Analytical Chemistry II.pdf

Analytical Chemistry II OUTLINE ▪ Acid-Base Titration ▪ Precipitation Titration ▪ Complexometric Titration Analytical Chemistry 2 METHODS OF ANALYSIS Titration ▪ a process by which a stoichiometrically equivalent quantity of standard solution is systematic...

Analytical Chemistry II OUTLINE ▪ Acid-Base Titration ▪ Precipitation Titration ▪ Complexometric Titration Analytical Chemistry 2 METHODS OF ANALYSIS Titration ▪ a process by which a stoichiometrically equivalent quantity of standard solution is systematically added to a known quantity of sample Titrant ▪ reagent that is added incrementally usually from a buret Acid-Base Titration 3 METHODS OF ANALYSIS Standard Solution ▪ reagent of exactly known concentration Primary Standard Solution ▪ prepared from an accurately weighed substance of high degree of purity Acid-Base Titration 4 METHODS OF ANALYSIS Secondary Standard Solution ▪ concentration is obtained by standardization using a primary standard solution Equivalence Point ▪ the point in a titration when the amount of added standard reagent is chemically equal to the amount of analyte Acid-Base Titration 5 METHODS OF ANALYSIS End Point ▪ point in a titration when a physical change that is associated with the condition of chemical equivalence occurs Acid-Base Titration 6 METHODS OF ANALYSIS (Skoog, 2014) Acid-Base Titration 7 TITRATION TECHNIQUES Types ▪ Direct Titration ▪ Back-Titration ▪ Displacement Titration Acid-Base Titration 8 TITRATION TECHNIQUES Direct Titration ▪ a process in which the analyte is made to react with the titrant after addition of an indicator Acid-Base Titration 9 TITRATION TECHNIQUES Back Titration ▪ a process in which the excess of a standard reagent used to react with an analyte is determined by titration with a second standard solution ▪ usually employed when a reaction is slow to go to completion, and a sharp end point cannot be obtained ▪ when the analyte forms precipitates at the pH required for its titration Acid-Base Titration 10 TITRATION TECHNIQUES Displacement Titration ▪ used when no indicator for the analyte is available in EDTA complexometric titration, an unmeasured excess of a solution containing the magnesium or zinc complex is introduced into the analyte solution if the analyte forms a more stable complex than