Analytical Chemistry PDF

Errors in Chemical Analysis Part 1 S...

Errors in Chemical Analysis Part 1 Systematic or Random or Gross or Error Determinate Indeterminate Blunder International Organization for Standardization (ISO) Affects Accuracy Precision Accuracy Yes; results are usually No; equal chance of Chemical Analysis and Testing Reproducible? constant vectors being ± No o 5725: accuracy of measurement methods and results Determinable? Yes o 3696: water for analytical laboratory use Eliminable or No, always present Yes; leads to correctable? Yes outliers o 9001: quality management systems (requirements) Yes; increase number Chemicals Minimizable? Yes of measurements o 45001: occupational health and safety management systems holding pipette in a wrong reagent or Example uncalibrated pipet different way during o 11014: SDS for chemical products (content & order of sections) instrument measurements Laboratory Practices Systematic o 17025: testing and calibration labs (competence requirements) o Possess deGinitive value, assignable cause, and are of the same o 15189: medical labs (quality & competence requirements) magnitude for replicate measurements made in the same way. Analytical Terminologies o Lead to bias in measurements Analyte – component of interest in the sample o Types Matrix – collection of all the components in the sample § Instrumental – by nonideal instrument behavior, faulty Sampling – process of collecting a small amount of a material whose calibrations, or by use under inappropriate conditions composition represents the bulk § Method – from non-ideal chemical or physical behavior of Aliquot – solution subjected to analysis analytical systems; hardest to deal with Blank – sample containing the matrix except the analyte § Personal – from carelessness, inattention, or personal Signal – measurement proportional to analyte concentration limitations of the experimenter Analytical Techniques Random – causes data to be more scattered/less symmetrical around the mean Characteristic Properties Instrumental Method Gross – large; causes a result to be either high or low Radiation Absorption Spectroscopy Measures of Accuracy & Precision (from ISO 5725-1:2023) Electrical Potential Potentiometry Trueness Electrical Charge Coulometry o Closeness between multiple test results and a true value Electrical Current Amperometry, Polarography Mass-to-Charge Ratio Mass Spectrometry o Measure of trueness is usually expressed in terms of bias Reaction Rate Kinetic Methods Accuracy Thermal Gravimetry o Closeness between a single test result and a true value Thermal Characteristics Differential Thermal Analysis o Refers to a combination of trueness and precision Differential Scanning Calorimetry o Common systematic error is called bias component Technique – any physical/chemical principle that can be used to Absolute Error Relative Error x!"#! − x!$%" study an analyte (e.g., Graphite Furnace AAS) E = x!"#! − x!$%" E$ = × 100% x!$%" Method – application of a technique for a speciGic analyte in a speciGic matric (e.g., GFAAS for Pb in water) Precision Procedure – set of written instructions on how to apply a method to o Closeness between test results obtained under stipulated a particular sample (e.g., APHA – American Public Health Association conditions and ASTM – American Society for Testing Materials) o Depends only on distribution of random errors and does not relate to the true value or the speciGied value Protocol – set of written guidelines for the analysis of a sample o Usually expressed in terms of imprecision and computed as a speciGied by an agency (e.g., EPA – Environmental Protection Agency) standard deviation of the test results; less precision is reGlected ClassiQication of Analyses According to Extent by a larger standard deviation. Complete/Exact Analysis – amount of each sample constituent is Deviation Average Deviation Standard Deviation quantitatively determined (e.g., blood analysis involves determination of glucose, Na, K, bilirubin, etc.) 1 ∑ d& d = x!"