1 Acids and Bases - the Three Definitions 1. The Arrhenius Definition of an Acid 2. Acid strength and pK a 3. K a, pK a, pK b 4. polyprotic acids, pK a1, pK a2, pK a3 5. K b and pK b 6. Base strength and pK b 7. The pH scale and the 8. Autoionization of water, K w 9. pH, pOH, and pK a

2 Acids and Bases - Simple Definitions Arrhenius Definition: Acids: increases [H + ] in aqueous solution Bases: increases [OH - ] in aqueous solution Bronsted-Lowry Definition: (based on proton transfer reactions) Acids: proton (H + ) donor Bases: proton (H + ) acceptor Lewis Definition: Acids: electron pair acceptor Bases: electron pair donor

3 K a and pK a Acetic Acid is a weak Arrhenius acid, which liberates H + in solutions CH 3 COOH (aq) = CH 3 COO - (aq) + H + (aq) K a = [CH 3 COO - ] [H + ] [CH 3 COOH] = 1.76 x The pK a is by definition the negative of log 10 K a : pK a = - log 10 (1.76 x ) = 4.75

4 Ionization Constants (1)

5 Ionization Constants (2)

6 K b and pK b Arrhenius bases liberate OH - in solution. K b is the equilibrium constant for this reaction. NH 4 OH (aq) = NH 4 + (aq) + OH - (aq) K b = [NH 4 + ] [OH - ] [NH 4 OH] = 1.76 x pK b = - log 10 K b (definition) pK b = - log 10 (1.8 x ) = 4.74

7 K a and Acid Strength The stronger the acid, the larger the K a and the smaller the pK a : CH 3 COOH (aq) = CH 3 COO - (aq) + H + (aq) K a = 1.76 x HCN (aq) = CN - (aq) + H + (aq) K a = 6.17 x pK a = 4.75 HNO 2 (aq) = NO 2 - (aq) + H + (aq) K a = 4.6 x pK a = 3.34 pK a = 9.21 stronger weaker

8 Polyprotic Acids pK a1, pK a2, pK a3 describe the dissociation of the first, second, and third ionizable protons. H 2 CO 3 (aq) = HCO 3 - (aq) + H + (aq) K a1 = 4.3 x HCO 3 - (aq) = CO 3 2- (aq) + H + (aq) K a2 = 5.6 x

9 K b and Base Strength The stronger the base, the larger the K b and the smaller the pK b : NH 4 OH (aq) = NH 4 + (aq) + OH - (aq) K b = 1.8 x pK b = 4.74 stronger weaker PO 4 3- (aq) + H 2 O (l) = HPO 4 2- (aq) + OH - (aq) K b = 4.5 x pK b = 1.34 Conclusion: phosphate anion is a stronger base than NH 4 OH.

10 Acidity/Basicity of a Solution and the pH Scale The degree of acidity or basicity of a solution is measured on the pH scale: pH = -log 10 [H + ] [H + ] pH 1 M M M M M M M M 14 low pH (≈0-1) is strongly acid high pH (≈13-14) is strongly basic pH 7 is a neutral solution pOH = -log 10 [OH - ]

11 Self-Ionization of Water The concentrations of H + and OH - are related by the self- ionization of water - H 2 O = H + + OH - K w = [H + ] [OH - ] = (at 25°C) What is the [H + ] in pure water? If x = the molarity of [H + ], H 2 O = H + + OH - K w = [H + ] [OH - ] = x xx 2= Therefore, x = [H + ] = [OH - ] = M in pure water at 25°C Pure water is pH 7.0. pH 7 a neutral solution, [H + ] = [OH - ]

12 pH and pOH: Measures of Acidic and Basicity Because of the self-ionization of water, [H + ] and [OH - ] are not independent quantities but are related by K w = [H + ] [OH - ] = pOH is a logarithmic measure of the [OH - ] concentration pH + pOH = 14 pOH = -log 10 [OH - ] From the expression for K w : -Log 10 K w = - log 10 [H + ] - log 10 [OH - ] = +14