that of magnesium or zinc, the following displacement reaction occurs and the liberated cation is then titrated with standard 𝑀𝑔𝑌 2− + 𝑀2+ → 𝑀𝑌 2− + 𝑀𝑔2+ Acid-Base Titration 11 REQUIREMENTS Reactions Used in Titrimetric Analysis ▪ Reaction must proceed according to a definite chemical equation (no side reaction). ▪ Reaction must be complete (in general, the reaction is essentially complete if K > 107) ▪ Equivalence point must be detected by some method e.g. indicator ▪ Reaction must be rapid Acid-Base Titration 12 REQUIREMENTS Primary Standard ▪ High purity ▪ Stability toward air ▪ Composition does not change with variations in relative humidity (absence of hydrate water) ▪ Available and relatively inexpensive ▪ Reasonably soluble in the titration medium ▪ Reasonably large molar mass to minimize relative error in weighing Acid-Base Titration 13 REQUIREMENTS Acid/Base Indicators ▪ have an indicator range (transition range) of approximately 𝑝𝐾𝑖𝑛 ± 1 ▪ a suitable indicator changes color within 1 drop of the titrant in excess of the equivalence point 𝐻𝐼𝑛 + 𝐻2 𝑂 ↔ 𝐼𝑛− + 𝐻3 𝑂+ 𝐻3 𝑂+ 𝐼𝑛− 𝐾𝑎 = 𝐻𝐼𝑛 Acid-Base Titration 14 REQUIREMENTS Table of Acid/Base Indicators (Skoog, 2014) Acid-Base Titration 15 TITRATION CURVE Acid/Base Indicators ▪ pH or pOH vs mL of titrant ▪ useful for determining whether: feasibility of titration appropriate indicator Acid-Base Titration 16 TITRATION CURVE Titration curves for HCl with NaOH Curve A: 50.00 mL of 0.0500 M HCl with 0.1000 M NaOH Curve B: 50.00 mL of 0.000500 M HCl with 0.00100 M NaOH (Skoog, 2014) Acid-Base Titration 17 TITRATION CURVE Titration curves for Acetic acid with NaOH Curve A: 0.1000 M acid with 0.1000 M base Curve B: 0.001000 M acid with 0.001000 M base (Skoog, 2014) Acid-Base Titration 18 ACID-BASE EQUILIBRIA Strong acids/bases ▪ completely dissociated, hence there is no Ka or Kb associated with them Weak acids/bases ▪ partially dissociated ▪ monofunctional: Ka or Kb ▪ polyfunctional: Ka1, Ka2, etc. or Kb1, Kb2, etc. Acid-Base Titration 19 ACID-BASE EQUILIBRIA Bronsted-Lowry Concept ▪ conjugate acid-base pairs: the stronger the acid, the weaker the conjugate base and vice versa; K a x Kb = K w 𝑎1 → 𝑏1 + 𝐻+ 𝑏2 → 𝐻+ + 𝑎2 Acid-Base Titration 20 ACID-BASE EQUILIBRIA 𝑯𝟑 𝑶+ in solutions of weak acids 𝐻3 𝑂+ 𝐴− 𝐻𝐴 + 𝐻2 𝑂 ↔ 𝐻3 𝑂+ + 𝐴− 𝐾𝑎 = 𝐻𝐴 2𝐻2 𝑂 ↔ 𝐻3 