#! − x* * = ,d d n s=. Ultimate Analysis – amount of each element is determined (e.g., n−1 analysis of gasoline for C, H, O, Pb, etc) Outlier Proximate/Partial Analysis – amount of a certain selected o Inconsistent value from a set constituent in a sample is determined (e.g., partial analysis of aspirin o IdentiGied by a statistical test (Dixon’s Q test or Grubb’s Test) tablets gives the amount of salicylic acid impurity) Grubb’s Test Dixon’s Q Test Types of Analyses According to Quantity ISO & ASTM recommended 1x#%#(")! − x*"'$"#! 1 1x#%#(")! − x*1 Q #!'! = G#!'! = According to Sample Quantity R s Macro Meso Micro Ultra-Micro Bias > 100 mg 10-100 mg 0.1-10 mg o Difference between expectation of test results and true value 100 µL 50-100 µL < 50 µL o Can be one or more systematic error components contributing to bias, a larger systematic difference from the accepted According to Analyte Quantity reference value is reGlected by a larger bias value. Major Minor Trace Ultra-Trace o Instrument Bias: estimated by mean of the error of indication >1% 0.01-1% 10–7–0.01% 10 ppt 0.1-10 ppt 0.1-100 ppm 104 ppm 100-104 ppm 100-105 ppb , HClO? , H@ SO? concentration of the analyte. V" W S4 X § Seldom used as they are potent oxidants SG: "+ :D7 Can compensate for certain § Used when ClA from HCl interferes by precipitation types of errors if these Strong Bases: NaOH, KOH, Ba(OH)@ inGluence both the analyte and the reference species to the same o Solvent: must be CO@ free proportional extent. § dH@ O (sometimes supersaturated with CO@ ) should be Internal Standard – reference species different to the analyte but is boiled brieGly then allowed to cool to RT before base chemically and physically similar to the analyte. It is added to all addition, as hot alkali solutions rapidly absorb CO@ samples and standards containing the analyte. § diH@ O does not contain signiGicant CO@ Example. A spectrophotochemical method for the quantitative analysis of Pb&1 in o Storage blood uses Cu&1 as an internal standard. A standard that is 1.75 ppb Pb&1 and 2.25 § Long Term: tightly capped LDPE; before capping, bottle is @ ppb Cu&1 yields \ $ ] of 2.37. A sample of blood spiked with the same @%& @A, squeezed to minimize interior air space. Over time though, @$ NaOH causes it to become brittle. concentration of Cu&1 gives \ ] of 1.80. What is the concentration of Pb&1 in @%& @B § Short Term (not more than 1-2 weeks): glass bottles; the blood? NaOH conc. will decrease slowly (0.1% to 0.3% per week) 1.80 if stored here due to formation of sodium silicates. C23!" +* 35667 = (1.75 ppb Pb&1 ) W X = 𝟏. 