The concept of pH and pKa

1. The concept of pH and pKa Lecture 3 Handout

2. Introduction • Why is pH so important for maintaining homeostasis? • pH of blood • pH and diseases

3. Introduction • pH = the measure of the acidity or alkalinity of a solution (pH stands for "power of hydrogen“) • a measure of the activity of dissolved hydrogen ions (H+) • for very dilute solutions  the molarity (molar concentration) of H+ may be used as a substitute with little loss of accuracy • In solution  hydrogen ions occur as a number of cations including hydronium ions (H3O+)

4. continued • pure water at 25 °C  the concentration of H+ equals the concentration of hydroxide ions (OH-) • "neutral" and corresponds to a pH level of 7.0 • Solutions  the concentration of H+ exceeds that of OH- have a pH value lower than 7.0 = acids • Solutions  OH- exceeds H+ have a pH value greater than 7.0 = bases • pH is dependent on ionic activity

6. Definition • pH = a measurement of the concentration of hydrogen ions in a solution • low pH values  associated with solutions with high concentrations of hydrogen ions • high pH values  solutions with low concentrations of hydrogen ions • Pure water  a pH of 7.0, and other solutions are usually described with reference to this value • Acids  solutions that have a pH less than 7 (i.e. more hydrogen ions than water) • Bases  a pH greater than 7 (i.e. less hydrogen ions than water)

7. continued • definitions of weak and strong acids, and weak and strong bases do not refer to pH • It describe whether an acid or base ionizes in solution

8. Explanation of pH • the number (pH) arises from a measure of the activity of hydrogen ions or their equivalent in the solution • pH scale = an inverse logarithmic representation of hydrogen proton (H+) concentration • pH unit is a factor of 10 different than the next higher or lower unit • a change in pH from 2 to 3 represents a 10-fold decrease in H+ concentration, and a shift from 2 to 4 represents a one-hundred (10 × 10)-fold decrease in H+ concentration

9. . The formula for calculating pH • αH+ denotes the activity of H+ ions, is dimensionless • Activity = a measure of the effective concentration of hydrogen ions (rather than the actual concentration) • other ions surrounding hydrogen ions will shield them and affect their ability to participate in chemical reactions

10. dilute solutions (tap water)  activity is approximately equal to the numeric value of the concentration of the H+ ion:denoted as [H+] ([H3O+])measured in moles per litre (also known as molarity)often convenient to define pH as

11. continued • log10 denotes the base-10 logarithm • therefore pH defines a logarithmic scale of acidity

12. continued • . For example, if one makes a lemonade with a H+ concentration of 0.0050 moles per litre, its pH would be:

13. continued • A solution of pH = 8.2 • have an [H+] concentration of 10−8.2 mol/L, or about 6.31 × 10−9 mol/L • its hydrogen activity αH+ is around 6.31 × 10−9 • solution at 25 °C, a pH of 7 indicates neutrality (i.e. the pH of pure water) • because water naturally dissociates into H+ and OH− ions with equal concentrations of 1×10−7 mol/L

14. continued • lower pH value (for example pH 3) indicates increasing strength of acidity • higher pH value (for example pH 11) indicates increasing strength of basicity • (pure water, when exposed to the atmosphere, will take in carbon dioxide, some of which reacts with water to form carbonic acid and H+, thereby lowering the pH to about 5.7)

15. Calculation of pH for weak and strong acids • stronger or weaker acids are a relative concept • a strong acid = a species which is a much stronger acid than the hydronium (H3O+) ion • the dissociation reaction (strictly HX+H2O↔H3O++X− but simplified as HX↔H++X−) goes to completion, i.e. no unreacted acid remains in solution • Dissolving the strong acid HCl (hydrochloric acid) in water: • HCl(aq) → H+ + Cl−

16. continued • in a 0.01 mol/L solution of HCl it is approximated that there is a concentration of 0.01 mol/L dissolved hydrogen ions • the pH is: pH = −log10 [H+]: pH = −log (0.01) It equals 2

