بسم الله الرحمن الرحيم ACID-BASE TITRATIONS Ashraf M. Mahmoud, Ph.D.

Contents Introduction Acid-base theories: Definition and limitations. Law of mass action & acid-base equilibrium in water. Buffer solutions: definition, types & importance in pharmacy. Neutralization indicators Neutralization titration curves Applications of acid-base titration in aqueous medium. Acid-base titrations in non-aqueous medium.

Introduction Aim: is to determine the quantity of the substance under analysis Classification of quntitative analysis According to method of analysis: I- Volumetric analysis II- Gravimetric analysis : Analysis by weight III- Instrumental analysis: HPLC, IR, UV-VIS spectrophotometry

Introduction Volumetric analysis: Standard ≠ Sample complete reaction Solution of exact known conc. Substance to be determined Ionic combination reactions: Neutralization (H2O formation) H+ + OH- H2O Precipitation Ag+ + Cl- AgCl ppt Complex formation Ag+ + 2CN- [Ag(CN)2]- B. Redox (electron-transfer) reactions: Involve change in the O.N. of the substance Ce4+ + Fe2+ Ce3+ + Fe3+

Requirements for the titration reactions Requirements for a titrimetric reaction: Simple reaction expressed by a chemical equation No side reaction Very rapid Availability of a suitable standard solution Ease of detection of the end point Sources of errors in titrimetry: Loss of sample 2. Contaminations 3. Non proper mixing 4. Weighing errors 5. dilution errors 6. reading errors 7. Use of wrong indicators 8. Personal errors

Standard solutions Standard solutions (St. soln): Emperical St. soln : No. of ml that react with substance Molar St. soln : gm. M.wt of sub./ 1L Normal St. soln : gm. eq.wt / 1L = M.wt / No of H+ or OH- Formal St. soln : gm. Formula wt / 1L Molal St soln : gm. M.wt of sub./ 1Kg % W/V : gm/100 ml % W/W : gm/100 gm % V/V : ml / 100 ml Ppm : mg / Kg

Primary Standards Primary Standards: Substances of definite known composition and high purity Easily obtained in a very pure form Easily tested for impurities Stable, non hygroscopic, non volatile Readily soluble Should have a high eq. wt to decrease the weighing errors React stoichiometrically with other sub. Examples: Pot. Acid phathalate, anhyd. Na2CO3 , KHCO3

Acid-Base Theories 1. Arrhenious Theory: Acid is the substance, which ionises into H+, while bases give OH-. This theory did not discuss the role of solvent in the ionisation. Brönsted-Lowry Theory: Acid is the substance, which produces or donates H+, a base accept H+. Acid  Proton + Conjugate base HCl  H+ + Cl- H2O  H+ + OH- The solvent in this theory, is involved in the reaction as acid or base, e.g. HCl + H2O  H3O+ + Cl- NH3 + H2O  NH4+ + OH- 3. Lewis Theory: Base is the substance that contains an atom with unshared pair of electrons (e.g. N, O, S, P), while an acid which accepts to share this electronic pair. HCl + :NH3  NH4+ + Cl- Neutralization is the formation of a co-ordinate bond between acid and base. Compounds with no OH- are alkaline (NH3): HCl + :NH3  NH4+ + Cl- Compounds with no H+ are acids (BCl3): BCl3 + :NEt3  Cl3B NEt3

Law of Mass Action & Acid-Base Equilibrium in Water A + B C + D f b The velocity of a chemical reaction is proportional to the product of the active masses of the reacting substances. Vf = Kf [A][B] Vb = Kb [C][D] Vf is the velocity of forward reaction, Vb is the velocity of backward reaction, Kf and Kb are the proportionality constants. At equilibrium: Vf = Vb and Kf [A][B] = Kb [C][D] [C] [D] Kf [A] [B] Kb = = K (Equilibrium constant)

Dibasic acid Tribasic acid, H3PO4: 2. Acid-Base Equilibrium in Water: HOAC H+ + OAC- Ka [H+] [OAC —] [HOAC] = Ka (Ionization or dissociation constant) H2A H+ + HA— K1 [H+] [HA — ] [H2A] K1 = Dibasic acid K1 =1 ry DC HA- H+ + A2— K2 [H+] [A2 — ] [HA — ] K2 = K2= 2ry DC Tribasic acid, H3PO4: H3PO4 H++ H2PO4— H+ + HPO4 2— H+ + PO43— K1 K2 K3 K1 = 1.1  102 K2 = 2.0  107 K3 = 3.6  1013

