# Acids and Bases. Problem Set: Chapter 17 questions 5-7, 9, 11, 13, 18, 43, 67a-d, 71 Chapter 18 questions 5-9, 26, 27a-e, 32

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1 Acids and Bases Problem Set: Chapter 17 questions 5-7, 9, 11, 13, 18, 43, 67a-d, 71 Chapter 18 questions 5-9, 26, 27a-e, 32

2 Arrhenius Theory of Acids An acid base reaction involves the reaction of hydrogen ions; and hydroxide ions to form water. All bases contain OH -. All acids contain H + : H + (aq) + OH - (aq) H 2 O (l) The problem with this theory is that it requires that base have an OH - group. Ammonia, NH 3, does not contain OH -, but is nonetheless a base. Another problem of Arrhenius theory is in its not considering the role of the solvent, H 2 O.

3 Bronsted-Lowry Theory An acid is a proton donor. A base is a proton acceptor. Both problems with the Arrhenius theory can be now taken care of. We now recognize that NH 3 acts as a base because of it s role as a hydrogen atom acceptor in the reaction. Moreover, we can include the solvent, H 2 O in our consideration:

4 Base Ionization Constant For the previous reaction, we can write the following equilibrium expression, called the base ionization constant. Note that water does not explicitly appear in the equilibrium expression because the reaction is taking place in water (pure liquid) K + - [NH4 ] [OH ] 5 b = = [NH3] In the reaction, NH 3 acts as a base (proton acceptor) and H 2 O acts as an acid (proton donator). The conjugate acid of NH 3 is NH 4+. The conjugate base of water in the reaction is OH -. We would refer to NH 4+ /NH 3 as a conjugate acid/base pair. Note: The larger the value of K b, the stronger the base. NH 3 is a weak base, that is there is a reasonable amount of unreacted NH 3

5 A Weak Acid Water can also act as base (proton acceptor), when it reacts with an acid such as acetic acid, to form the hydronium ion, H 3 O + Acetic acid gives up a proton to form the acetate ion. CH 3 CO 2 H/CH 3 CO 2- form a conjugate acid base pair. Hydronium ion

6 Acid Ionization Constants For the acid reaction we can write the acid ionization equilibrium constant, K a K [CH CO ][H O a = = [CH3CO2H] ] The value of K a is a measure of the strength of the acid in water. The larger the value of K a, the further the equilibrium lies to the right, the stronger the acid. Recall: for a base, the larger the value of K b, the stronger the base. Regardless of the value of K a or K b, if the acid or base ionization reaction does NOT go to completion, we call them weak acids and weak bases

7 A Strong Acid Hydrochloric acid will react in the following way in water: HCl (aq) + H 2 O (l) H 3 O + (aq) + Cl - (aq) We write a single arrow for the reaction since the reaction is complete. The K a for the reaction is about The large value of K a implies that the equilibrium lies completely to the right. Because the acid dissociates completely, we call this a strong acid.

8 Comparison of Extent of Ionization of Acetic Acid and HCl What does complete dissociation mean? To what extent does HCl dissociate in water, and how does this compare to a weak acid such as acetic acid. Let s calculate the fraction of the acid in the A - form after the reaction: HA (aq) + H 2 O (l) H 3 O + (aq) + A - (aq) HA H 3 O + A - I nitial (mol/l) C HA 0 0 C hange (mol/l) -x +x +x E quilibrium (mol/l) C HA -x +x +x C HA is the initial formal concentration of the acid

9 Cont d K [A ][H3O [HA] - + a = = ] [C x HA 2 - x] x 2 + K a x K a C HA = b ± b 4ac K a ± K a + 4K x = = 2a 2 - [A ] x fraction of ionized acid = = C C HA HA a C HA CH 3 CO 2 H C HA = 0.01M K a 1.8 x 10-5 x 4.15 x 10-4 M x/c HA *100% 4.15% HCl C HA = 0.01M ~ 1 x x 10-3 M %

10 Relative Strength of Acids and Bases The stronger an acid, the weaker it s conjugate base e.g.: HCl dissociates completely in water. It s conjugate base, Cl -, has virtually no tendency to take a proton from H 3 O + (or H 2 O).

11 Non-Aqueous Solvents Note that HClO 4, HI, HBr, HCl, H 2 SO 4 and HNO 3 are all strong acids. We cannot tell which acid is stronger because they all dissociate completely in water to yield H 3 O + Water is said to have a levelling effect on the acids the strong acids all appear to have the same strength. To differentiate them, we need to use a solvent that is a weaker base then water (acetic acid or diethyl ether) HClO 4 dissociates completely in diethylether. It is a stronger acid than HCl

12 What we learned so far: Acid is a proton donor, Base is a proton acceptor Acids and bases react with H 2 O Strong acids and strong bases completely ionize when react with H 2 O Weak acids and bases reach equilibrium with their conjugate bases and acids when react with H 2 O: 1) HA + H 2 O A - + H 3 O + Weak acid ionization constant: - [A ][H O [HA] 3 Ka = + ] 2) B + H 2 O BH + + OH - Weak acid ionization constant: K b = [BH ][OH [B] + ]