𝟑𝟑 𝐩𝐩𝐛 2.37 § Never Store In: glass-stoppered containers; causes stopper to “freeze” after a brief period. Minimizing Errors in Analytical Procedures Primary Standards Highly puriGied compound that serves as a reference material in Method Introduces titrations and in other analytical methods interferents; may degrade analyte sensitivity and Saturation Requirements: detectability though matrix modi?ier o Highly purity, atmospherically stable, and non-hydrated so that Matrix non-interferent that removes dependency of analytical solid composition does not change with humidity variations Modi?ication response to interferent concentration; e.g., a buffer o Reasonably large MM so that the relative error associated with masking agent weighing the std is minimized Masking reacts selectively with interferents to form a o Reasonable solubility in the titration medium non-interfering complex o Modest cost solvent; may affect ability to detect analyte or to Dilution for Acid Titrants for Base Titrants accurately/precisely measure its response Na& COC (most common) Matrix Matching matrix constituents KHCF HF OD , KHP (HOCH& )C CNH& /TRIS PhCO& H NaBD OE ∙ 10H& O/Borax Part 2 KH(IOC)& HgO Equivalents Strong Acid-Base Titrations Number of equivalents (n) – amount of one chemical species reacting stoichiometrically with another chemical species State Acidimetry Alkalimetry Equivalent Weight Equivalent Normality 𝐩𝐇 eq Initial 14 + log(c5 n6) − log(c7 n7 ) MW or FM mass N= mol B mol HA EW = eq = L n5 − n87 U X n87 − n5 U X n EW N = M × eq Pre VB;C 14 + log T mol HA Y − log T mol B Y V5 + V87 V87 + V5 In acid-base equilibria, n: o Acids: number of replaceable/acidic H < At VB;C 7 o Bases: number of H < required to neutralize each mole of base mol HA mol B n87 − n5 U X n5 − n87 U X Post VB;C − log T mol B Y 14 + log T mol HA Y Example. For the reaction: V87 + V5 V87 + V5 HC POD + 2NaOH → Na& HPOD + 2H& O EM of HC POD = FM/2 EM of NaOH = FM/1 Example. Calculate the pH during the titration of 50.00 mL of 0.0500 M NaOH In redox equilibria, n is the number of electrons gained/lost per mole with 0.1000 M HCl at 25 ˚C after the addition of the following volumes of reagent: of the species Identify the moles of base: Example. In the half-reactions below, determine n of the reactants. 0.0500 mmol NaOH mol NaOH = 50.00 mL × = 2.50 mmol 𝐚𝐜𝐢𝐝𝐢𝐜 1 mL 𝐌𝐧𝐎+ 𝟒 +⎯⎯- 𝐌𝐧 𝟐1 Identify the equivalence point volume: Oxidation state of Mn in 𝑀𝑛𝑂2+ : 1 mmol HCl 1 mL Mn = +7 VGH2 = 2.50 mmol NaOH × × = 25.0 mL In 𝑀𝑛31 : 1 mmol NaOH 0.1000 mmol HCl Mn = +2 (a) 24.50 mL 0.1000 mmol HCl MnO+ + 2 must gain 5 e , thus n = 5. mol HCl added = 24.50 mL × = 2.450 mmol 𝐚𝐜𝐢𝐝𝐢𝐜 1 mL 𝐂𝟐 𝐎𝟐+ 𝟒 +⎯⎯- 𝐂𝐎𝟐 1 mmol NaOH Oxidation state of C in 𝐶3 𝑂23+ : 2.50 mmol NaOH − \2.450 mmol HCl × ] 𝑝H = 14 + log z 1 mmol HCl { C = +3 50.00 mL + 24.50 mL In 𝐶𝑂3 : C = +4 = 10.83 C3 O3+ + 2 must lose one e , but since there are two carbons, thus n = 2. (b) 25.00 mL In solubility and complexometric equilibria, n: 𝑝H = 7.00 o Metal: ion charge (c) 25.50 mL 0.1000 mmol HCl o Anion: metal ion equivalents that one mole of anion reacts with mol HCl added = 24.50 mL × = 2.550 mmol Example. In the reactions below, determine n of the reactants. 1 mL 1 mmol HCl 𝐀𝐠 1 + 𝐂𝐥+ → 𝐀𝐠𝐂𝐥 2.550 mmol HCl − \2.50 mmol NaOH × ] 𝑝H = − log z 1 mmol NaOH { = 3.18 EM of AgNO4 = FM/1 50.00 mL + 25.50 mL EM of KCl = FM /1 𝐁𝐚𝟐1 + 𝐒𝐎𝟐+ 𝟒 → 𝐁𝐚𝐒𝐎𝟒 EM of Ba(NO4)3 = FM/2 EM of Na3 SO2 = FM/2 Weak Monoprotic Acid-Base Titrations 𝐀𝐠 1 + 𝟐𝐂𝐍 + → 𝐀𝐠(𝐂𝐍)+ 𝟐 EM of AgNO4 = FM/1 Acidimetry Alkalimetry State EM of KCN= FM/(1/2) or 2(FM) 𝐩𝐇 K9 Initial 14 + log \ c − log ]K : c87 Neutralization Titrations K: 5 Titrant – standardized reagent with known exact concentration mol B mol A+ Pre n5 − n87 U X n5 U X End Point pK : + log T mol HA Y pK : + log T mol B Y V; Other Elemental Analysis Based on Neutralization Titration Production of each CO@A > cJ6> =9%(L9$- consumes 2OH A , thus, CO@ EL$' = − × 100% c9=%$ Element Convert To Reaction Details uptake does not alter add excess HCl