𝑂+ + 𝑂𝐻− 𝐾𝑤 = 𝐻3 𝑂+ 𝑂𝐻− MBE: 𝐻3 𝑂+ = 𝐴− + 𝑂𝐻− ≅ 𝐴− 𝐶𝐻𝐴 = 𝐻𝐴 + 𝐴− Acid-Base Titration 21 ACID-BASE EQUILIBRIA 𝑯𝟑 𝑶+ in solutions of weak acids 𝐻3 𝑂+ 2 𝐾𝑎 = 𝐶𝐻𝐴 − 𝐻3 𝑂+ 𝑖𝑓 𝐶𝐻𝐴 > 1000𝐾𝑎 𝐻3 𝑂+ = 𝐾𝑎 𝐶𝐻𝐴 𝑖𝑓 𝐶𝐻𝐴 ≤ 1000𝐾𝑎 𝐻3 𝑂+ 2 + 𝐾𝑎 𝐻3 𝑂+ − 𝐾𝑎 𝐶𝐻𝐴 = 0 Acid-Base Titration 22 ACID-BASE EQUILIBRIA Salts of weak electrolytes ▪ react with water to produce either hydrogen or hydroxide ions 𝑂𝐴𝑐 − + 𝐻2 𝑂 ↔ 𝐻𝑂𝐴𝑐 + 𝑂𝐻 − b1 a2 a1 b2 + 𝑁𝐻4 + 𝐻2 𝑂 ↔ 𝑁𝐻3 + 𝐻3 𝑂+ a1 b2 b1 a2 Acid-Base Titration 23 ALPHA (𝜶) EXPRESSIONS 𝜶 = fraction of species ▪ For a monoprotic weak acid HA: 𝐻3 𝑂+ 𝐴− 𝐻𝐴 + 𝐻2 𝑂 ↔ 𝐻3 𝑂+ + 𝐴− 𝐾𝑎 = 𝐻𝐴 𝐻𝐴 𝐻𝐴 𝐻𝐴 𝐻3 𝑂+ 𝛼0 = 𝛼𝐻𝐴 = = − = = 𝐶𝐻𝐴 𝐻𝐴 + 𝐴 𝐻𝐴 𝐻3 𝑂+ + 𝐾𝑎 𝐻𝐴 + 𝐾𝑎 𝐻3 𝑂+ 𝐴− 𝐴− 𝐴− 𝐾𝑎 𝛼1 = 𝛼𝐴− = = − = + − = + +𝐾 𝐶𝐻𝐴 𝐻𝐴 + 𝐴 𝐻3 𝑂 𝐴 𝐻3 𝑂 𝑎 + 𝐴− 𝐾𝑎 Acid-Base Titration 24 ALPHA (𝜶) EXPRESSIONS 𝜶 = fraction of species ▪ For a tripotic weak acid H3A: 𝐻3 𝑂+ 3 𝛼0 = 𝛼𝐻3 𝐴 = 𝐻3 𝑂+ 3 + 𝐻3 𝑂+ 2 𝐾𝑎1 + 𝐻3 𝑂+ 𝐾𝑎1 𝐾𝑎2 + 𝐾𝑎1 𝐾𝑎2 𝐾𝑎3 𝐻3 𝑂+ 2 𝐾𝑎1 𝛼1 = 𝛼𝐻2 𝐴− = 𝐻3 𝑂+ 3 + 𝐻3 𝑂+ 2 𝐾𝑎1 + 𝐻3 𝑂+ 𝐾𝑎1 𝐾𝑎2 + 𝐾𝑎1 𝐾𝑎2 𝐾𝑎3 Acid-Base Titration 25 ALPHA (𝜶) EXPRESSIONS 𝜶 = fraction of species ▪ For a tripotic weak acid H3A: 𝐻3 𝑂+ 𝐾𝑎1 𝐾𝑎2 𝛼2 = 𝛼𝐻𝐴2− = 𝐻3 𝑂+ 3 + 𝐻3 𝑂+ 2 𝐾𝑎1 + 𝐻3 𝑂+ 𝐾𝑎1 𝐾𝑎2 + 𝐾𝑎1 𝐾𝑎2 𝐾𝑎3 𝐾𝑎1 𝐾𝑎2 𝐾𝑎3 𝛼3 = 𝛼𝐴3− = 𝐻3 𝑂+ 3 + 𝐻3 𝑂+ 2 𝐾𝑎1 + 𝐻3 𝑂+ 𝐾𝑎1 𝐾𝑎2 + 𝐾𝑎1 𝐾𝑎2 𝐾𝑎3 Acid-Base Titration 26 EXAMPLE What is the pH of a solution that is 0.400 M in formic acid and 1.00 M in sodium formate? 𝐻𝐶𝑂𝑂𝐻 + 𝐻2 𝑂 ↔ 𝐻3 𝑂+ + 𝐻𝐶𝑂𝑂− 𝐾𝑎 = 1.80 𝑥 10−4 𝐻𝐶𝑂𝑂− + 𝐻2 𝑂 ↔ 𝐻𝐶𝑂𝑂𝐻 + 𝑂𝐻− 𝐾𝑏 = 5.56 𝑥 10−11 Analytical Chemistry 27 EXAMPLE Because the Ka for formic acid is orders of magnitude larger than the Kb for formate, the solution is acidic, and Ka determines the H3O+ concentration 𝐻3 𝑂+ 𝐻𝐶𝑂𝑂 − 𝐾𝑎 = = 1.80 𝑥 10−4 𝐻𝐶𝑂𝑂𝐻 𝐻𝐶𝑂𝑂 − ≈ 𝑐𝐻𝐶𝑂𝑂− = 1.00 𝑀 𝐻𝐶𝑂𝑂𝐻 ≈ 𝐶𝐻𝐶𝑂𝑂𝐻 = 0.400 𝑀 0.400 𝐻3 𝑂+ = 𝑥1.80 𝑥 10−4 = 7.20 𝑥 10−5 1.00 Analytical Chemistry 28 EXAMPLE Notice that our assumptions that 𝐻3 𝑂+ ≪ 𝑐𝐻𝐶𝑂𝑂𝐻 and that 𝐻3 𝑂+ ≪ 𝑐𝐻𝐶𝑂𝑂− are valid, thus 𝑝𝐻 = −𝑙𝑜𝑔 7.20 𝑥 10−5 = 4.14 Analytical Chemistry 29 EXAMPLE Calculate the hydronium ion concentration in 0.120 M nitrous acid. 𝐻𝑁𝑂2 + 𝐻2 𝑂 ↔ 𝐻3 𝑂+ + 𝑁𝑂2− Ka= 7.1 x 10-4 Analytical Chemistry 30 EXAMPLE 𝐻3 𝑂+ 𝑁𝑂3− 𝐾𝑎 = = 7.1 𝑥 10−4 𝐻𝑁𝑂2 𝐻3 𝑂+ = 𝑁𝑂3− 𝐻𝑁𝑂2 = 0.120 − 𝐻3 𝑂+ 𝐻3 𝑂+ 𝐻3 𝑂+ −4 𝐾𝑎 = = 7.1 𝑥 10 0.120 − 𝐻3 𝑂+ Analytical Chemistry 31 EXAMPLE Assuming 𝐻3 𝑂+ ≪ 0.120 then 𝐻3 𝑂+ 2 𝐾𝑎 = = 7.1 𝑥 10−4 0.120 𝐻3 𝑂+ = 9.2 𝑥 10−3 𝑀 OR Solving for the quadratic equation 𝐻3 𝑂+ = 8.9 𝑥 10−3 𝑀 Analytical Chemistry 32 BUFFERS ▪ resist large changes in pH when an acid or base is added or when the solution is diluted ▪ usually made from a weak acid-conjugate base pair or a weak base-conjugate acid pair ▪ buffer action of buffer consisting of HA and A- Addition of acid: 𝐴− + 𝐻3 𝑂+ ↔ 𝐻𝐴 + 𝐻2 𝑂 Addition of base: 𝐻𝐴 + 𝑂𝐻 − ↔ 𝐴− + 𝐻2 𝑂 the conjugate base reacts with H3O+ added to the buffer; the conjugate acid reacts with OH- added to the buffer solution, thereby resisting a large change in pH Acid-Base Titration 33 BUFFERS pH of buffers consisting of HA and A- ▪ Two competitive equilibria: 𝐻3 𝑂+ 𝐴− 𝐻𝐴 + 𝐻2 𝑂 ↔ 𝐻3 𝑂+ + 𝐴− 𝐾𝑎 = 𝐻𝐴 𝐾𝑤 𝑂𝐻 − 𝐻𝐴 𝐴− + 𝐻2 𝑂 ↔ 𝐻𝐴 + 𝑂𝐻− 𝐾𝑏 = = 𝐾𝑎 𝐴− MBE: 𝐻𝐴 = 𝐶𝐴 − 𝐻3 𝑂+ + 𝑂𝐻− 𝐴− = 𝐶𝑁𝑎𝐴 + 𝐻3 𝑂+ − 𝑂𝐻− Since 𝐻3 𝑂+ and 𝑂𝐻− have very little difference, then both may be neglected in the MBEs. However, if 𝐶𝐻𝐴 ≤ 1000𝐾𝑎 , then either 𝐻3 𝑂+ or 𝑂𝐻 − must be retained in the MBEs. Acid-Base Titration 34 BUFFERS pH of buffers consisting of HA and NaA 𝐻3 𝑂+ 𝐴− 𝐾𝑎 = 𝐻𝐴 Taking the log of both sides of the equation and rearranging gives the Henderson-Hasselbalch Equation 𝐴− 𝑝𝐻 = 𝑝𝐾𝑎 + 𝑙𝑜𝑔 𝐻𝐴 Acid-Base Titration 35 BUFFERS pH of buffers consisting of B and BH+ 𝐵𝐻+ 𝑂𝐻− 𝐵 + 𝐻2 𝑂 ↔ 𝐵𝐻+ + 𝑂𝐻− 𝐾𝑏 = 𝐵 𝐵𝐻+ 𝑝𝑂𝐻 = 𝑝𝐾𝑏 + 𝑙𝑜𝑔 𝐵 Acid-Base Titration 36 BUFFERS Buffer Capacity ▪ the number of moles of a strong acid or a strong base that causes 1.00 L of the buffer to undergo a 1.00- unit change in pH ▪ the higher the concentration of the two buffer components, the greater is the buffer capacity Acid-Base Titration 37 BUFFERS Buffer Capacity ▪ the closer the ratio of [HA] to [A-], the greater is the buffer capacity, maximum when [HA] = [A-] 𝑝𝐻 = 𝑝𝐾𝑎 ▪ the pKa of the acid chosen must lie within ± 1 unit of the desired pH in order for the buffer to have a reasonable capacity Acid-Base Titration 38 pH OF AMPHIPROTIC SALTS 𝐻3 𝑂+ 𝐴2− 𝐻𝐴− + 𝐻2 𝑂 ↔ 𝐴2− + 𝐻3 𝑂+ 𝐾𝑎2 = 𝐻𝐴− 𝐾𝑤 𝐻2 𝐴 𝑂𝐻− 𝐻𝐴− + 𝐻2 𝑂 ↔ 𝐻2 𝐴 + 𝑂𝐻− 𝐾𝑏2 = = 𝐾𝑎1 𝐻𝐴− + 𝐾𝑎2 𝐶𝑁𝑎𝐻𝐴 + 𝐾𝑤 𝐶𝑁𝑎𝐻𝐴 𝐻3 𝑂 = ≅ 𝐾𝑎1 𝐾𝑎2 𝑖𝑓 ≫ 1 𝑎𝑛𝑑 𝐶𝑁𝑎𝐻𝐴 𝐾𝑎1 1+ 𝐾𝑎1 𝐾𝑎2 𝐶𝑁𝑎𝐻𝐴 ≫ 𝐾𝑤 Acid-Base Titration 39 EXAMPLE Calculate the pH change that takes place when a 100- mL portion of 0.0500 M NaOH is added to 400 mL of the buffer solution that is 0.200 M in NH3 and 0.300 M in NH4Cl. The initial pH of the buffer solution is 9.07. 𝑁𝐻4+ + 𝐻2 𝑂 ↔ 𝑁𝐻3 + 𝐻3 𝑂+ 𝐾𝑎 = 5.70 𝑥 10−10 𝑁𝐻3 + 𝐻2 𝑂 ↔ 𝑁𝐻4+ + 𝑂𝐻− 𝐾𝑏 = 1.75 𝑥 10−5 Analytical Chemistry 40 EXAMPLE Adding NaOH converts part of the NH4+ in the buffer to NH3 𝑁𝐻4+ + 𝑂𝐻 − ↔ 𝑁𝐻3 + 𝐻2 𝑂 The analytical concentrations of NH3 and NH4Cl then become 0400 𝑥 0.20 + 100 𝑥 0.0500 85.0 𝑐𝑁𝐻3 = = = 0.170 𝑀 500 500 0400 𝑥 0.30 − 100 𝑥 0.0500 85.0 𝑐𝑁𝐻4𝐶𝑙 = = = 0.230 𝑀 500 500 Analytical Chemistry 41 EXAMPLE When substituted into the acid dissociation-constant expression for NH4+, these values yield 𝐻3 𝑂+ 𝑁𝐻3 𝐾𝑎 = + = 5.70 𝑥 10−10 𝑁𝐻4 𝐻3 𝑂+ 0.170 = 5.70 𝑥 10−10 0.230 0.230 𝐻3 𝑂+ = 5.70 𝑥 10−10 𝑥 = 7.71 𝑥 10−10 𝑀 0.170 𝑝𝐻 = − log 7.71 𝑥 10−10 = 9.11 ∆𝑝𝐻 = 9.11 − 9.07 = 0.04 𝑖𝑛𝑐𝑟𝑒𝑎𝑠𝑒 Analytical Chemistry 42 MIXTURE OF BASES Two Separate Titration Method ▪ one titration uses phenolphthalein (phth, pH 8.0 - 9.6) 𝑉𝑝ℎ𝑡ℎ = 𝑉𝐻𝑐𝑙 required to reach eq. pt. ▪ another titration uses bromocresol green (bcg, pH 3.8 - 5.3) or methyl orange (mo, pH 3.1 – 4.4) 𝑉𝑏𝑐𝑔 = 𝑉𝑚𝑜 = 𝑉𝐻𝑐𝑙 required to reach eq. pt. Acid-Base Titration 43 MIXTURE OF BASES Double Indicator Method ▪ one titration using 2 indicators ▪ phth is added at the start of titration 𝑉1 = 𝑉𝐻𝑐𝑙 required to reach eq. pt. ▪ bcg or mo is added when phth changes color 𝑉2 = 𝑎𝑑𝑑𝑖𝑡𝑖𝑜𝑛𝑎𝑙 𝑉𝐻𝑐𝑙 required to reach the 2nd eq. pt. Acid-Base Titration 44 Kjeldahl Method Determination of Organic Nitrogen Sample bound nitrogen Concentrated H2SO4 𝑁𝐻4 + Distilled into excess strong acid 𝑁𝐻3 𝑙𝑖𝑏𝑒𝑟𝑎𝑡𝑒𝑑 Excess acid is back-titrated with standard base Acid-Base Titration 45 Protein Content in Sample % 𝑝𝑟𝑜𝑡𝑒𝑖𝑛 = %N x factor 6.25 for meats 6.38 for dairy products 5.70 for cereals Acid-Base Titration 46 TITRATION CURVE ▪ before equivalence point, determine amount of unreacted analyte ▪ at equivalence point, use Ksp ▪ beyond equivalence point, determine amount of excess titrant Precipitation Titration 47 TITRATION CURVE Effect of Concentration ▪ A: 50.00 mL of 0.05000 M NaCl titrated with 0.1000 M AgNO3 ▪ B: 50.00 mL of 0.00500 M NaCl titrated with 0.01000 M AgNO3 (Skoog, 2014) Precipitation Titration 48 TITRATION CURVE Effect of Concentration ▪ the greater the concentration of analyte and titrant, the ∆𝑝𝐴𝑔 greater , steeper slope at ∆𝑉 equivalence point region (sharper endpoint) (Skoog, 2014) Precipitation Titration 49 TITRATION CURVE Reaction Completeness ▪ The smaller the value of Ksp, the greater K and the more complete is the reaction, the ∆𝑝𝐴𝑔 greater , steeper slope ∆𝑉 at equivalence point region (sharper endpoint) (Skoog, 2014) Precipitation Titration 50 INDICATORS Precipitation Titration Involving Silver ▪ Mohr Method: formation of a colored precipitate ▪ Volhard Method: formation of a colored complex ▪ Fajans’ Method: adsorption of a colored organic compound (weak acid or base); for precipitates passing through the colloidal state Precipitation Titration 51 MOHR METHOD Reaction 𝐴𝑔+ + 𝑋 − ↔ 𝐴𝑔𝑋(𝑠) Endpoint 2𝐴𝑔+ + 𝐶𝑟𝑂42− ↔ 𝐴𝑔2 𝐶𝑟𝑂4(𝑠) (𝑏𝑟𝑖𝑐𝑘 𝑟𝑒𝑑) Application Direct: Cl-, Br-, CN- with Ag+ as titrant Indirect: Ag+ + Cl- (measured excess); back titrate Cl- with Ag+ Limitations pH range of 6-10 Acidic solution: 2𝐶𝑟𝑂42− + 2𝐻 + ↔ 𝐶𝑟2 𝑂72− + 𝐻2 𝑂 Basic solution: 2𝐴𝑔+ + 𝑂𝐻 − ↔ 2𝐴𝑔𝑂𝐻(𝑠) ↔ 𝐴𝑔2 𝑂 + 𝐻2 𝑂 Precipitation Titration 52 VOLHARD METHOD Reaction 𝐴𝑔+ + 𝑆𝐶𝑁 − ↔ 𝐴𝑔𝑆𝐶𝑁(𝑠) Endpoint 𝐹𝑒 3+ + 𝑆𝐶𝑁 − ↔ 𝐹𝑒𝑆𝐶𝑁 2+ (𝑏𝑙𝑜𝑜𝑑𝑦 𝑟𝑒𝑑) Application Direct: Ag+ with SCN- as titrant Indirect: halide ions X + Ag+ (measured excess); back-titrate Ag+ with SCN- In the indirect analysis of Cl-, AgCl must be filtered first before back-titration to prevent low Cl- analysis because AgSCN is less soluble than AgCl: 𝐴𝑔𝐶𝑙 + 𝑆𝐶𝑁 − ↔ 𝐴𝑔𝑆𝐶𝑁(𝑠) + 𝐶𝑙 − Limitations pH range must be acidic Basic solution: 𝐹𝑒 3+ + 𝐻2 𝑂 ↔ 𝐹𝑒 𝑂𝐻 3(𝑠) + 3𝐻 + Precipitation Titration 53 FAJANS METHOD ▪ uses an adsorption indicator, an organic compound that adsorbs onto or desorbs from the surface of the solid in a precipitation titration ▪ the adsorption or desorption occurs near the equivalence point and results not only in a color change but also in the transfer of color from the solution to the solid or vice versa Precipitation Titration 54 DEFINITION Lewis acid ▪ electron pair acceptor (e.g. Ca2+, Mg2+, Zn2+) Lewis base ▪ electron pair donor (ligand); must have at least a lone pair of electrons, (e.g. NH3) Complexometric Titration 55 DEFINITION Chelate ▪ a cyclic complex formed when a cation is bonded by two or more donor groups contained in a single ligand https://en.wikipedia.org/wiki/Chelation Dentate ▪ means having tooth-like projections Complexometric Titration 56 DEFINITION Coordination Number ▪ number of covalent bonds that a cation tends to form with electron donors Complexometric Titration 57 TITRATION