3. Dissociation of Water: H2O H+ + OH Kw [H+] [OH ] [H2O] Kw = Since water is slightly ionised, the value of [H2O] may be regarded as unity, hence: [H+][OH ] = KW (ionic product of water = 1 1014  at 25 °C). In pure water, [H+] = [OH ] = 1  107- Solution pH [H+] > [OH ] [H+] = [OH ] [H+] < [OH ] Acidic Neutral Alkaline < 7 7 > 7 14 pH Scale

Hydrogen ion exponent “pH” pH = —log [H+] pOH = —log [OH-] [H+][OH ] = KW = 1014 pH + pOH = 14 Acid Neutral Alkaline Solution pH [H+] mole/L [OH ] mole/L 1.0 2.0 3.0 4.0 5.0 6.0 0.1 0.01 0.001 0.0001 0.00001 0.000001 0.00000000000001 0.0000000000001 0.000000000001 0.00000000001 0.0000000001 0.000000001 0.00000001 7.0 0.0000001 8.0 9.0 10.0 11.0 12.0 13.0 14.0

pH of Acids, Bases, and Solutions 1. pH of Strong Acid or Bases: Strong acids or bases are completely dissociated, the [H+] or [OH-]: 0.1 N HCl gives [H+] = 1/10, pH = — log 101— = 1.0 0.1 N NaOH, pKW = pH + pOH, 14 = pH + 1 pH =13 2. pH of Weak Acids: HOAC H+ + OAC Ka Ka = [H+] [OAC ] / [HOAC] Since [H+] = [OAC-] and the degree of dissociation is very low Ka = [H+]2 / Ca ( Ca is total acid concentration).  [H+]2 = Ca  Ka [H+] = Ca  Ka pH = ½ pCa + ½ pKa 3. pH of Weak Bases: Base concentration is Cb . Dissociation constant of base is Kb. pH = pKW– ½ pCb – ½ pKb

pH of Salt Solutions 1. Salts of Strong Acids and Strong Bases (KCl) : Neutral, pH = 7. 2. Salts of Strong Acids and Weak Bases (NH4Cl) : Acidic, pH  7. NH4Cl + H2O NH4OH + HCl pH = ½ pKW – ½ pKb + ½ pCs 3. Salts of Weak Acids and Strong Bases (NaOAC) : Alkaline, pH  7. CH3COONa + H2O CH3COOH + NaOH pH = ½ pkW + ½ pka – ½ pCs 4. Salts of Weak Acids and Weak Bases (NH4OAC) : Acidic or alkaline ?. It depends on the dissociation constant of the acid or base. AB + H2O AH + BOH pH = ½ pKW + ½ pKa – ½ pKb

Henderson Equations for Buffer Solutions 1. Definition: Solutions that resist change in pH, upon the addition of small amounts of acids or alkalies. Henderson Equations for Buffer Solutions 2. Types: 1 - Weak acid and its salt: Example: acetic acid and sodium acetate. pH = pKa + log [A ]/[HA] [A ] = salt concentration pH = pKa + log [salt]/[Acid] [salt]/[acid] is the buffer ratio When [salt] = [acid], pH = pKa 2- Weak base and its salt: Example : ammonia and ammonia chloride pOH = pKb + log [salt] / [base] pH = pKw - pOH pH = pKW – pKb – log [salt] / [base]

Buffer Solutions 4. Mechanism of Buffer Action: a. First Type of Buffer H+ + OAC HOAC OH + HOAC OAC + H2O b. Second Type of Buffer H+ + NH4OH NH4+ + H2O OH + NH4Cl NH4OH + Cl

Buffer Capacity Definition: - The number of gm equivalent of strong acid or strong base required to change the pH of 1 L of buffer solution by one pH unit. In general, the buffer capacity is maintained within the range 1:10 - 10:1. Buffers show maximum buffering action when: pH = pKa ± 1. 3. Importance of buffer solutions in pharmacy a- Control of pH of liquid formulations (syrups, pH of 2.0 – 8.0), parenteral, (pH 4.0 – 9.0), eye drops (pH of 7.4, optimize stability, solubility or biological compatibility of the dissolved drug). b- The pH of blood is very well buffered. c- Common pharmaceutical buffer is Sorenson’s phosphate buffer which is composed of disodium hydrogen phosphate and potassium dihydrogen phosphate having a pH range 6.0 – 8.0.