13 Autoprotolysis of Water Electrical conductivity measurements indicate that even the purest water has a finite electrical conductivity. Electrical conduction in water requires the presence of ions. Finite conductivity remains due to the self ionization of water (autoprotolysis) which stems from it s amphiprotic nature (ability to act both as an acid and a base): H 2 O (l) + H 2 O (l) K w = [H 3 O + ][OH - ] ~ 1.0 x (25 o C) H 3 O + (aq) + OH - (aq) K w is referred to as the ion product of water Definition: pk w = - log(k w )

14 Pure water What is the [H 3 O + ] in pure water at 25 o C (0 o C,50 o C,100 o C)? 2 H 2 O (l) H 3 O + (aq) + OH - (aq) 55M 2x x x [H 3 O + ] = [OH - ] = x K w = [H 3 O + ] [OH - ] = x 2 T ( o C) K w x = [H O = + 3 ] K w [H 3 O + ]= [OH - ]

15 Hydronium ion in solution σ- Highlypolarized molecule σ In solution, the hydronium ion is likely highly solvated. This figure shows a H 3 O + surrounded by 4 water molecules, H 11 O 5+. Other hydrated species, such as H 9 O 4 + are also postulated to exist.

16 ph Soren Sorenson defined ph back in The potential of hydrogen ion, or ph of a solution is defined to be: ph = -log [H + ] = -log[h 3 O + ] (Strictly ph = -log a H3O+ ) poh = -log [OH - ] (Strictly poh = -log a OH ) How are ph and poh related? K w = [H 3 O + ][OH - ] = 1.0 x log K w = -log [H 3 O + ][OH - ] = -log pk w = -log [H 3 O + ] log [OH - ] = 14 ph + poh = 14 Note: poh is not used practically! If you ever need to calculate it, then it is simply: poh = 14 - ph

17 Why is ph so Important! 1. For reaction in aqueous solutions, reaction rates will typically depend on ph. For example, practically all enzymatic reactions have maximum value at optimal ph. This is important for for biological functioning. The electrical charge of most biological molecules will depend on ph due to ph influence on the ionization of weak bases and week acids which are components of those molecules.

18 Three ionizable groups in an amino acid, e.g. lysine H H : + N H H H H H + H.. N H O H H H H H H O H At ph < 9 amino groups are protonated and the molecule acquires +2 charge. At high ph > 3 the carboxyl group deprotonates and the molecule acquires 1 charge. Therefore, 1) for ph < 3 the charge is +2 2) for ph between 3 and 9 the charge is +1 3) for ph > 9 the charge is 1

19 ph Scale Pure Water

20 phs of Strong Acids and Bases Strong acids and bases completely dissociate in water. HNO 3(aq) + H 2 O H 3 O + (aq) + NO 3 - (aq) Mg(OH) 2 Mg +2 (aq) + 2 OH - (aq) Calculating the ph, poh, or other quantities is usually trivial in such cases. There are exceptions in dilute solution

21 Calculations for Strong Acids & Bases using ICE table What is the ph, poh, [H 3 O + ], [OH - ] and [NO 3- ] for a 0.01 M solution of nitric acid? HNO 3(aq) H 3 O + NO 3 - (aq) I (mol/l) C (mol/l) E (mol/l) [H 3 O + ] = 0.01M; [NO 3- ] = 0.01, ph = -log 0.01 = -log10-2 = 2.00 [OH - ] = K w /[H 3 O + ] = 1 x / 0.01 = 1 x M poh = 14 ph = 14-2 = 12.0

22 Dilute Solutions Q: What is the ph of a M solution of HNO 3? A: ph = -log [0.001] = 3.00 Q: What is the ph of a 1 x 10-5 M solution of HNO 3? A: ph = -log [1 x 10-5 ] = 5.0 Q: What is the ph of a 1 x 10-7 M solution of HNO 3? A: ph = -log [1 x 10-7 ] = 7.0?? Can this be correct? Q: What is the ph of a 1 x 10-9 M solution of HNO 3? A: ph = -log [1 x 10-9 ] = 9.0?? Definitely incorrect!! A dilute solution of an acid CANNOT be basic. What s the problem?

23 Solution to dilute acid problem Problem: we ignored the autoprotolysis of H 2 O!! There are two sources of H 3 O + : HNO 3(aq) + H 2 O H 3 O + (aq) + NO 3 - (aq) 2 H 2 O H 3 O + (aq) + OH - (aq) The total charge should be zero Information we can use to solve the problems is as follows: For the 1 st equation: C HNO3 = [NO 3- ] = 1.0 x 10-9 M For the 2 nd equation: K w = [H 3 O + ][OH - ] = 1.0 x (1) Charge Balance Equation: for a neutral solution the number of moles of positive charge must be equal to the number of moles of negative charge. In the current case: [H 3 O + ] = [NO 3- ] + [OH - ] (2)

24 Cont d Mass Balance Equation: there is usually a mass balance that can be written in equilibrium problems. In the current case, we could write: total H 3 O + = H 3 O + from nitric acid + H 3 O + from dissociation of water. The amount of H 3 O + from nitric acid is equal to C HNO3 since HNO 3 dissociates completely The amount of H 3 O + from H 2 O dissociation must be equal to [OH - ], since water dissociates 1:1 (1 H + for each OH - ), [H 3 O + ] = C HNO3 + [OH - ] (3) or [H 3 O + ] = [NO 3- ] + [OH - ] Note: that in this problem, the charge balance (2) and mass balance equations (3) are identical.

