1. Environmental Engineering Course Note 5 (Homogeneous Transformation) Joonhong Park Yonsei CEE Department 2015. 4. 1. 2015-12-08

2. 3. C. Acid-Base Reaction - Acid-base reaction & hydrogen ion - Strong acid/weak acid - Carbonate system 3. D. Oxidation-Reduction Reactions - Oxidation state - Corrosion – Combustion - Microbial redox processes - BOD 2015-12-08

3. Review: Homogenous Reactions Homogenous reactions are governed by relations which require that certain entropy, enthalpy, and energy balances be obeyed among the components or species participating in transformation processes that occur within a single phase. * Transformation via proton (H+) transfer in water (acid-base reaction): Most of this type of reactions are elementary transformation processes; Fast equilibrium. Transformation via electron transfer (oxidation-reduction reaction): Some of this type of reactions are non-elementary; Kinetic problems. 2015-12-08

4. Proton transfer reaction when the proton, H + (H 3 O + ), is involved as the electron-pair acceptor. pH is master variable - pH = - log {H + } or –log {H 3 O + } - H + is the major reactive component of water - Also important in air quality control (e.g. acid rain). Acid-Base Reactions 2015-12-08

5. Acid: a substance that tends to donate or lose a hydrogen ion. (tends to reduce pH) Base: a substance that tends to accept or gain a hydrogen ion. (tends to increase pH) Acid-base reaction: in which a proton is transferred from the acid to the base. Ex. HCl (acid) + H 2 O (base)  H 3 O + (acid)+ Cl - (base) NH 3 (base) + H 2 O (acid)  NH 4 + (acid) + OH - (base) Here Cl - is the conjugate base of HCl NH 4 + is the conjugate acid of NH 3 Acid-Base Reactions 2015-12-08

6. H 2 O  H + + OH - K’ = [H + ][OH - ]/[H 2 O] [H 2 O] = 55.5 mole/L Kw = K’[H 2 O] =[H + ][OH - ] Dissociation constant for water, Kw Log(Kw) = -4470.99*T -1 + 6.0875 – 0.01706 * T (here T=absolute temperature) pH of Pure Water 2015-12-08

7. Example: What is the pH of pure water at 10 and 25 o C? Log(Kw) = -4470.99/T + 6.0875 – 0.01706 T (here T=absolute temperature) At 10 o C, T=283 K Kw = 10 -14.55 M 2 = [H + ][OH - ] According to stoichiometry, [H + ] = [OH - ]. [H + ] = Kw 0.5 = 10 -7.27 M => pH = 7.27 (pH of water is not always 7) At 25 o C, T=298 K Kw = 10 -14.00 M 2 pH =7.00 pH of Pure Water 2015-12-08

8. Acid Dissociation Constant HA  H + + A - Acid dissociation constant K A = [H + ][A - ]/[HA] p K A = pH – log [A - ]+log[HA] If p K A = pH, [A - ] = [HA] If p K A > [HA] If p K A >> pH, [A - ] << [HA] Strength of an acid is quantified by its K A values SpeciespK A Hydrochloric acid Sulfuric acid Nitric acid Acetic acid Carbonic acid Hydrogen sulfide Ammonium Bicarbonate Hydrogen phosphate Bisulfide HCl H 2 SO 4 HNO 3 CH 3 COOH H 2 CO 3 H 2 S NH 4 + HCO 3 - HPO 4 2- HS - -3 -1.2 4.7 6.35 7.1 9.23 10.33 12.32 12.9 2015-12-08

9. Effect of Acid Addition on pH Example: pH of a solution containing a monoprotic acid HA  H + + A - If 0.001 mol of a monoprotic acid is added to water to make 1 L of solution, what is the equilibrium pH at 25 o C? Answer) Electro-neutrality relationship provides [H + ] = [OH - ] + [A - ] (1) Water dissociation Kw = [H + ][OH - ] (2) Acid dissociation K A = [H + ][A - ]/[HA] (3) Material balance on A, C T = [A - ] + [HA] = 0.001 M (4) Substitute for [HA] from the eq. (4) K A = [H + ][A - ]/(C T - [A - ]) => [A - ]= C T K A /(K A +[H + ]) (5) 2015-12-08

10. (Continued) Electro-neutrality relationship provides [H + ] = [OH - ] + [A - ] (1) Water dissociation Kw = [H + ][OH - ] (2) Acid dissociation K A = [H + ][A - ]/[HA] (3) Material balance on A, C T = [A - ] + [HA] = 0.001 M (4) [A - ]= C T K A /(K A +[H + ]) (5) Rearrange eq.(2) into [OH - ]= Kw /[H + ] (6) Substitute eq.(5) and eq. (6) into eq. (1) [H + ] = Kw /[H + ] + C T K A /(K A +[H + ]) (7) Effect of Acid Addition on pH 2015-12-08

11. (Continued) If the acid is strong, K A >> [H + ] [H + ] = Kw /[H + ] + C T (8) If the acid is weak, should solve the equation (7). An approximation: [H + ] >> [OH - ] => eq.(1) will be simplified into [H + ] = [A - ] (9) Substitute this into eq. (5). Then [H + ]= C T K A /(K A +[H + ]) (10) Effect of Acid Addition on pH 2015-12-08

12. Carbonate system CO 2 (g) H 2 CO 3 (aq) + H 2 O  HCO 3 - + H 3 O + HCO 3 - + H 2 O  CO 3 2- + H 3 O + K a,1 =10 -6.35 CO 3 2- + Ca 2+ CaCO 3 (s) Ks KHKH H 2 O + CO 2 (aq) KmKm K a,2 =10 -10.33 pH of pristine rainwater is 5.64. The figure explains why. 2015-12-08

13. Carbonate system 0 2468 10 1214 CTCT H 2 CO 3 HCO 3 - CO 3 2- pK 1 =6.35pK 2 =10.33 pH < 4.5 C T ~ [H 2 CO 3 ] 4.5 < pH < 8.3 C T ~ [H 2 CO 3 ] + [HCO 3 - ] 8.3 < pH <12.3 C T ~ [HCO 3 - ] + [CO 3 2- ] 12.3 < pH C T ~ [CO 3 2- ] 2015-12-08

14. Alkalinity and pH Buffering Definition: the ability of water solution to resist against pH changes. Example: Alkalinity in carbonate system (eq./L) = [OH - ] + [HCO 3 - ] + 2[CO 3 2- ] –[H + ] (other species that increase alkalinity =HPO 4 2-, H 2 PO 4 -, HS -, NH 3 Measurement: (1) Titrate the solution by adding strong acid until the pH decreases to 4.5. (2) Determined as the moles of strong acid protons added per liter of solution 2015-12-08