CURVE Titration of 60.0 mL of a solution that is 0.020 M in metal M with A: a 0.020 M solution of the tetradentate ligand D to give MD as the product B: a 0.040M solution of the bidentate ligand B to give MB2 C: a 0.080 M solution of the unidentate ligand A to give MA4 The overall formation constant for each (Skoog 2014) product is 1020 Complexometric Titration 58 TITRATION CURVE Multidentate ligands are preferred over unidentate ligands because they: ▪ generally react more completely with cations (sharper end points) ▪ ordinarily react with metal ions in a single step process (sharper end points) (Skoog 2014) Complexometric Titration 59 EDTA Ethylenediaminetetraacetic acid (EDTA) (Skoog 2014) 𝐻4 𝑌 + 𝐻2 𝑂 ↔ 𝐻3 𝑌 − + 𝐻3 𝑂+ 𝐾𝑎1 𝐻3 𝑌 − + 𝐻2 𝑂 ↔ 𝐻2 𝑌 2− + 𝐻3 𝑂+ 𝐾𝑎2 𝐻2 𝑌 2− + 𝐻2 𝑂 ↔ 𝐻𝑌 3− + 𝐻3 𝑂+ 𝐾𝑎3 𝐻𝑌 3− + 𝐻2 𝑂 ↔ 𝑌 4− + 𝐻3 𝑂+ 𝐾𝑎4 Complexometric Titration 60 EDTA 𝑌 4− 𝑌 4− 𝛼4 = = 𝐶𝑦 𝐻4 𝑌 + 𝐻3 𝑌 − + 𝐻2 𝑌 2− + 𝐻𝑌 3− + 𝑌 4− 𝐾𝑎1 𝐾𝑎2 𝐾𝑎3 𝐾𝑎4 𝛼4 = + 4 𝐻 + 𝐻 + 3 𝐾𝑎1 + 𝐻 + 2 𝐾𝑎1 𝐾𝑎2 + 𝐻 + 𝐾𝑎1 𝐾𝑎2 𝐾𝑎3 + 𝐾𝑎1 𝐾𝑎2 𝐾𝑎3 𝐾𝑎4 𝛼4 , the fraction of EDTA in the Y4- form, increases with increasing pH EDTA titrations are done in basic pH to ensure enough Y4-, which is the form needed in titration Complexometric Titration 61 FORMATION CONSTANTS 𝑀𝑌 (𝑛−4) absolute 𝑀𝑛+ + 𝑌 4− ↔ 𝑀𝑌 (𝑛−4) 𝐾𝑓 = 𝑛+ 4− = 𝐾𝑎𝑏𝑠 formation 𝑀 𝑌 constant 𝑀𝑌 (𝑛−4) since 𝑌 4− = 𝛼4 𝐶𝑌 , then 𝐾𝑓 = 𝑀𝑛+ 𝛼4 𝐶𝑌 𝑀𝑌 (𝑛−4) effective ′ 𝑤ℎ𝑒𝑟𝑒 𝛼4 𝐾𝑓 = = 𝐾𝑒𝑓𝑓 = 𝐾𝑓 formation 𝑀𝑛+ 𝛼4 constant Whereas Kf or Kabs is constant, Keff or Kf’ depends on pH Complexometric Titration 62 EDTA TITRATION Indicators ▪ also form chelates with metal ions (e.g. Eriochrome Black T (EBT) and Calmagite → 𝐻2 𝐼𝑛− ) ▪ EBT decomposes slowly with standing ▪ order of stability of complexes 𝐶𝑎𝑌 2− > 𝑀𝑔𝑌 2− > 𝑀𝑔𝐼𝑛− > 𝐶𝑎𝐼𝑛− Complexometric Titration 63 EDTA TITRATION CURVE Effect of pH Influence of pH on the titration of 0.0100 M Ca2+ with 0.0100 M EDTA As pH increases, 𝛼 increases and ∆𝑝𝐶𝑎 increases (steeper slope) ∆𝑉 (Skoog 2014) at the equivalence point Complexometric Titration 64 EDTA TITRATION CURVE Effect of completeness of reaction Titration curves for 50.0 mL of 0.0100 M solutions of various cations at pH 6.0. (Skoog 2014) As Kf increases, the reaction becomes more complete ∆𝑝𝑀 increases (steeper slope) ∆𝑉 Complexometric Titration 65 EDTA TITRATION CURVE Minimum pH needed for the