25 Substitute (1) into (3): + K w [H O ] = CHNO3 + [H O [H O ] = C HNO3 + Solution to problem C 2 HNO3 2 From the definition: K w =[OH - ][H 3 O + ] ] + 4K If C HNO3 = 1 x 10-9 M, we get [H 3 O + ] = 1.01 x 10-7 M ph = -log [1.01 x 10-7 M] ph = Exact solutions as a function of C HNO3 are shown on the following graph. ph w [H 3 O + ] 2 -C HNO3 [H 3 O + ] K w = 0 Dilute Nitric Acid 3 1E-09 1E-08 1E-07 1E-06 1E-05 1E-04 1E-03 C_HNO3 [M] Approximation Exact

26 What we learned so far: - Strong acids fully dissociate: HA + H 2 O A - + H 3 O + - ph of strong acids simply depends on their concentrations: 1. High concentration: C HA >> 2K w 1/2 ph -log C HA 2. Low concentration: C HA 2K w 1/2 2 CHA + CHA + 4K ph = log 2 3. Very low concentration: C HA << 2K 1/2 w w ph log K w Note: the equation for low concentrations is general and applicable to high concentrations as well

27 Formulas of Weak Acids Example: Chloroacetic acid Empirical Formula: C 2 H 3 O 2 Cl Molecular Formula: C 2 H 3 O 2 Cl Acid Formula: HC 2 H 2 O 2 Cl Condensed Formula: CH 2 ClCOOH or CH 2 ClCO 2 H Lewis Structure:

28 pk a and pk b The following are general formulas for the K a s and K b s of monofunctional weak acids and weak bases HA + H 2 O H 3 O + + A - B + H 2 O BH + + OH - K a K b = = [A ][H O ] [BH + 3 [HA] ][OH [B] + ] pk a = -log K a pk b = -log K b The stronger the weak acid, the larger its K a, and thus the smaller its pk a. Similar argument is valid for strength of bases: the stronger the weak basis, the larger its K b, and thus the smaller its pk b

29 pk a = ph at which a half of HA is ionized ([A - ] = [HA]) K a = [A ][H O ] + 3 [HA] 1 C HA = [HA] + [A - ] K a = [H 3 O + ] pk a = - log K a = -log [H 3 O + ] = ph by definition Assignment: Define pk b in a similar way

30 K a s of Weak acids

31 Weak Acid/Weak Base Problems fall in 3 categories 1. Calculate K b or K a for a solution of a known concentration if ph is measured 2. Calculate ph of a solution when the extent of dissociation is minimal 3. Calculate ph of a solution when the extent of dissociation is significant

32 Finding K a Hypochlorous acid, HOCl, is used as a disinfectant in pools and water treatment. A solution of HOCl of concentration C HA (where C HA >> 2K w 1/2 ) has a known ph. Find K a Create an ICE table HOCl + H 2 O H 3 O + + OCl - Initial C HA 0 0 Change -x + x + x Equilib C HA -x x x K a = [H 3 O + ][OCl - ] [HOCl] But, we should know [H 3 O + ] from ph

33 Cont d ph = -log [H 3 O + ] -ph = log [H 3 O + ] [H 3 O + ] = x = 10 -ph K a [H O ][OCl ] x 10 [HOCl] C -x C = = = HA HA 2pH ph Solve solve the problem if ph = 4.18 for C HA = M Ka = =

34 Finding ph of Weak Acid Solution Boric acid, B(OH) 3, is used as a mild antiseptic. What is the ph of a an aqueous solution of boric acid of concentration C HA? What is the degree of ionization of boric acid in this solution? Assume that K a of boric acid is known and that water self-ionization is negligible. Although it s molecular formula does not imply this to be an acid, the hydrogen ion arises principally from the reaction Note: B(OH) 3 is an acceptor of OH -, that is equivalent to donating H + B(OH) 3 (aq) + 2H 2 O B(OH) 4- + H 3 O + To solve, create ICE table again. HBo is symbol for boric acid Bo - is the symbol for its conjugate base B(OH) 4-. K a

35 K a Continued HBo H 3 O + + Bo - Initial C HA 0 0 Change -x +x +x Equilibrium C HA - x x x [H O ][Bo ] x [HBo] C -x = = Solution: x = HA K + K + 4K C 2 a a a HA 2 x 2 + K a x K a C HA = 0 Where x=[h 3 O + ]=[Bo - ] K + K + 4K C ph= logx = log 2 2 a a a HA The degree of ionization by definition is [A - ]/C HA [A ] K + K + 4K C = C 2C HA 2 a a a HA HA Solve solve the problem for C HA = M and K a = 5.9 x x = = C HA 4