17. continued • weak acids • dissociation reaction does not go to completion • equilibrium is reached between the hydrogen ions and the conjugate base • equilibrium reaction between methanoic acid and its ions: • HCOOH(aq) ⇌ H+ + HCOO− • We must know  the value of the equilibrium constant of the reaction for each acid in order to calculate its pH • In the context of pH  this is termed the acidity constant (Ka) of the acid • Ka = [hydrogen ions][acid ions] / [acid]

18. continued • For HCOOH: Ka = 1.6 × 10−4 • When calculating the pH of a weak acid, it is usually assumed that the water does not provide any hydrogen ions • it simplifies the calculation, and the concentration provided by water, 1×10−7 mol/L, is usually insignificant

19. continued • With a 0.1 mol/L solution of methanoic acid (HCOOH), the acidity constant is equal to: Ka = [H+][HCOO−] / [HCOOH] • Given that an unknown amount of the acid has dissociated, [HCOOH] will be reduced by this amount, while [H+] and [HCOO−] will each be increased by this amount

20. continued • [HCOOH] may be replaced by 0.1 − x, and [H+] and [HCOO−] may each be replaced by x, giving us the following equation: • Solving this for x yields 3.9×10−3 = the concentration of hydrogen ions after dissociation • the pH is −log(3.9×10−3) or about 2.4

21. pH can be measured • by addition of a pH indicator into the solution under study • by using a pH meter together with pH-selective electrodes • by using pH paper, indicator paper that turns colour corresponding to a pH on a colour key

22. pH in body fluids

23. Acids • An acid (often represented by the generic formula HA [H+A-])  any chemical compound that, when dissolved in water, gives a solution with a hydrogen ion activity greater than in pure water (a pH less than 7.0) • an acid as a compound which donates a hydrogen ion (H+) to another compound (called a base)

24. continued • In water the following equilibrium occurs between a weak acid (HA) and water, which acts as a base: • HA(aq) + H2O ⇌ H3O+(aq) + A-(aq) • acidity constant (or acid dissociation constant) is the equilibrium constant for the reaction of HA with water:

25. Strong acids have large Ka values (the reaction equilibrium lies far to the right; the acid is almost completely dissociated to H3O+ and A-) • Strong acids include the heavier hydrohalic acids: hydrochloric acid (HCl), hydrobromic acid (HBr), and hydroiodic acid (HI)

26. continued • Weak acids  have small Ka values (i.e. at equilibrium significant amounts of HA and A− exist together in solution; modest levels of H3O+ are present; the acid is only partially dissociated) • Most organic acids  weak acids • nitrous acid, sulfurous acid and hypochlorous acid are all weak acids

27. Neutralization • the reaction between an acid and a base, producing a salt and neutralized base • hydrochloric acid and sodium hydroxide form sodium chloride and water: • HCl(aq) + NaOH(aq) → H2O(l) + NaCl(aq)

28. continued • Neutralization  the basis of titration, where a pH indicator shows equivalence point when the equivalent number of moles of a base have been added to an acid • It is often wrongly assumed that neutralization should result in a solution with pH 7.0 (is only the case with similar acid and base strengths during a reaction)

29. continued • Neutralization with a base weaker than the acid  weakly acidic salt • E.g. weakly acidic ammonium chloride (produced from the strong acid hydrogen chloride and the weak base ammonia) • neutralizing a weak acid with a strong base gives a weakly basic salt, e.g. sodium fluoride from hydrogen fluoride and sodium hydroxide

30. Biological occurrence of acids • In humans  hydrochloric acid is a part of the gastric acid secreted within the stomach: • hydrolyze proteins and polysaccharides • converting the inactive pro-enzyme, pepsinogen into the enzyme, pepsin

31. Bases • A strong base  a base which hydrolyzes completely, raising the pH of the solution towards 14 • weak bases (ammonia) • Arrhenius bases  water-soluble and these solutions always have a pH greater than 7 • alkali is a special example of a base, where in an aqueous environment, hydroxide ions (also viewed as OH−) are donated

32. Bases and pH • pure water  molecules dissociate into hydronium ions (H3O+) and hydroxide ions (OH−), according to the following equation: • 2H2O(l) → H3O+(aq) + OH−(aq) • concentration, measured in molarity (M or moles per dm³), of the ions  indicated as [H3O+] and [OH−]

