH = – log 10 [OH – ] [H + ] = 10 –pH [OH – ] = 10 –pOH pH + pOH = 14

24. pH Calculations pH pOH [H + ] [OH - ] pH + pOH = 14 pH = -log 10 [H + ] [H + ] = 10 -pH pOH = -log 10 [OH - ] [OH - ] = 10 -pOH [H + ] [OH - ] = 1 x10 -14

25. pH for Strong Acids Strong acids dissociate completely in solution Strong alkalis (bases) also dissociate completely in solution. only need to know the concentration It is easy to calculate the pH of strong acids and strong bases; you only need to know the concentration. Strong acids are so named because they react completely with water, leaving no undissociated molecules in solution.

26. pH Exercises a)pH of 0.02M HCl pH = – log 10 [H + ] = – log 10 [0.020] = 1.6989 = 1.70 b)pH of 0.0050M NaOH pOH = – log 10 [OH – ] = – log 10 [0.0050] = 2.3 pH = 14 – pOH = 14 – 2.3 =11.7 c)pH of solution where [H +] is 7.2x10 -8 M pH = – log 10 [H+] = – log 10 [7.2x10 -8 ] = 7.14 (slightly basic)

27. [OH - ] [H + ] pOH pH 10 -pOH 10 -pH -Log 10 [H + ] Log 10 [OH - ] -Log 10 [OH - ] 14 - pOH pH pH 1.0 x 10 -7 [OH - ] [OH - ] 1.0 x 10 -7 [H + ] [H + ]

28. pH and pOH pH = - log 10 [H 3 O + ][H 3 O + ] = 10 -pH pOH = - log 10 [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

29. pH of dilute aqueous solutions of strong acids monoprotic diprotic HA(aq) H 1+ (aq) + A 1- (aq) 0.3 M pH = - log 10 [H + ] pH = - log 10 [0.3M] pH = 0.48 e.g. HCl, HNO 3 H 2 A(aq) 2 H 1+ (aq) + A 2- (aq) 0.3 M0.6 M0.3 M pH = - log 10 [H + ] pH = - log 10 [0.6M] pH = 0.78 e.g. H 2 SO 4 pH = ?

30. A sample of orange juice has a hydrogen-ion concentration of 2.9 x 10 -4 M. What is the pH? pH = -log 10 [H + ] pH = -log 10 (2.9x10 -4 ) pH = 3.54

31. pH = - log [H + ] pH = 4.6 pH = - log 10 [H + ] 4.6 = - log 10 [H+] - 4.6 = log 10 [H+] - 4.6 = antilog [H+] Given: 2 nd log 10 x antilog multiply both sides by -1 substitute pH value in equation take antilog of both sides determine the [hydrogen ion] choose proper equation [H + ] = 2.51x10 -5 M You can check your answer by working backwards. pH = - log 10 [H + ] pH = - log 10 [2.51x10 -5 M] pH = 4.6

32. Most substances that are acidic in water are actually weak acids. Because weak acids dissociate only partially in aqueous solution, an equilibrium is formed between the acid and its ions. The ionization equilibrium is given by: HX(aq) H + (aq) + X - (aq) where X - is the conjugate base.

33. pH calculations for Weak Acids and Weak Bases For Weak Acids pH = -Log 10 For Weak Bases pOH = Log 10 pH = 14 - pOH

34. Calculating pH - weak acids A weak acid, HA, dissociates as followsHA (aq) H + (aq) + A¯ (aq) (1) Applying the Equilibrium Law K a = [H + (aq) ] [A¯ (aq) ] mol dm -3 (2) [HA (aq) ] The ions are formed in equal amounts, so [H + (aq) ] = [A¯ (aq) ] therefore K a = [H + (aq) ] 2 (3) [HA (aq) ] Rearranging (3) gives[H + (aq) ] 2 = [HA (aq) ] K a therefore[H + (aq) ] = [HA (aq) ] K a A weak acid is one which only partially dissociates in aqueous solution

35. pH of solutions of weak concentrations Weak Acid pH of a 1M solution of ethanoic acid with a Ka value of 1.8 x 10 -5 pH = -Log 10 pH = 2.3723

36. pH of solutions of weak concentrations Weak Base pH of a 0.2M solution of ammonia with a K b value of 1.8 x 10 -5 pOH = -log 10 pOH = 2.7319 pH = 14 – 2.7319 pH = 11.2681

37. Theory of Acid Base Indicators Acid-base titration indicators are quite often weak acids. For the indicator HIn The equilibrium can be simply expressed as HIn (aq, colour 1) H + (aq) + In - (aq, colour 2) The un-ionised form (HIn) is a different colour to the anionic form (In¯).