36 Conditions for small degree of ionization [A ] K + K + 4K C = C 2C HA 2 a a a HA If K a /C HA << 1 (K a << C HA ) then the degree of ionization is small. Indeed, if K a << C HA then K a2 << K a C HA and thus K a << (4K a C HA ) 1/2. Then, 2 x Ka + Ka + 4KaCHA 4KaCHA = = = K/C a HA << 1 C 2C 2C HA HA HA Important consequence: K a /C HA << 1 then 2 Ka + Ka + 4KaCHA x = = K C, and ph = log K C 2 HA ( ) a HA a HA

37 Conditions for high degree of ionization [A ] K + K + 4K C = C 2C HA 2 a a a HA If K a /C HA >> 1 (C HA << K a ) then the degree of ionization is high. Indeed, if K a /C HA << 1 then: 2 2 4KaCHA CHA Ka + K 2 a + Ka K 2 a + Ka 1+ 4 Ka + Ka + 4KaCHA Ka Ka degree of ionization = = = = 2C 2C 2C C x = =,where x = CHA 2 2x K K HA K a + + CHA a HA HA HA HA Degree of ionization for C HA << K a is equal to: ( + ) ( + + ) a 2 2 ( 1+ 4x) 1 ( ) x 1+ 4x x x+1 limx 0 = limx 0 = limx 0 = limx 0 = 2x 2x 2x 1+ 4x+1 2x 1+ 4x x 1 4x 2 2 = limx 0 = limx 0 = limx 0 = = 1 2x 1 4x +1 2x 1 4x x Thus, if C HA << K a, the degree of ionization is high

38 Example: Dependence of degree of ionization on C HA For a strong acid: K a is always >> C HA (remember that Ka >> 1, but CHA 1) Therefore, the degree of ionization is always high For a weak acid K a >> C HA only at very low concentrations; it is when the degree of ionization may be high

39 Dissociation of Weak Bases By analogy, create an ICE table for dissociation of a weak base, B. B + H 2 O BH + + OH - K b = [BH + ][OH - ] [B] Initial C B 0 0 Change -x +x + x Equilib C B -x x x If K b << [B] [OH ] = K b C B If K b << [B] [OH ] = - K K 2 b + b + 2 4K b C B

40 Polyprotic Acids (and bases) Acids (or bases) that generate more than one H + (OH - ) upon dissolving in aqueous solution typically undergo a series of acid/base equilibria. Consider H 3 PO 4 : H 3 PO 4 + H 2 0 H 3 O + + H 2 PO - 4 K a1 = 7.5 x 10-3 H 2 PO 4- + H 2 0 H 3 O + + HPO 2-4 K a2 = 6.2 x 10-8 HPO H 2 0 H 3 O + + PO 3-4 K a3 = 4.8 x Intermediate species can act as both an acid and a base. We say they are amphiprotic PO H 2 O HPO OH - K b1 = 2.1 x 10-2 HPO H 2 O H 2 PO 4- + OH - K b2 = 1.6 x 10-7 H 2 PO 4- + H 2 O H 3 PO 4 + OH - K b3 = 1.3 x Note: Ions react with water. Earlier we saw only neutral molecules reacting with newtral molecules and ions with ions

41 Calculating ph for Weak Polyprotic Acids We can make several assumptions about ionisation of weak polyprotic acids: 1. Essentially all the H 3 O + is produced in the first ionization step. The acid is weak, thus K a1 << 1. Thus the extent of ionization is low. Thus, [H 2 PO 4- ]<< C H4PO4. Thus, the amount of H3O produced in the 2 nd and 3 rd equilibria is small. 2. [H 2 PO 4- ] [H 3 O + ]. Since K a2 << 1, then very little of H 2 PO 4- is ionized (unless the concentration of H 2 PO 4- is so low that the level of ionization becomes high). 3. [HPO 4 2- ] K a2. This is the result of assumption 2 [HPO ][H O ] K [HPO ] [HPO ]=K a = = a2 [H2PO 4 ] 4. [PO 4 3- ] K a2 K a3 /[H 3 O + ]. This is the result of [PO ][H O ] [PO ][H O ] K K 3 K [PO ]= [HPO ] K [H O ] a2 a a = = a2 3

42 Calculating ph for Weak Polyprotic Acids Continued Using the first assumption as conclude that ph of a weak polyprotic acid is determined by the first equilibrium: ph = -log[h O 3 + ] = log - K K 2 a + 1 a K where H n A is a general formula for a plyprotic acid with n protons Note: the 3 assumptions allow to find not only ph but also the concentrations of all intermediates: H 2 PO 4-, HPO 4 2-, and PO 4 3- Home assignment: Solve example 17-9 from the text a 1 C H n A

43 Other Polyprotic Acids Home assignment: Solve example from the text

44 Relationship Between pk a of an Acid and pk b of its Conjugate Base CH 3 CO 2 H (aq) + H 2 O (l) H 3 O + (aq) + CH 3 CO 2 - (aq) acetic acid acetate + [CH3CO2 ][H3O ] 5 K a = = [CH3CO2H] But let us also consider the hydrolysis reaction of acetate, where acetate acts as a base: CH 3 CO - 2 (aq) + H 2 O (l) OH - (aq) + CH 3 CO 2 H (aq) acetate acetic acid [CH3CO2H][OH ] 10 K b = = [CH3CO2 ]