13 Acidity, Basicity, pH, and pOH pH or pOH can be used to measure acidity [H + ] pH pOH 1 M M M M M M M M 14 0 low pH or high pOH is strongly acid pH 7 is a neutral solution high pH or low pOH is strongly acid

14 Measurement of pH: the pH Meter pH varies linearly with output voltage and can be measured over the range pH 0 to pH 14

15 Acids and Bases – Simple Definitions Arrhenius Definition: Acids: increases [H + ] in aqueous solution Bases: increases [OH - ] in aqueous solution Bronsted-Lowry Definition: (based on proton transfer reactions) Acids: proton (H + ) donor Bases: proton (H + ) acceptor Lewis Definition: Acids: electron pair acceptor Bases: electron pair donor

16 Bronsted-Lowry Definition Many proton transfer reactions occur in aqueous solution. These are also acid-base neutralizations according to the Bronsted- Lowry definition (but not according to the Arrhenius definition). For example, weak acids can neutralize weak bases by a proton transfer reaction. In such reactions there are always two acids and two bases. HNO 2 (aq) + NH 3 (aq) = NO 2 - (aq) + NH 4 + (aq) acid base base acid The acids are the proton donors, the bases are proton acceptors.

17 Bronsted-Lowry Acid/Base Pairs Each species participating in a proton transfer reaction can exist in a protonated form and a de-protonated form. The protonated form is the Bronsted acid, and the de-protonated form is the Bronsted base. Thus one speaks of “conjugate acid/base pairs”. In any Bronsted acid/base neutralization, there are 1.Two Bronsted conjugate acids 2.Two Bronsted conjugate bases 3.Two Bronsted conjugate acid/base pairs HNO 2 (aq) + NH 3 (aq) = NO 2 - (aq) + NH 4 + (aq) Bronsted acidBronsted base conjugate acid/base pair Bronsted baseBronsted acid conjugate acid/base pair

18 Bronsted-Lowry Acid-Base Neutralizations H 2 PO 4 - (aq) + HCO 3 - (aq) = HPO 4 2- (aq) + H 2 CO 3 (aq) HCl(g) + NH 3 (g) = NH 4 Cl (s) 2 NH 3 (g) + CO 2 (g)  NH 2 CONH 2 (aq) + H 2 O(l) Which of the following reactions are acid/base neutralizations in the Bronsted-Lowry picture? Pick out the conjugate acid/base pairs. H 3 O + (aq) + OH - (aq) = 2 H 2 O (l) Note: any Arrhenius acid (or base) is also a Bronsted acid (or base) AcidBase Acid Base not Bronsted-Lowry Bronsted-Lowry Acid Base

19 In the Bronsted-Lowry Definition, many species can function either as Acids OR Bases H 2 PO 4 - (aq) + HCO 3 - (aq) = HPO 4 2- (aq) + H 2 CO 3 (aq) H 2 PO 4 - (aq) + HCO 3 - (aq) = H 3 PO 4 (aq) + CO 3 2- (aq) In this reaction, H 2 PO 4 - functions as a Bronsted acid (why?) In this reaction, H 2 PO 4 - functions as a Bronsted base (why?) Whether a chemical species is a Bronsted-Lowry acid or base can depend on the reaction it is in. Is H 2 PO 4 - an acid or a base?

20 Relationship of K a and K b for a Bronsted Acid/Base Pair A - + H 2 O = HA + OH - [HA] [OH - ] [A - ] K b = HA + H 2 O = A - + H 3 O + [A - ] [H 3 O + ] K a = conj acid conj base H3O+H3O+ H2OH2O conj acid conj base OH - H2OH2O A K a can be defined for any conjugate acid, and a K b for its conjugate base. Note that K a. K b = K w [HA] Back to 5