titration of various cations with EDTA (Skoog 2014) Complexometric Titration 66 AUXILIARY COMPLEXING AGENTS ▪ are added to prevent precipitation of the hydrous oxides (e.g. NH3) 𝑍𝑛2+ + 𝑌 4− ↔ 𝑍𝑛𝑌 2− 𝑍𝑛𝑌 2− 𝑍𝑛𝑌 2− 𝐾𝑓 = 2+ 4− = 𝑍𝑛 𝑌 𝛼𝑍𝑛 𝐶𝑍𝑛 𝛼𝑌 𝐶𝑌 𝑍𝑛𝑌 2− 𝛼𝑍𝑛 𝛼𝑌 𝐾𝑓 = = 𝐾𝑒𝑓𝑓 = 𝐾 𝐶𝑍𝑛 𝐶𝑌 𝑍𝑛2+ 𝛼𝑍𝑛 = 𝑍𝑛2+ + 𝑍𝑛 𝑁𝐻3 2+ + 𝑍𝑛 𝑁𝐻3 2+ 2 + 𝑍𝑛 𝑁𝐻3 2+ 3 + 𝑍𝑛 𝑁𝐻3 2+ 4 Complexometric Titration 67 AUXILIARY COMPLEXING AGENTS Effect of completeness of reaction As NH3 concentration ∆𝑝𝑀 increases decreases ∆𝑉 (less steep slope) at the equivalence point region (Skoog 2014) Complexometric Titration 68 LIEBIG TITRATION 𝐵𝑎𝑠𝑖𝑠: 2𝐶𝑁 − + 𝐴𝑔+ ↔ 𝐴𝑔(𝐶𝑁)− 2 𝐾~1021 Endpoint: appearance of turbidity due to the precipitation of silver cyanide + − 𝐴𝑔 + 𝐴𝑔(𝐶𝑁)2 ↔ 2𝐴𝑔𝐶𝑁(𝑠) + − 𝑜𝑟 𝐴𝑔 + 𝐴𝑔(𝐶𝑁)2 ↔ 𝐴𝑔 𝐴𝑔 𝐶𝑁 2 (𝑠) Deniges modification: iodide ion is added since AgI is less soluble than silver cyanide NH3 is added Ag(NH3)2+ forms which retards the precipitation of AgI until very near the equiv. pt. Complexometric Titration 69 EXAMPLE Determine the pH of the resulting solution of 50.00 mL of 0.0500 M HCl titrated with various amounts of 0.1000 M NaOH at 25°C. (a) 10mL; (b)25.10 mL Analytical Chemistry 70 EXAMPLE Before any base is added, the solution is 0.0500 M in 𝐻3 𝑂+ , and 𝑝𝐻 = −𝑙𝑜𝑔 𝐻3 𝑂+ = − log 0.0500 = 1.30 𝑛𝑜. 𝑚𝑚𝑜𝑙 𝐻𝐶𝑙 𝑟𝑒𝑚𝑎𝑖𝑛𝑖𝑛𝑔 𝑎𝑓𝑡𝑒𝑟 𝑎𝑑𝑑𝑖𝑜𝑛 𝑜𝑓 𝑁𝑎𝑂𝐻 𝑐𝐻𝐶𝑙 = 𝑡𝑜𝑡𝑎𝑙 𝑣𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛 𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑛𝑜. 𝑚𝑚𝑜𝑙 𝐻𝐶𝑙 − 𝑚𝑚𝑜𝑙 𝑁𝑎𝑂𝐻 𝑎𝑑𝑑𝑒𝑑 = 𝑡𝑜𝑡𝑎𝑙 𝑣𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛 50.00 𝑚𝐿 𝑥 0.0500 𝑀 − 10.00 𝑚𝐿 𝑥 0.1000 𝑀 = 50 + 10 𝑚𝐿 = 2.50 𝑥 10−2 𝑀 Analytical Chemistry 71 EXAMPLE 𝑝𝐻 = −𝑙𝑜𝑔 𝐻3 𝑂+ = − log 2.50 𝑥 10−2 𝑀 = 1.60 𝑛𝑜. 𝑚𝑚𝑜𝑙 𝑁𝑎𝑂𝐻 𝑎𝑑𝑑𝑒𝑑 − 𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑛𝑜. 𝑜𝑓 𝑚𝑚𝑜𝑙𝑒𝑠 𝐻𝐶𝑙 𝑐𝑁𝑎𝑂𝐻 = 𝑡𝑜𝑡𝑎𝑙 𝑣𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛 25.10 𝑚𝐿 𝑥 0.100 𝑀 − 50.00 𝑚𝐿 𝑥 0.050 𝑀 = 50 + 25.10 𝑚𝐿 = 1.33 𝑥 10−4 𝑀 𝑝𝑂𝐻 = −𝑙𝑜𝑔 𝑂𝐻 − = − log 1.33 𝑥 10−4 𝑀 = 3.88 𝑝𝐻 = 14.00 − 𝑝𝑂𝐻 = 10.12 Analytical Chemistry 72 REFERENCES Skoog, Douglas A, Donald M West, and Stanley R Crouch. 2014. Fundamentals Of Analytical Chemistry 9E. Australia: Cengage Learning®. Valera, Florenda. n.d. "Intro And Review Of Basic Concepts In Anal Chem". Presentation, University of the Philippines - Diliman. Analytical Chemistry 73