38. Theory of Acid Base Indicators Applying Le Chatelier's equilibrium principle: Addition of acid favours the formation of more HIn (colour 1) HIn (aq) H + (aq) + In - (aq) because an increase on the right of [H + ] causes a shift to left increasing [HIn] (colour 1) to minimise 'enforced' rise in [H + ].

39. Theory of Acid Base Indicators Applying Le Chatelier's equilibrium principle: Addition of base favours the formation of more In - (colour 2) HIn (aq) H + (aq) + In - (aq) The increase in [OH - ] causes a shift to right because the reaction H + (aq) + OH - (aq) ==> H 2 O (l) Reducing the [H + ] on the right so more HIn ionises to replace the [H + ] and so increasing In - (colour 2) to minimise 'enforced' rise in [OH - ]

40. Theory of Acid Base Indicators Summary In acidic solution HIn (aq) H + (aq) + In¯ (aq) In alkaline solution

41. Theory of Acid Base Indicators Acid-base titration indicators are also often weak bases. For the indicator MOH The equilibrium can be simply expressed as MOH (aq, colour 1) OH - (aq) + M + (aq, colour 2)

42. Theory of Acid Base Indicators Applying Le Chatelier's equilibrium principle: Addition of base favours the formation of more MOH (colour 1) MOH (aq) M + (aq) + OH - (aq) because an increase on the right of [OH - ] causes a shift to left increasing [MOH] (colour 1) to minimise 'enforced' rise in [OH - ].

43. Theory of Acid Base Indicators Applying Le Chatelier's equilibrium principle: Addition of acid favours the formation of more M + (colour 2) MOH (aq) M + (aq) + OH - (aq) The increase in [H + ] causes a shift to right because the reaction H + (aq) + OH - (aq) ==> H 2 O (l) Reducing the [OH - ] on the right so more MOH ionises to replace the [OH - ] and so increasing M + (colour 2) to minimise 'enforced' rise in [H + ]

44. Acid Base Titration Curves Strong Acid – Strong Base Strong Acid – Weak Base Weak Acid – Strong Base 25 cm 3 of 0.1 mol dm -3 acid is titrated with 0.1 mol dm -3 alkaline solution. Weak Acid – Weak Base

45. Choice of Indicator for Titration Indicator must have a complete colour change in the vertical part of the pH titration curve Indicator must have a distinct colour change Indicator must have a sharp colour change

46. Indicators for Strong Acid Strong Base Titration Both phenolphthalein and methyl orange have a complete colour change in the vertical section of the pH titration curve

47. Indicators for Strong Acid Weak Base Titration Only methyl orange has a complete colour change in the vertical section of the pH titration curve Phenolphthalein has not a complete colour change in the vertical section on the pH titration curve. Methyl Orange is used as indicator for this titration

48. Indicators for Weak Acid Strong Base Titration Only phenolphthalein has a complete colour change in the vertical section of the pH titration curve Methyl has not a complete colour change in the vertical section on the pH titration curve. Phenolphthalein is used as indicator for this titration

49. Indicators for Weak Acid Weak Base Titration Neither phenolphthalein nor methyl orange have completely change colour in the vertical section on the pH titration curve No indicator suitable for this titration because no vertical section

50. indicatorpH range litmus5 - 8 methyl orange3.1 - 4.4 phenolphthalein8.3 - 10.0

51. Colour Changes and pH ranges

52. Methyl Orange

53. Phenolphthalein

54. Universal indicator components IndicatorLow pH colorTransition pH rangeHigh pH color Thymol blue (first transition) red 1.2–2.8 orange Methyl Orange red 4.4–6.2 yellow Bromothymol blue yellow 6.0–7.6 blue Thymol blue (second transition) yellow 8.0–9.6 blue Phenolphthalein colourless 8.3–10.0 purple

55. Students should be able to: calculate the pH of dilute aqueous solutions of strong acids and bases distinguish between the terms weak, strong, concentrated and dilute in relation to acids and bases calculate the pH of weak acids and bases (approximate method of calculation to be used – assuming that ionisation does not alter the total concentration of the non-ionised form) define acid-base indicator explain the theory of acid-base indicators justify the selection of an indicator for acid base titrations