combining capacity for H> O<. N NHC(Z) NHC + HCl → NHD Cl and back titrated Using Acid-Range Indicators (e.g., BCG, MO) with NaOH o At the end point using an acid-range indicator (i.e., bromocresol S SO&(Z) SO& + H& O& → H& SOD titrate with NaOH green), each CO@A > will have reacted with 2H> O < add excess o Since the amount of H> O< consumed is identical to the amount CO& (Z) CO& + Ba(OH)& C Ba(OH)& and back → BaCOC + H& O of OH A lost, no error results. titrate with HCl Using Basic-Range Indicators – CO@A > would have reacted only with Cl HCl(Z) – one H> O< at the end point, leading to a negative systematic error F SiFD (Z) 3SiFD + 2H& O titrate with NaOH CO@A → 2H& SiF\ + SiO& > presence does not cause error provided the same indicator is used for both standardization and analysis. End point sharpness is decreased Complexometric Titrations Alkalinity Titration Justus von Liebig – developed complexometric titrations of CN A and Alkalinity – measure of water sample’s acid-neutralizing capacity; ClA using Ag < and Hg @< as titrants assumed to arise mainly from OH A , HCOA > , & CO> @A Gerold Schwarzebach – Girst utilized EDTA titration with Double Indicator Titrations – employed to determine alkalinity if metallochromic dyes as indicators alkaline sources are limited to OH A , HCOA @A Metallochromic Indicators > , & CO> Constituents 𝐕𝐏𝐇 and 𝐕𝐁𝐂𝐆 Constituents 𝐕𝐏𝐇 and 𝐕𝐁𝐂𝐆 o Organic dyes that form stable complexes with metals (e.g., 1 Eriochrome Black T and Calmagite) NaOH V2O = VPQR NaOH, Na& COC V2O > VPQR 2 o Must bind to metals less strongly than EDA 1 Na& COC , 1 o For EBT: Na& COC V2O = VPQR V2O < VPQR 2 NaHCOC 2 § Useful pH is 8-10 to maintain the blue color in the free state. NaHCOC V2O = 0 § Approaching the equivalence point, excess metal ion reacts with indicator to form complexes (red solution). Example. A mixture contains NaOH, NaHCOC , and Na& COC , either alone or in § Solution turns blue with the Girst slight excess of EDTA in permissible combination. The mixture was titrated with 0.250 M HCl, requiring 26.20 mL for the phenolphthalein endpoint and an additional 15.20 mL to reach the absence of metal ions. the bromocresol green endpoint. How many milligrams of the component(s) are Auxiliary Complexing Agent – ligand, such as NH> , tartrate, citrate, present in the mixture? or triethanolamine, that binds the metal strongly enough to prevent its reaction with other reagent but weakly enough to give up the metal V2O = 26.20 mL and VPQR = 41.40 mL when EDTA is added. 1 V = 20.7 < V2O Masking Agent 2 PQR o Protects some of the analyte components from reacting with the / V2O > VPQR , hence only 𝐍𝐚𝐎𝐇 and 𝐍𝐚𝟐 𝐂𝐎𝟑 occurs in the mixture. The following & titrant equilibria occurs: o Prevents a species from interfering in the analysis of another OH I + H 1 → H& O CO&I 1 I o Example: Al>< mixed with Mg @< can be measured by Girst C + H → HCOC /J.&0 VW masking Al>< with F A , leaving only Mg @< to react with EDTA. HCO&IC + H 1 → H& COC Demasking Agent The 15.20 mL of HCl required to reach the BCG (third equilibrium) endpoint is o Releases metal ion from a masking agent. also the amount utilized to singly-neutralize CO&I C (second equilibrium). Hence: //.0 VW o Example: CN A complexes are demasked with formaldehyde OH I + H 1 → H& O Blocking Agents /J.&0 VW CO&I C + H1 → HCOI C o Indicators must give up metal ion to EDTA, thus a metal is said /J.