Neutralization Indicators 1. Definition: Weak acid or weak base which changes colour with the change in pH. Phenolphthalein and methyl orange are the most used. 2. Theories of Colour Changes: a. Ostwald Theory: indicators are either weak organic acids or bases, in which undissociated molecules differ in colour from their ions. HIn H+ + In (Acidic indicator as phenolphthalein) InOH OH + In+ (Basic indicator as methyl orange) Chromophore Theory: colour change depends on the presence of unsaturated chromophoric group in the indicator molecule (e.g. NO2, NO, N=N, C=C, etc. ). Higher max (colour) Auxochromes (OH or NH2 ) with chromophore  colour intensity. Protons donating-accepting leads to structural arrangement

Neutralization Indicators 3. Indicator Constant: Weak acid or weak base which changes colour with the change in pH. HIn H+ + In Unionized ionized (acidic) (basic colour) pH = PKIn + log [basic colour]/ [acidic colour] When [basic colour] = [acidic colour] pH = PKIn Middle tint of an indicator

Neutralization Indicators 4. Effective Range of an Indicator: pH = PKIn  1 Ratio =1:10 & 10:1 a c i d o l u r % 9 . 1 7 6 5 4 3 p K - + b s R e B U f n g

Indicator pH range Acidic colour Basic colour Phenolphthalein o-Cresolphthalein Thymolphthalein Thymol blue (acid range) Thymol blue (basic range) Bromophenol blue Bromophenol red Bromothymol blue Phenol red Cresol red Methyl yellow Methyl orange Methyl red Alizarin yellow R pH range Acidic colour   Colourless Red Pink Blue Yellow Blue-violet Violet Basic colour 8.2 – 10.0 9.3 – 10.5 3.3 – 4.4 1.2 – 2.8 8.0 – 9.6 3.0 – 4.6 4.8 – 6.4 6.0 – 7.0 6.4 – 8.0 7.2 – 8.8 2.9-4.0 3.1-4.4 4.2-6.2 10.1-12.0

Neutralization Indicators 6. Screened, Mixed and Universal Indicators Screened Indicators. A mixture of an indicator + dye Give more sharper colour change Example: (methyl orange & indigo carmine) Mixed indicators. A mixture of two indicators having similar pH range but showing contrasting colour. Universal (multi-range) indicators. A mixture of indicators, its colour change extends over a considerable pH range. Used for rough determination of pH, but not suitable for titration.

Neutralization (Acid-Base) Titration Curves - The titration curve is a plot of pH values versus the volume of titrant. - They are constructed to study the feasibility of the titration and to help in choosing an indicator for the titration. - Graphical determination of the End Point and the pH at this point.

1. Strong Acid – Strong Base (HCl – NaOH) 40.0 mL of 0.1 M HCl Before addition of any NaOH: pH = pCa = — log [H+] = — log 0.1 = 1 After addition of 10 mL of NaOH: pH = pCa = — log [H+] = — log (0.1 30 / 50) = — log 0.06 = 1.22 After addition of 20 mL of NaOH: pH = pCa = — log [H+] = — log (0.1 20 / 60) = — log 0.033 = 1.48 After addition of 30 mL of NaOH: pH = pCa = — log [H+] = — log (0.1 10 / 70) = — log 0.014 = 1.85 After addition of 40 mL of NaOH (at the equivalence point): pH = pOH = ½ pKW =7.0 After the equivalence point (after addition of 50 mL NaOH): pH = pKW – pCb = 14 – ( — log 0.110/90) pH = 14 – ( — log 0.01) = 14 – 1.95) = 12.05

Titration Curve for Strong Acid – Strong Base (HCl – NaOH) PR MO PP AY MR Titration Curve for Strong Acid – Strong Base (HCl – NaOH)

2. Weak Acid – Strong Base (HOAC – NaOH) 40.0 mL of 0.1 M HOAC Before addition of any NaOH: pH = ½ pKa + ½ pCa = ½ (4.74) + ½ ( — log 0.1) = 2.37 + 0.5 = 2.87 After addition of 20 mL of NaOH (Buffer): pH = pKa + log [salt] / [acid] = 4.74 + log 1 = 4.74 + 0 = 4.74 After addition of 40 mL of NaOH (at the equivalence point): pH = ½ pKW + ½ pKa – ½ pCs = 7 + 2.37 – ½(1.3) = 8.72 After the equivalence point (after addition of 50 mL NaOH): pH = pKW – pOH = 14 – (- log 0.110/90) pH = 14 – ( — log 0.01) = 14 – 1.95) = 12.05

pKa Titration Curves for Strong Acid ( – ) or Weak acid ( – ) with Strong Base

Titration Curve for Weak Base – Strong Acid (NH4 OH – NaOH) pKb Titration Curve for Weak Base – Strong Acid (NH4 OH – NaOH)

Titration of 100 mL of diprotic acid (H2A) with NaOH pH at 1 st E.P. = ½ (pK1 + pK2 ) = ½ (2.12 + 7.12) = 4.66 (M.O.) pH at 2 st E.P. = ½ pKW + ½ pKa — ½ pCs = 9.94 (Ph.Ph.)

(NEUTRALIZATION REACTIONS) ACID-BASE TITRATIONS (NEUTRALIZATION REACTIONS) APPLICATIONS

Direct Titration Methods 1. Determination of Acids & Bases Strong acids are titrated with standard alkaline: MO or Ph.Ph. Weak acids are titrated with standard alkaline: Ph. Ph. not M.O. Acids which are insoluble in water (as benzoic acid) should be first dissolve in neutralized ethanol and then titrated with NaOH: Ph. Ph. Acid salts (KH-phthalate, KHSO4 & KH-tartarate) are titrated with NaOH: Ph.Ph. Boric acid as a weak monobasic acid (K2 = 5.8  1010-), is titrated with standard NaOH after addition of polyhydroxy compounds (e.g. glycerol): Ph.Ph. Strong base are titrated with standard acid: MO or Ph.Ph. Weak bases are titrated with standard acid: M.O. not. Ph. Ph.

2. Double-Indicator Titrations Direct titration of a mixture of two monobasic acids to determine the quantity of each acid by the use of two indicators. The difference in the ionization constants of the two acids must be at least 104. Thus, it is possible to titrate HCl in the presence of boric acid (Ka = 5.5 1010 ) or HCl in the presence of acetic acid (Ka = 1.8 105 ). H+ of HCl  ionization of HOAC by common ion effect; NaOH neutralizes HCl first. After completion of the reaction, NaOH neutralizes AOAC.

3. Titration of Easily Hydrolysable Salts (Displacement Titration) These salts are formed from either: – A strong base & a very weak acid (borax & Na2CO3). or – Strong acid & a very weak base (FeCl3 & AlCl3). b. Titration of Borax (Na2B4O7) Na2B4O7 + 7 H2O  2 NaOH + 4 H3BO3 2 NaOH + 2 HCl  2 NaCl + 2 H2O ( M.O. )   ( Ph.Ph ) Titration of a Mixture of Borax & Boric Acid ?.

b. Titration of Sodium Carbonate (Na2CO3) Na2CO3 + HCl  NaHCO3 + NaCl pH = 8.35 Ph. Ph. K1= 4.2107 NaHCO3 + HCl  CO2 + H2O + NaCl pH = 3.8 M.0. K2 = 4.8  1011 Boiled solution Kb1  106 (required for a sharp E.P.), the pH break is decreased by the formation of CO2, beyond the first E.P. Kb2  106 : the second E.P. is not very sharp. It can be sharpened by boiling off the CO2 . – Titration of a Mixture of Na2CO3 & NaHCO3 ?. – Titration of a Mixture of Na2CO3 & NaOH ?. – Titration of a Mixture of Na2CO3 & Na2B4O7 ?.

Indirect (Back or Residual) Titration Methods Used when direct titration is not suitable as in: – Volatile substance as ammonia or formic acid (loss). – Substance, which require heating with standard reagent. – Insoluble substance as ZnO, CaO, and BaCO3. – Substance needed excess reagent for rapid quantitative reaction (lactic acid). Carried out as follow: A known excess standard solution is first added and allowed to react completely with the sample. The residual quantity of the added standard is then determined. ZnO + 2HCl  ZnCl2 + H2O A known weight of ZnO is treated with a known excess standard HCl, the excess HCl is then back titrated with standard NaOH (M.R.). 1. Determination of insoluble oxides and Carbonates (ZnO , CaO & CaCO3)

2. Determination of Esters (Aspirin: acetylsalicylic acid) Determination of mixture of CaO and CaCO3 – Total by adding known excess standard HCl and back titration with standard NaOH (M.O.) – CaO by adding 10% neutral sucrose , alcohol, and titrating with standard acid (Ph.Ph.). The indicator losses its colour before [H+] is not strong enough to attack the insoluble CaCO3. 2. Determination of Esters (Aspirin: acetylsalicylic acid) R—COOR + NaOH R—COONa + ROH Reflux / Heat A known weight of the ester is refluxed with a known excess of standard NaOH. The residual NaOH is back titrated with standard acid (Ph.Ph.).