33. continued • their product is the dissociation constant of water; has the value 10−7 M • A base accepts (removes) hydronium ions (H3O+) from the solution, or donates hydroxide ions (OH−) to the solution • Both actions will lower the concentration of hydronium ions, and thus raise pH • an acid donates H3O+ ions to the solution or accepts OH−, thus lowering pH

34. continued • base dissociation constant (or Kb)  a measure of basicity • pKb is the negative log of Kb and related to the pKa by the simple relationship pKa + pKb = 14 • Alkalinity is a measure of the ability of a solution to neutralize acids to the equivalence points of carbonates or bicarbonates

35. Neutralization of acids • When dissolved in water, the strong base sodium hydroxide decomposes into hydroxide and sodium ions: • NaOH → Na+ + OH− • in water hydrogen chloride forms hydronium and chloride ions: • HCl + H2O → H3O+ + Cl− • When the two solutions are mixed, the H3O+ and OH− ions combine to form water molecules:

36. continued • H3O+ + OH− → 2 H2O • If equal quantities of NaOH and HCl are dissolved  the base and the acid exactly neutralize, leaving only NaCl (table salt) in solution

37. Confusion between alkali and base • The terms "base" and "alkali" are often used interchangeably, since most common bases are alkalis • . It is common to speak of "measuring the alkalinity of soil" when what is actually meant is the measurement of the pH (base property). In a similar manner, bases that are not alkalis, such as ammonia, are sometimes erroneously referred to as alkaline • not all or even most salts formed by alkali metals are alkaline; this designation applies only to those salts that are basic

38. continued • most electropositive metal oxides are basic; only the soluble alkali metal and alkaline earth metal oxides can be correctly called alkalis • This definition of an alkali as a basic salt of an alkali metal or alkaline earth metal does appear to be the most common, based on dictionary definitions (however conflicting definitions of the term alkali do exist)

39. Weak acid/weak base equilibria • In order to lose a proton, it is necessary that the pH of the system rise above the pKa of the protonated acid • decreased concentration of H+ in that basic solution shifts the equilibrium towards the conjugate base form (the deprotonated form of the acid)

40. continued • In lower-pH (more acidic) solutions, there is a high enough H+ concentration in the solution to cause the acid to remain in its protonated form, or to protonate its conjugate base (the deprotonated form) • Solutions of weak acids and salts of their conjugate bases form buffer solutions

41. The Henderson–Hasselbalch equation • describes the derivation of pH as a measure of acidity (using pKa, the acid dissociation constant) in biological and chemical systems. • also useful for estimating the pH of a buffer solution and finding the equilibrium pH in acid-base reactions • Two equivalent forms of the equation:

42. and

43. continued • pKa is − log(Ka) • where Ka is the acid dissociation constant that is:

44. continued • In these equations: • A − = the ionic form of the relevant acid • Bracketed quantities such as [base] and [acid] denote the molar concentration of the quantity enclosed • In analogy to the above equations, the following equation is valid:

45. continued • B + denotes the salt of the corresponding base B

46. Inorganic buffer • A buffer solution = an aqueous solution consisting of a mixture of a weak acid and its conjugate base or a weak base and its conjugate acid • has the property that the pH of the solution changes very little when a small amount of acid or base is added to it • Buffer solutions are used as a means of keeping pH at a nearly constant value in a wide variety of chemical applications

47. In a simple buffer solution  an equilibrium between a weak acid, HA, and its conjugate base, A- HA + H2O  H3O+ + A−

48. continued • hydrogen ions are added to the solution  the equilibrium moves to the left (as there are hydrogen ions on the right-hand side of the equilibrium expression) • hydroxide ions are added  the equilibrium moves to the right (as hydrogen ions are removed in the reaction H+ + OH- → H2O) • some of the added reagent is consumed in shifting the equilibrium and the pH changes by less than it would do if the solution were not buffered

49. The acid dissociation constant for a weak acid, HA, is defined as

50. Simple manipulation with logarithms gives the Henderson-Hasselbalch equation, which describes pH in terms of pKa: