(Benjamin, Chapt. 3; pg.131-150) David Reckhow CEE 680 #6 1 - PowerPoint PPT Presentation

Print version Updated: 28 January 2020 Lecture #6 Acids & Bases: Analytical Solutions (Stumm & Morgan, Chapt.3 ) (Benjamin, Chapt. 3; pg.131-150) David Reckhow CEE 680 #6 1

Definitions  Early  Acids  turns blue litmus red  tastes sour  neutralizes bases  reacts with active metals to evolve H 2  Bases  turns red litmus blue  tastes bitter  feels soapy David Reckhow CEE 680 #6 2

Definitions (cont.) H H O H  Arrhenius (1887)  Acids O H H H  solutions which contain an excess of H O O hydrogen ions  e.g., HNO 3 = H + + NO 3 - H H  H + doesn’t exist free in solution  Bases  solutions which contain an excess of hydroxide ions David Reckhow CEE 680 #6 3

Definitions (cont.)  Bronsted-Lowry (1923)  Acids: (proton donor)  any substance that can donate a proton to any other substance  Bases: (proton acceptor)  any substance that accepts a proton from any other substance • Acid strength of a conjugate Acid 1 + Base 2 = Acid 2 + Base 1 acid-base pair is measured H 3 O + - relative to the other pair HNO 3 + H 2 O = + NO 3 • the stronger the acid, the H 3 O + OCl - HOCl + H 2 O = + weaker the conjugate base, and vice versa + H 3 O + NH 4 + H 2 O = + NH 3 H 3 O + OH - H 2 O + H 2 O = + David Reckhow CEE 680 #6 4

Definitions (cont.)  Lewis  Acids  can accept and share a long pair of electrons  Bases  can donate and share a lone pair of electrons A more general definition: includes metal ions as acids David Reckhow CEE 680 #6 5

pH: the intensity factor Alkalinity: a capacity factor David Reckhow CEE 680 #6 6

What are the limits of pH?  How low can you go?  Volcanic lakes  Lake Katanuma in Japan; pH = 1.7 Nordstrom et al., 2000  Hot springs [ES&T 34:254]  Near Ebeko Volcano in Russia; pH = -1.7  Acid mine drainage  Richmond mine near Redding CA, pH = -3.6 From: Brezonik & Arnold, 2011 David Reckhow CEE 680 #6 7

Effect of proton acceptor  Strong acid in water  HCl + H 2 O = H 3 O + + Cl - H O O Cl H Cl H H H H  Weak acid in organic solvent (ethanol) + + Cl -  HCl + C 2 H 5 OH = C 2 H 5 OH 2 H O CH 3 Cl H O CH 3 Cl H C H C H 2 H 2 David Reckhow CEE 680 #6 8

Acid/Conjugate Base  Weak acids do not substantially donate a proton  e.g., H 2 CO 3 , HAc, H 2 S, HOCl  The stronger an acid is the weaker its conjugate base. The stronger a base is the weaker its conjugate acid H O O Cl H Cl H H H H David Reckhow CEE 680 #6 9

Acids & Bases  pH of most mineral-bearing waters is 6 to 9. (fairly constant)  pH and composition of natural waters is regulated by reactions of acids & bases  chemical reactions; mostly with minerals  carbonate rocks: react with CO 2 (an acid)  CaCO 3 + CO 2 = Ca +2 + 2HCO 3 -  other bases are also formed: NH 3 , silicates, borate, phosphate  acids from volcanic activity: HCl, SO 2  Biological reactions: photosynthesis & resp.  Sillen: Ocean is result of global acid/base titration David Reckhow CEE 680 #6 10

Acids & Bases (cont.)  Equilibrium is rapidly established  proton transfer is very fast  we call [H + ] the Master Variable  because Protons react with so many chemical species, affect equilibria and rates  Strength of acids & bases  strong acids have a substantial tendency to donate a proton. This depends on the nature of the acid as well as the base accepting the proton (often water). David Reckhow CEE 680 #6 11

Autodissociation of water + + − ↔ H 2 O H OH  Actually donation of proton to neighboring water + + 15.5 − ↔ 2 H O H O OH 14.15 2 3 15.0 14.10 14.05 pKw 14.00 14.5 13.95 13.90 + − { H }{ OH } 14.0 13.85 = K pK w 13.80 w 20 21 22 23 24 25 26 27 28 29 30 { H O } 13.5 Temperature oC 2 13.0 ≈ + − { H }{ OH } 12.5 − ≈ 14 o 10 @ 25 C 12.0 0 20 40 60 80 100 See Table 3.1 in Benjamin Temperature o C CEE 680 #6 12 D id R kh

Mathematical Expression of Acid/Base Strength  Equilibrium constant  acids: HA = H + + A -  HCl + H 2 O = H 3 O + + Cl - [ ][ ] + − H Cl  HCl = H + + Cl - = ≈ 3 K a 10 [ ]  Bases: B + H 2 O = BH + + OH - HCl + + OH -  NH 3 + H 2 O = NH 4 [ ][ ] + − NH OH 10 − = = 4 . 76 K b 4 [ ] NH 3 David Reckhow CEE 680 #8 13

Relationship between K a and K b + pair  For the NH 3 /NH 4 [ ] [ ] + H NH + = NH 3 + H + 10 − = = 9 . 24 [ ] 3  NH 4 K a + NH + + OH -  NH 3 + H 2 O = NH 4 4 [ ][ ] + − NH OH  combining = = 10 − 4 . 76 K b 4 [ ] NH 3 [ ] [ [ ][ ] ]     + + − H NH NH OH     − − = = 9 . 24 4 . 76 3 4 K K [ ] 10 10    [ ]  a b + NH NH     4 3 [ ][ ] + − 10 − = = 14 . 00 K K H OH =K w a b See Table 3.1 (pg.94) for values of K w at various pHs David Reckhow CEE 680 #8 14

NAME EQUILIBRIA pKa HClO4 = H+ + ClO4- Perchloric acid -7 STRONG HCl = H+ + Cl- Hydrochloric acid -3 H2SO4= H+ + HSO4- Sulfuric acid -3 (&2) ACIDS HNO3 = H+ + NO3- Nitric acid -0 H3O+ = H+ + H2O Hydronium ion 0 CCl3COOH = H+ + CCl3COO- 0.70 Trichloroacetic acid HIO3 = H+ + IO3- Iodic acid 0.8 CHCl2COOH = H+ + CHCl2COO- 1.48 Dichloroacetic acid HSO4- = H+ + SO4-2 2 Bisulfate ion H3PO4 = H+ + H2PO4- Phosphoric acid 2.15 (&7.2,12.3) Fe(H2O)6+ 3 = H+ + Fe(OH)(H2O)5+ 2 2.2 (&4.6) Ferric ion CH2ClCOOH = H+ + CH2ClCOO- 2.85 Chloroacetic acid C6H4(COOH)2 = H+ + C6H4(COOH)COO- 2.89 (&5.51) o-Phthalic acid C3H5O(COOH)3= H+ + C3H5O(COOH)2COO- 3.14 (&4.77,6.4) Citric acid HF = H+ + F- 3.2 Hydrofluoric acid HCOOH = H + + HCOO- 3.75 Formic Acid C2H6N(COOH)2= H+ + C2H6N(COOH)COO- 3.86 (&9.82) Aspartic acid C6H4(OH)COOH = H+ + C6H4(OH)COO- 4.06 (&9.92) m-Hydroxybenzoic acid C2H4(COOH)2 = H+ + C2H4(COOH)COO- 4.16 (&5.61) Succinic acid C6H4(OH)COOH = H+ + C6H4(OH)COO- 4.48 (&9.32) p-Hydroxybenzoic acid HNO2 = H+ + NO2- Nitrous acid 4.5 FeOH(H2O)5+ 2 + H+ + Fe(OH)2(H2O)4+ Ferric Monohydroxide 4.6 CH3COOH = H+ + CH3COO- 4.75 Acetic acid Al(H2O)6+ 3 = H+ + Al(OH)(H2O)5+ 2 4.8 Aluminum ion David Reckhow CEE 680 #8 15

NAME FORMULA pKa C2H5COOH = H+ + C2H5COO- 4.87 Propionic acid H2CO3 = H+ + HCO3- Carbonic acid 6.35 (&10.33) H2S = H+ + HS- Hydrogen sulfide 7.02 (&13.9) H2PO4- = H+ + HPO4-2 7.2 Dihydrogen phosphate HOCl = H+ + OCl- 7.5 Hypochlorous acid Cu(H2O)6+ 2 = H+ + CuOH(H2O)5+ Copper ion 8.0 Zn(H2O)6+ 2 = H+ + ZnOH(H2O)5+ Zinc ion 8.96 B(OH)3 + H2O = H+ + B(OH)4- Boric acid 9.2 (&12.7,13.8) NH4+ = H+ + NH3 Ammonium ion 9.24 HCN = H+ + CN- 9.3 Hydrocyanic acid C6H4(OH)COO- = H+ + C6H4(O)COO-2 9.32 p-Hydroxybenzoic acid H4SiO4 = H+ + H3SiO4- Orthosilicic acid 9.86 (&13.1) C6H5OH = H+ + C6H5O- 9.9 Phenol C6H4(OH)COO- = H+ + C6H4(O)COO-2 9.92 m-Hydroxybenzoic acid Cd(H2O)6+ 2 = H+ + CdOH(H2O)5+ Cadmium ion 10.2 HCO3- = H+ + CO3-2 Bicarbonate ion 10.33 Mg(H2O)6+ 2 = H+ + MgOH(H2O)5+ Magnesium ion 11.4 HPO4-2 = H+ + PO4-3 Monohydrogen phosphate 12.3 Ca(H2O)6+ 2 = H+ + CaOH(H2O)5+ Calcium ion 12.5 H3SiO4- = H+ + H2SiO4-2 Trihydrogen silicate 12.6 HS- = H+ + S-2 Bisulfide ion 13.9 H2O = H+ + OH- Water 14.00 NH3 = H+ + NH2- Ammonia 23 OH- = H+ + O-2 Hydroxide 24 CH4 = H+ + CH3- Methane 34 David Reckhow CEE 680 #8 16

Analytical Solutions  Basic Approach  combine mass balances with thermodynamic equilibria  consider exact solutions, as well as approximations  similar approaches used for other topics in CEE 680  Four principal steps  1. List all species present  2. List all independent equations  equilibria, mass balances, proton balance (or electroneutrality equation)  3. Combine equations and solve for proton  4. Solve for other species David Reckhow CEE 680 #8 17

General Example  1. List all species present  H + , OH - , HA, A - Four total  2. List all independent equations  equilibria  K a = [H + ][A - ]/[HA] 1  K w = [H + ][OH - ] 2  mass balances  [HA]+[A - ] = C (formal or “analytical” concentration) 3  proton balance (or electroneutrality equation)  PBE: Σ (proton rich species) = Σ (proton poor species)  ENE: Σ (cationic species) = Σ (anionic species)  [H + ]=[OH - ]+[A - ] 4 David Reckhow CEE 680 #8 18

General Example (cont.)  3. Combine equations and solve for proton  use PBE or ENE and eliminate non-H + species by substituting in the other equations  4. Solve for other species David Reckhow CEE 680 #8 19