&0 VW to block the indicator if it does not freely dissociate from it HCO&I C + H1 → H& COC Simplifying: o Cannot be used for the direct titration //.0 VW o Example: EBT is blocked by Cu@< , Ni@< , Co@< , Cr >< , Fe>< , Al>< OH I + H 1 → H& O Complexing Agents C0.D VW CO&I C + 2H 1 → H& COC Nitriloacetic acid (NTA; N(CH@ COOH)> ) – chelator for Ca@< , Co@< , Calculating: Cu@< , Fe>< 0.250 mol HCl 1 mol NaOH mg NaOH = 11.0 × 10IC L HCl × × Trans-1,2-diaminocyclohexanetetraacetic acid 1 L HCl 1 mol HCl 40 g NaOH 10C mg NaOH (DCTA) – chelator for Na< × × = 𝟏𝟏𝟎 𝐦𝐠 𝐍𝐚𝐎𝐇 Diethylene-triaminepentaacetic acid or 1 mol NaOH 1 g NaOH 0.250 mol HCl 1 mol Na& COC Pentetic acid (DTPA) – formation constant ~100 x mg Na& COC = 30.4 × 10IC L HCl × × greater than EDTA 1 L HCl 2 mol HCl C 106 g Na& COC 10 mg Na& COC Ethylenediaminetetraacetic acid (EDTA) × × = 𝟒𝟎𝟑 𝐦𝐠 𝐍𝐚𝟐 𝐂𝐎𝟑 1 mol Na& COC 1 g Na& COC o Most widely used hexadentate chelator Warder Method o Neutral EDTA is tetraprotic o Direct titration of carbonate mixtures o Reagent-wise, it occurs as Na@ H@ Y ∙ 2H@ O o Limitations: diffused endpoints, possible CO@ loss, and large o Y ?A is the form that binds to metals errors in OH A and CO@A > calculation since amounts are based on o MY ?A is unstable at very low/high pH, thus two measurements titrations are done at buffered pH (10-12) Winkler Method EDTA Titration Techniques o Indirect titration of carbonate mixtures Direct Titration – simple and most convenient; standard EDTA is slowly added to the metal until the endpoint is achieved © Y.S. Masuda (2024). NOT FOR PUBLIC DISTRIBUTION.  Back Titration Example. A 0.4482-g sample of impure NaCN is titrated with 39.68 mL of 0.1018 o Excess standard EDTA added to analyte to ensure complexation M AgNOC to reach the endpoint. Report the purity of the sample as % NaCN. 0.1018 mol AgNOC 2 mol NaCN 49.0072 g NaCN 100% o Excess EDTA is back titrated with a standard solution of a second 0.03968 L × × × × metal ion 1 L AgNOC 1 mol AgNOC 1 mol NaCN 0.4482 g 𝐠 o Used when direct titration fails: % 𝐍𝐚𝐂𝐍 = 𝟖𝟖. 𝟑𝟒% 𝐠 § Analyte precipitates in the absence of EDTA § Analyte reacts too slowly with EDTA Part 3 § Analyte blocks the indicators Displacement Titration Argentometric Methods o Analyte is added to a metal-EDTA complex o Analyte displaces EDTA from the metal and the metal is Precipitation Titrimetry o One of the oldest analytical techniques (mid-1800s) subsequently titrated with standard EDTA o One of the earliest methods was the analysis of K @ CO> and o Used when the metal does not have a suitable indicator K @ SO? in potash using Ca(NO> )@ as titrant. Indirect Titration – anion is Girst precipitated with a metal cation & Argentometric Titration – use of AgNO> as a precipitant the precipitate is washed, dissolved and titrated with standard EDTA Method Volhard Mohr Fajans Displacement Titrations Titration Back Direct EDTA is commonly used in water hardness determination. X I , C& O&I D , Unmeasured excess of a solution containing Mg-EDTA or Zn-EDTA is Analyte ClI , Br I , CN I ClI , Br I , I I , SCN I AsOCI D , SCN I introduced into the analyte. If the analyte forms a more stable Ag 1 (for excess) complex, Mg or Zn is displaced. Displaced ions are then titrated. Titrant & SCN I Ag 1 Hardness (ppm CaCO3) (for back) o Total aqueous polyvalent ion concentration (mainly Ca & Mg) pH 6-9; slightly Medium pH acidic acidic basic o Measure of capacity of water to produce soap adsorption o Other metal ions Girst treated with EDTA at pH 10 in NH> , giving Indicator FeC1 CrO&I indicator (e.g., D (yellow) total Ca & Mg concentrations while titration at pH 13 without DCF) NH> precipitates Mg(OH)@ leaving Ca to react with EDTA. blood-red