45 K a K b [CH3CO2 ][H3O = [CH CO H] K ak b = [H3O K K = K a b w 3 + ] 2 [OH ] + ] [CH3CO2H][OH [CH CO ] pk + pk = pk OR pk + pk = 14 at 25 C a b w a b This is a general result, the K a of an acid and the K b of it s conjugate base are related. From this we can write three equivalent statements The higher the K a of an acid, the lower the K b of its conjugate base. The lower the pk a of an acid, the higher the pk b of its conjugate base. The stronger an acid is, the weaker is it s conjugate base! 3 2 ]

46 Salts Solutions of salts are very common in chemistry, biological systems, environmental matrices, etc. We can now predict in a qualitative sense (and in some cases quantitatively) the ph of solutions of acids, bases and salts. Salts of strong acids/strong bases Example solution of MgBr 2, salt of strong acid + strong base 2HBr (aq) Weak conjugate acid of strong base + Mg(OH) 2 (aq) 2 H 2 O (l) + MgBr 2 (aq) formation MgBr 2 (aq) Mg 2+ (aq) + 2 Br - (aq) Mg +2 (aq) + H 2 O dissolution No reaction Br - Weak conjugate (aq) + H 2 O base of strong acid Weak conjugate acid and base do not hydrolyze (do not react with water) ph = 7 No reaction

47 Salt of Strong Acid/Weak Base Salts of strong acids/weak bases Example aqueous solution of NH 4 NO 3, which is salt of strong acid (HNO 3 ) and weak base (NH 3 ): HNO 3(aq) + NH 3(aq) NH 4 NO 3 (aq) formation Weak conjugate base of strong acid Strong conjugate acid of weak base NH 4 NO 3 (aq) NH + 4 (aq) + NO - 3 (aq) dissolution NO - 3 (aq) + H 2 O No reaction NH + 4 (aq) + H 2 O H 3 O + (aq) + NH 3 (aq) reaction! Conjugate acid of the weak base is strong thus it will hydrolyze ph < 7

48 Salt of Weak Acid/Strong Base Salts of weak acids/strong bases Example solution of NaF, salt of weak acid + strong base NaOH (aq) + HF (aq) H 2 O (l) + NaF formation (aq) NaF Na + (aq) + F - (aq) dissolution Weak conjugate acid of strong base Strong conjugate base of weak acid Na + (aq) + H 2 O No reaction F - (aq) + H 2 O HF (aq) + OH - (aq) reaction! Conjugate base of the weak acid is strong, it will hydrolyze ph > 7

49 Salt of Weak Acid/Weak Base Salts of weak acids/weak bases -conjugate base of the weak acid will hydrolyze, as will the conjugate acid of the weak base. One must look at the pk a and pk b to predict the ph of solution. Example solution of C 2 H 5 NH 3 C 7 H 5 O 2,(ethylammonium benzoate), salt of weak acid + weak base C 7 H 5 O 2 H (aq) + C 2 H 5 NH 2(aq) C 2 H 5 NH 3 C 7 H 5 O 2 (aq) formation C 2 H 5 NH 3 C 7 H 5 O 2 (aq) C 2 H 5 NH 3 + (aq) +C 7 H 5 O 2 - (aq) Strong conjugate acid of weak base Strong conjugate base of weak acid dissolution C 2 H 5 NH 3 + (aq) + H 2 O H 3 O + (aq) + C 2 H 5 NH 2 (aq) reaction! C 7 H 5 O 2 - (aq) + H 2 O C 7 H 5 O 2 H (aq) + OH - (aq) How do we predict which wins out in this competition? reaction!

50 Conjugate Acid/Base competition pk a of C 7 H 5 O 2 H= 4.20; pk b of C 7 H 5 O 2- = = 9.8 pk b of C 2 H 5 NH 2 = 3.37; pk a of C 2 H 5 NH 3+ = = 10.6 Since the pk b of the basic part of the salt (i.e. benzoate) is lower than the pk a of the acidic part of the salt (ethylammonium), benzoate s base strength is stronger than ethylammonium s acid strength. The base should win out and we predict the final solution will be basic, ph>7. (Another way to look at this is to compare the pk a and pk b of the acid and base that form the salt. Since ethylamine is a stronger base than benzoic acid is an acid, then the conjugate base wins the conjugate acid and the resultant solution of the salt must be basic.)

51 Acid-Base Properties of Salts Summary Acidic Cation Anion or Basic Example neutral neutral neutral NaCl neutral conj acid of weak base conj acid of weak base conj base of basic NaF weak acid neutral acidic NH 4 Cl conj base of weak acid depends on K a & K b values Al 2 (SO 4 ) 3

52 How Does Acidity & Basicity Depend on Structure?

53 Structure related acidity K a = 2.9x10-8 Hypochlorous acid K a = 1.1x10-2 Chlorous acid K a = strong? Chloric acid K a = strong! Perchloric acid Very strong oxidizing Agent, explosive! Acetic acid ethanol K a =1.8 x 10-5 K a =1.3 x Acidity is not only related to structure of acid (energy of OH bond), but also to the stability of anion product. Resonance in acetate ion stabilizes this structure weak acid. For ethoxide ion (other alcohols are similar), the charge is localized on O -, it behaves as relatively strong base. Ethanol is therefore a very weak acid.

54 Structure Related Basicity of Amines Hydrocarbon attachments have little electron withdrawing ability. Alkyl amines are stronger base than NH 3. The effect is illustrated when comparing base strength of cyclohexylamine (nonaromatic) and aniline (aromatic). Lone pair electrons on N are responsible for base behaviour of amines, by binding to H +. Electronegative groups attached to N lower electron density, reducing strength of base. Aromatic amines have additional electron withdrawing effects due to delocalization on aromatic ring. An additional illustration of the effect of an electron withdrawing group on base strength of an aromatic amine.

55 Lewis Acids & Bases Lewis Acid: electron pair acceptor Lewis Base: electron pair donor Bronsted-Lowry (proton donor) (proton acceptor) To identify Lewis acids, look for species (ions, atoms, etc ) that have valence shells that can accept electron pairs. Example: H + Lewis acid To identify Lewis bases, look for species that have lone pair electrons that can be donated to form a covalent bond. Examples: :NH 3 :OH - Lewis bases....

56 Identifying Lewis Acids and Bases in Chemical Reactions 1. Draw the Lewis structures of the reacting molecules 2. Decide on the direction of electrons moving between the molecules 3. The molecule that accepts electron(s) is a Lewis acid, the molecule that donates electron(s) is a Lewis base Example: NH 3 + BF 3 NH 3 BF.. 3 H :F:.. H - N: B - F:.. H :F:.. Electron donor Lewis base Electron acceptor Lewis acid.. H :F:.. H N B - F:.. H :F:..

57 Complex Ions as Lewis Acids Al 3+ ions are formed upon dissolving AlCl 3 in water. Al 3+ can form coordinate covalent bonds with water: Lewis acid Al O : H H Lewis base Al O H H 6 3+ Hydrated metal ion in solution is an example of complex ion

58 Complex Ions as Lewis Acids Continued {Al(H 2 O) 6 } 3+ is a Lewis acid; it reacts with water: {Al(H 2 O) 6 } 3+ + H 2 O {Al(OH)(H 2 O) 5 } 2+ + H 3 O + Thus, the solution of AlCl 3 in water is acidic Salts of some other metal ions (in particular transition metal ions) hydrolyze and thus express acidic properties Another example is FeCl 3

59 More Acids and Bases: Buffers

60 Acids, Bases and the Common Ion Effect Consider the following acid equilibrium of a weak acid HF + H 2 O H 3 O + + F - K a = [H 3 O + ][F - ] [HF] By LeChatelier s principle, we predict the HF dissociation should be driven left, suppressing the dissociation H + + Cl - HCl (aq) What happens when we add some strong acid to the mixture? HCl completely dissociates, adding free H 3 O + to solution. This is a common ion to the weak acid equilibrium

61 More quantitative a) Determine [F - ] in a solution of 0.500M HF. b) Determine [F - ] in a solution of 0.500M HF and 0.10M HCl. K HF = 6.6x10-4. a) A solution of a weak acid. Let s use the quadratic. 2 HF HF HF HF + K K K C [ H ] = [ F ] = [F - ] = M

62 Continued b) Use ICE table. Let HF and HCl dissociate separately. HF + H 2 O H 3 O + + F - K a = [H 3 O + ][F - ] Initial [HF] weak acid C HF 0 0 strong acid 0 C HCl 0 Change -x + x + x Equilib C HF -x C HCl +x x K 2 a ( C + ) C HCl HCl x x KC Kx = C x+ x x x = x a HF a HCl + ( K+C ) x KC = 0 a HCl a HF 2 ( K+C ) + ( K+C ) + 4KC = = a HCl a HCl a HF 3

63 Continued Comparison a) no common ion, [F-] = M b) Common ion, [F-] = M 5 X less! This is one example of the common ion effect. When a strong acid supplies the common ion, H 3 O +, the ionization of a weak acid is suppressed. When a strong base supplies the common ion, OH -, the ionization of a weak base is suppressed.

64 What About Adding a Strong Base to a Weak Acid Consider the following acid equilibrium of a weak acid HF + H 2 O H 3 O + + F - By LeChatelier s principle, we predict the HF dissociation should be driven right, suppressing the withdrawal of H 3 O + OH - + Na + NaOH (aq) K a = [H 3 O + ][F - ] [HF] What happens when we add some strong base to the mixture? NaOH completely dissociates, adding free OH - to solution. OHwithdraws H 3 O + forcing the reaction to produce additional H 3 O +

65 Adding Salt of Weak Acid to Weak Acid Consider the following acid equilibrium of a weak acid HF + H 2 O H 3 O + + F - K a = [H 3 O + ][F - ] [HF] By LeChatelier s principle, we predict the HF dissociation should be driven left, suppressing the dissociation F - + Na + NaF (aq) What happens when we add some NaF? NaF is a strong electrolyte, therefore it completely dissociates, adding free F - to the solution. This is a common ion to the weak acid equilibrium. Reaction consumes the excess of F -

66 Buffers Choose the correct answer(s). Definitions of buffer in the Cambridge Dictionary of English. Buffer- something or someone that helps protect against harm Friends are excellent buffers in times of crisis Buffer- a foolish old man. Some old buffer was saying that nothing needed to be changed Buffer- a nudist, someone that enjoys dressing in the buff. Some young buffer was saying that nothing needed to be changed since there was nothing to change into.