brick-red o Temporary: Ca & Mg(HCO> )@ presence; removed by boiling Endpoint FeSCN &1 Ag & CrOD (#) opaque pink o Permanent: presence of CaCl@ , CaSO? , MgCl@ , MgSO? , etc.; complex precipitate cannot be removed by boiling Example. A 100.0-mL sample is analyzed for hardness, requiring 23.63 mL of Volhard Method 0.0109 M EDTA. Report the sample’s hardness as mg CaCOC /L. Developed by Jacob Volhard 0.0109 mol EDTA 1 mol CaCOC 100.09 × 10C mg CaCOC Measured excess of AgNO> is added and excess Ag < is back-titrated 0.2363 L × × × with standard KSCN. 1L 1 mol EDTA 1 mol CaCOC 100 × 10 LIC Strongly acidic environment is advantageous over other halide 𝐦𝐠 𝐂𝐚𝐂𝐎𝟑 >A = 𝟐𝟓𝟖 𝐩𝐩𝐦 𝐂𝐚𝐂𝐎𝟑 titrations because CO@A @A > , C@ O? , & AsO? do not interfere. 𝐋 '*'5_!" Example. Titration of Ca&1 and Mg &1 in a 50.00-mL sample of hard water Titrant Addition XI + Ag 1 1 (V"'#%$"7 "X)"##) ⇌ AgX (#) + Ag ("X)"##) required 23.65 mL of 0.01205 M EDTA. A second 50.00-mL aliquot was made !+!$'*! ]+,././0×/0()! strongly basic with NaOH to precipitate Mg &1 as Mg(OH)&. The supernatant was During Titration Ag 1 I ("X)"##) + SCN ⇌ AgSCN(#) titrated with 14.53 mL of the EDTA solution. Calculate the concentration of CaCOC +*7+)'!6$ (100.09 g/mol) and MgCOC (84.32 g/mol) in the sample in ppm. At End Point FeC1 + SCN I ⇌ FeSCN &1 Total moles of metals: Titration: back 0.01205 mmol EDTA 1 mmol metals >A mol (Ca&1 + Mg &1) = 23.65 mL × × Analyte: X A , C@ O@A ? , AsO? , SCN A 1 mL 1 mmol EDTA 𝐦𝐨𝐥 (𝐂𝐚𝟐1 + 𝐌𝐠 𝟐1) = 𝟎. 𝟐𝟖𝟒𝟗𝟖𝟐𝟓 𝐦𝐦𝐨𝐥 (𝐂𝐚𝟐1 + 𝐌𝐠 𝟐1 ) Titrant: AgNO> (for excess titration) & KSCN (for back-titration) Moles of Ca :2+ Medium: acidic 0.01205 mmol EDTA 1 mmol Ca&1 Indicator: Fe>< in the form of ferric alum, FeNH? (SO? )@ 14.53 mL × × = 𝟎. 𝟏𝟕𝟓𝟎𝟗 𝐦𝐦𝐨𝐥 𝐂𝐚𝟐1 1 mL 1 mmol EDTA Endpoint: formation of soluble blood-red FeSCN @< complex Moles of Mg2+: Disadvantage: AgCl is more soluble than AgSCN, hence the following 0.2849825 mmol − 017509 mmol = 𝟎. 𝟏𝟎𝟗𝟖𝟗𝟐𝟓 𝐦𝐦𝐨𝐥 𝐌𝐠 𝟐1 reaction occurs to a signiGicant extent near the end of the back- ppm CaCO3: 0.17509 mmol Ca&1 1 mmol CaCOC 100.09 mg CaCOC titration, causing endpoint fading & titrant overconsumption: × × = 𝟑𝟓𝟎 𝐩𝐩𝐦 𝐂𝐚𝐂𝐎𝟑 AgCl(#) + SCN I ⇌ AgSCN(#) + ClI 50.00 × 10IC L 1 mmol Ca&1 1 mmol CaCOC ppm MgCO3: Overcome by removing AgCl prior to back-titration. 0.1098925 mmol Mg &1 1 mmol MgCOC 84.32 mg MgCOC Example. Iodide in a 0.6712-g sample is determined by Volhard method titration. × × After adding 50.00 mL of 0.05619 M AgNOC and allowing the precipitate to form, 50.00 × 10IC L 1 mmol Mg &1 1 mmol MgCOC the remaining Ag 1 is back-titrated with 0.05322 M KSCN, requiring 35.14 mL to 𝐩𝐩𝐦 𝐌𝐠𝐂𝐎𝟑 = 𝟏𝟖𝟓 𝐩𝐩𝐦 𝐌𝐠𝐂𝐎𝟑 reach the end point. Report the % iodide in the sample. Example. The thallium in a 9.57-g sample of rodenticide was oxidized to TlC1 and 0.05619 mol Ag 1 treated with an unmeasured excess of Mg/EDTA solution. Titration of the a0.05000 L × g− 1 L Ag 1 1 mol I + 126.90 g I + liberated Mg &1 required 12.77 mL of 0.03610 M of EDTA. Calculate the %Tl (204.4 ` ha gU X 0.05322 mol SCN + 1 mol Ag 1 1 mol Ag 1 1 mol I + g/mol) in the sample U0.03514 L × + Xa + g 1 L SCN 1 mol SCN 0.03610 mol ETDA 1 mol Mg &1 1 mol TlC1 204.4 g TlC1 × 100 0.01277 L × × × × 0.6712 g 1 L EDTA 1 mol EDTA 1 mol Mg &1 1 mol TlC1 % 𝐈 = 𝟏𝟕. 𝟕𝟔% 9.57 g % 𝐓𝐥 = 𝟎. 𝟗𝟖𝟓% Mohr Method Developed by Karl Friedrich Mohr Titrant Analyte Product Indicator Suitable only for the titration of ClA , Br A , and CN A Br I , ClI , SCN I , CN I , neutral Hg(II) Hg(NOC )& various Before the equivalence point, Ag-precipitate solubility must be less thiourea complexes II than that of Ag-indicator, otherwise the latter would precipitate out. AgNOC Ag(CN)I & titrate to 7irst Indicator Quantity turbidity of AgI o Too little: Ag concentration will be higher at EQP before any CN I AgI Ag @ CrO? precipitation occurs NiSOD Ni(CN)&I titrate to 7irst D turbidity of AgI o Too much: color change will be difGicult to see due to intense Cu&1 Cu(CN)&I yellow color D KCN Hg &1 Hg(CN)& various pH Dependency Ni&1 Ni(CN)&I D o Optimal: pH 6-9; CaCO> is added to reduce sample acidity o > pH 9: Ag will precipitate with OH A Liebig Method o < pH 6: CrO@A @A ? (yellow) decomposes to Cr@ OO (bright orange), Widely used complexometric titration using monodentate CN A obstructing the endpoint ]+,./.F&×/0(). AgNO> is added to a solution of alkali CN A with KI indicator until During Titration '*'5_!" !+!$'*! !%$3+7 Ag(CN)A@ formation is complete. Further addition of AgNO> results in ClI + Ag 1 ⇌ AgCl(#) AgCN(%) formation When CN A is exhausted, Girst excess of AgNO> _"556` ]+,././×/0()! At End Point +*7+)'!6$ !+!$'*! reacts with I A to cause permanent turbidity due to AgI(%) CrO&ID + Ag 1 ⇌ Ag & CrOD(#) ]'.J.\×/0()* During Titration 2KCN + AgNOC ⇌ KAg(CN)& + KNOC Titration: direct ]+,.F.0×/0()- Analyte: ClA , Br A , and CN A At End Point KI + AgNOC ⇌ AgI + KNOC Titrant: Ag < Titration: direct Medium: slightly basic Analyte: CN A Indicator: CrO@A? (yellow) Titrant: AgNO> Endpoint: formation of brick-red Ag & CrOD (#) precipitate Indicator: KI Example. A 50.00-mL sample was subjected to Mohr titration for ClI Endpoint: permanent turbidity due to AgI determination. A few drops of K & Cr& OD indicator was added to the sample. The © Y.S. Masuda (2024). NOT FOR PUBLIC DISTRIBUTION.  sample consumed 15.70 mL of 0.0800 M AgNOC solution. Calculate the amount of Summary of Techniques chloride (mg/L) in the sample. Ranking in terms of oxidizing ability: MnOA ?< > Cr@ O@A 0.0800 mol Ag 1 1 mol Cl+ 35.45 g Cl+ 1000 mg ? ~Ce O > I@ ?< A a0.01570 L × 1L × 1 mol Ag 1 × 1 mol Cl+ × 1g g 𝐦𝐠 Ce is stronger than MnO? when in HClO? or HNO> but weaker = 𝟖𝟗𝟏 0.05000 L 𝐋 when in HCl and H@ SO? Method Permanga- Ceri- Dichro- Iodi- Iodo- Fajans Method Titration Direct Indirect Titrant MnO2+ Ce21 Cr3 O?3+ I3 S3 O43+ Developed by Kazimierz Fajans none or Analyte is precipitated with Ag <. Excess negatively charged analyte 1˚ STD C3 O23+ none S3 O43+ IO4+ C3 O3+ 2 surrounds precipitate, forming a negatively charged colloid. weakly Excess Ag < binds to the negative colloid, forming a positive colloid. acidic to pH acidic < pH 9 mildly Negatively charged adsorption indicator adsorbs onto positive colloid basic "X)"## ]+,./.F&×/0(). "X)"## '*'5_!" !+!$'*! +*7+)'!6$ !%$3+7 '*'5_!" Indicator MnO+ 2 redox indicator starch During Titration XI + Ag 1 + DCF I ⇌ AgX (#) + XI (ferroin) (Ph3 NH) disappearance (X I adsorbed onto AgX)I Endpoint faint pink red to green to dark blue of dark blue *"Z'!+a"5_ )b'$Z"7 )6556+7 blue violet !+!$'*! +*7+)'!6$ Ag 1 + AgX (#) + DCF I ⇌ At End Point [(Ag 1 adsorbed onto AgX) − DCF I ] 1 Permanganimetry ,Q- '7#6$3"7 6*!6 (6#+!