67 Chemical buffer a chemical system that resists change Example: any chemical system in equilibrium can be considered as a buffer since it will resist to a change introduced by adding or removing its components. Removing B increases the quotient. The system responses by shifting the equilibrium to the left. aa + bb + cc dd + ee + ff K eq = d e f [D] [E] [F] [A] [B] [C] a b c

68 Acid/Base buffer a system that resists changes to ph caused by addition of excess acid or base An acid-base equilibrium is a ph buffer H A + H 0 A - + H If we add a strong acid (H 3 O + ) to this system then, according to the LeChatelier s principle, the equilibrium shifts to the left to resist to the increase of H 3 O +. The system will resist to ph change by the strong acid until it has A - present. If we add a strong base (OH - ) to this system then, according to the LeChatelier s principle, the equilibrium shifts to the right to resist to the decrease of H 3 O +. The system will resist to ph change by the strong base until it has HA present. An optimum buffer has to have about equal amounts of HA and A -. It can not be achieved by simply dissolving the weak acid in water, since its ionization level is low: [A - ] eq << [HA] eq

69 Acid/Base buffer systems can be made by mixing AH and A - (or B and BH + ) were the source of A - (or BH + ) is an appropriate salt A mixture of a weak acid, HA, and it s conjugate base, A - O O O Benzoic acid O OH CH 3 acetic acid H O benzoate O O CH 3 acetate Add as sodium salts, NaA, for example A mixture of a weak base, B, and it s conjugate acid, HB N H H 3 C CH + 3 Add as N CH H 3 C CH 3 3 CH 3 chloride trimethylamine trimethylammonium salt, HBCl for example

70 Weak Acids and Bases Widely Used as Buffers

71 Q: What is ph of a buffer made of a weak acid, HA, and its conjugate base, A - in equal concentrations (e.g. 0.1 M)? K Initial HA + H 2 O H 3 O + + A - weak acid conj base Change -x +x + x Equilib 0.1-x +x 0.1+x a = [H O 3 + ] eq [HA] [A eq ] 3 Ka = + [H O ][0.1 + x] [0.1 - x] Note: Direct addition of A - suppresses ionization of HA more than in the case of only HA dissolved. As a result x <<< 0.1 [H 3 O + ] = K a ph = pk a

72 Henderson-Hasselbalch (H-H) Equation 3 K a = + [H O ][A [HA] + -log[h 3O ] = logk a + -log[h3o ] = logka ] Solve for [H 3 O + ] - Take log of both sides log[ha] + [A ] + log [HA] log[a K [HA] [H O + a 3 ] = [A ] ph = pk log [A ] a + ph = pk log C [HA] a + C ] From previous ICE table, we see that in general: [HA] = C HA x and [A - ] = C A- + x. However, when x<<c HA, we can assume that [HA] = C HA and [A - ] = C A - A - HA Note: In the previous example we had C HA =C A-, In general, C HA C A-

73 Buffer Ratio, Buffer Capacity, Buffer Range Definitions: 1. Buffer ratio is C A- /C HA 2. Buffer capacity is the amount of strong acid or base the buffer is able to neutralize with ph changing one unit only 3. Buffer range, is the ph range over which a buffer effectively neutralizes added acids or bases Properties: 1. Buffer capacity increases with proportional increasing the concentrations of buffer components (keep C A- /C HA = const). 2. Buffer capacity is maximum when [A - ]/[HA] = 1 (ph = pk a ) 3. Buffer capacity is reasonable when 0.1 < C A- /C HA < Buffer range can be found from the H-H equation by substituting the last constraint (0.1 < C A- /C HA < 10) into the H-H equation and using log0.1 = -1, log10 = 1: Buffer Range = pka ± 1

74 How to prepare a buffer 1. What is the required ph of the buffer? 2. Find an appropriate HA/A - system from tables; pk a for such a system has to be within 1 unit of the required ph 3. Use the H-H equation to find the buffer ratio, R = C A- /C HA, you will need for the desired ph. 4. Determine the required buffer capacity = the concentration of strong acid or base that could impact the buffer. a) If you expect adding a strong acid, choose the total concentration of buffer components as: (1+ 0.1R)(1+ R) CHA + C > [strong acid to be added] A 0.9R b) If you expect adding a strong base, choose the total concentration of buffer components as: (R + 0.1)(1+ R) CHA + C > [strong base to be added] A 0.9R

75 5. Calculate the concentrations of C A- and C HA in the buffer using known: C A- /C HA (from 3) C HA + C A- (from 4) 6. Calculate the masses of components for required volume 7. Wight and dissolve buffer components

76 Example: Make 1 L of a buffer with ph 3.5 capable of buffering the addition of M HCl 1) Required ph = 3.5 2) Pick the buffer HA/A - system Acid pk a Citric Acid 3.13 Benzoic acid 4.20 Acetic acid 4.77 Carbonic acid 6.36 Ammonium ion 9.25 Citric acid has pk a closest to the desired buffer ph.

77 3) Determine ratio of C A- /C HA of citric acid needed. Use either HH- equation or equilibrium expression ph log = C C HA pk A HA a = + C A = 10 C log ph C C ph pk a A HA pk a C A = R = 10 = C HA 2.34

78 4) Required buffer capacity is M of HCl. Lets chose the total concentration of buffer components. When we add a strong acid then, (1+ 0.1R)(1+ R) CHA + C > [strong acid to be added] A 0.9R C + C - HA A > M ( )( ) Lets take C HA + C A- = 0.01 M, which is 5 times more than the required miniumum M

79 5) Calculate the concentrations of buffer components using the results from 3) and 4): We require: C A- /C HA = 2.34 (1) and C A- + C HA = 0.01M (2) 2 unknowns 2 equations from (1) C A- = 2.34 C HA, substitute into (2) to get: 2.34 C HA + C HA = 0.01M C HA = M C A- = 2.34 C HA C A- = 0.007M Note: To introduce A - into the buffer we can: (i) Use sodium salt of citric acid, NaA, that completely dissociates in water: NaA Na + + A - or (ii) React citric acid with NaOH: HA + NaOH Na + + A - + H 2 O

80 6) Calculate the masses of components (i) Using Sodium salt of citric acid: Molar Weight of citric acid, C 6 H 8 O 7 : MW HA = 192.1g/mole Molar Weight of monosodium citrate, NaC 6 H 7 O 7: MW NaA = 214.1g/mole We are preparing V = 1L with final concentrations of HA and NaA equal to and M respectively, thus: mass HA = C HA V MW HA = =0.003 mol/l 1L g/mol = 0.576g mass NaA = C NaA V MW NaA = = mol/l 1L g/mol = 1.50g 7) Weigh 0.576g of citric acid and 1.50g of monosodium citrate and dissolve them in 1 L of water. Mix vigorously. The buffer is ready!

81 6) Calculate the masses of components (ii) Using reaction of citric acid with NaOH Since citric acid is in this case a sole source of HA and A - the concentration of citric acid has to be equal to the total concentration of buffer components chosen: C citric acid = C HA + C A- = 0.01 M The mass of citric acid to be taken to obtain the concentration of 0.01 M in 1 L is: mass HA = C citric acid V MW citric acid = = 0.01 mol/l 1 L g/mol = 1.921g 7) Weigh g of citric acid, dissolve in 1L of water (resulting ph 2.62), and neutralize with NaOH until ph = 3.5. The components in the mixture would be the same as in (i) (ADD SUGAR AND ENJOY YOUR BEVERAGE)

82 Blood as a Buffer ph of blood is / ph is maintained by a series of buffer systems, in particular: H 2 CO 3 /HCO 3-, phosphate, amines and proteins. ph regulation in body is critical since functioning of enzymes is highly ph dependent. Alkalosis raising of ph resulting from hyperventilation, or exposure to high elevations (altitude sickness). Acidosis lowering of ph in blood by organ failure, diabetes or long term protein diet.

83 in the lungs CO 2(g) At elevation, P CO2(g) is lowered CO 2(aq) + H 2 O H 2 CO 3(aq) What causes alkalosis at high elevation? a multiple equilibrium hypothesis. in blood H 2 CO 3(aq) + H 2 O H 3 O + + HCO 3 - pk a = 6.4 The bicarbonate buffer is is essential At ph 7.4 from HH eq: ph increases! for controlling blood ph [HCO ] 3 [H CO ] ~10 2 3

84 Acid/Base Titrations Acid base titrations are examples of volumetric techniques used to analyze the quantity of acid or base in an unknown sample. Acid + Base H 2 O + salt Lets assume that we need to find the concentration of acid by titration with base. This is done by detecting the point at which we have added an equal number of equivalents of base to the acid. This is the equivalence point. For neutralization of an unknown monoprotic acid (A) with a base (B), we have at equivalence: moles of acid = moles of base C A V A = C B V B C = C A B V V We detect the equivalence point with a ph meter or by identifying the end-point with an acid base indicator. B A

85 ph Indicators Acid-base indicators are highly colored weak acids or bases. When added at low concentrations they do not influence ph but indicate changing ph by changing their color: HIndicator Indicator - color 1 color 2 Color transition occurs for 0.1< [Indic - ]/[HIndic]<10 ph pk [In ] log [HIn] pk ind ind transition = a + = a ± In general there are three colors: acid, transition and base Example. Bromthymol blue Yellow Green Blue One of the forms may be colorless - phenolphthalein (colorless to pink) 1

86 The colour transition range for an indicator is pk a + 1 phenolphthalein

87 Indicator Examples bromthymol blue methyl red

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