+a"5_ )b'$Z"7 )6556+7 KMnO? Titration: Direct o Strong oxidant and easily reducible Analyte: ClA , Br A , I A , SCN A o Intense violet color Titrant: Ag < o Not available as a primary standard, standardized with: Indicator: adsorption indicator § As@ O> Indicator pH Sample § Pure Fe wire Fluorescein ≥7 ClI , Br I , I I , SCN I § Mohr’s salt, (NH? )@ Fe(SO? )@ (H@ O)P Dichloro`luorescein ≥4 § NaC@ O? (> 60 ˚C to speed up reaction) Eosin ≥2 Br I , I I , SCN I At the beginning of the titration, violet color persist Endpoint: opaque pink for several seconds before it disappears. Redox Titrimetric Methods As Mn@< is formed, the reaction proceeds more Claude Berthollet (1787) – introduced method for quantitative rapidly due to autocatalysis. analysis of chlorine water (mixture of Cl@ , HCl, & HOCl) based on its o Preparation: dilute solution is boiled to hasten the oxidation of ability to oxidize indigo, a dye that is colorless in its oxidized state water, then Giltered using clean sintered glass to remove brown Joseph Gay-Lussac (1814) – developed a similar method for MnO@ (%). This is stored in a dark bottle to avoid decomposition. determining chlorine in bleaching powder. o pH Dependency Redox Titration Curve § < 1: reduced to Mn@< Equivalence Point Treatment § Neutral or Alkaline: reduced to brown MnO@ (%) Before Use the half reaction of the analyte At Use equivalence point equation § Strongly Alkaline (2 M NaOH): reduced to green MnO@A ? After Use the half reaction of the titrant o Auto-Decomposition: MnO@ impurities catalyzes KMnO? o Symmetrical Equivalence Point: occurs if the stoichiometry of decomposition the redox titration is 1:1 o Endpoint Fading Over Time: KMnO? reacts with Mn@< to o Asymmetrical Equivalence Point: occurs if the stoichiometry decompose to MnO@ (%) of the redox titration is not 1:1; the equivalence point is either Titration: direct closer to the top or the bottom of the curve’s sharp rise Titrant: KMnO? Titration of Mixtures Medium: acidic o Possible if their standard state potentials or formal potentials Indicator: KMnO? differ by at least 200 mV. Endpoint: faint pink o First to be titrated is the stronger reducing agent or the species Example. Titration of a 0.2121 g pure Na& C& OD (134 g/mol) required 43.31 mL of easily oxidized (lowest/most negative reduction potential) KMnOD. What is the normality and molarity of the KMnOD solution? Indicators for Redox Titrimetric Methods Recall n = 5 for 𝑀𝑛𝑂23+ and n = 2 for 𝐶3 𝑂23+. At the EQP, 𝑒𝑞 𝑁𝑎3 𝐶3 𝑂2 = 𝑒𝑞 𝐾𝑀𝑛𝑂2 eq 0.2121 g Na3 C3 O2 2 eq Na3 C3 O2 1 eq KMnO2 Self Indicator L KMnO2 = × × 0.04331 L KMnO2 134 g Na3 C3 O2 1 eq Na3 C3 O2 = 𝟎. 𝟎𝟕𝟑𝟏 𝐍 o Used when titrant’s oxidized and reduced form differ in color Molarity: o Example: MnOA ? mol KMnO2 = 0.0731 eq KMnO2 1 mol KMnO2 × = 𝟎. 𝟎𝟏𝟒𝟔 𝐌 SpeciQic Indicator L 1L 5 eq KMnO2 Example. A 16.42-mL volume of 0.1327 M KMnO2 is needed to oxidize 25.00 mL of a o Reagent that forms a colored compound with a speciGic oxidized FeSO2 solution in an acidic medium. What is the concentration of the FeSO2 solution in or reduced form of the titrant or the analyte. normality and molarity? o Example: n = 5 for 𝑀𝑛𝑂23+ and n = 1 for 𝐹𝑒 31 § Starch produces a blue color with iodine eq 0.01642 L KMnO2 0.1327 mol KMnO2 5 eq KMnO2 1 eq FeSO2 FeSO2 = × × × Active fraction of starch is amylose, a polymer of the L 0.02500 L FeSO2 1 L KMnO2 1 mol KMnO2 1 eq KMnO2 eq sugar α-d-glucose. FeSO2 = 𝟎. 𝟒𝟑𝟓𝟖 𝐍 L In the presence of starch, iodine forms IP chains Molarity: mol 0.04358 eq FeSO2 1 mol FeSO2 inside the amylose helix; color turns dark blue FeSO2 = × = 𝟎. 𝟒𝟑𝟓𝟖 𝐌 L 1L 1 eq FeSO2 § SCN A forms a soluble red complex with Fe>< Redox Indicator o Substances that do not participate in titration, but whose Iodimetry oxidized and reduced forms differ in color. Oxidation of an analyte (reductant) with I@ solutions. o Transition potential of indicator & equivalence point potential Starch-Triiodide Complex – I@ is more soluble when it reacts with I A should be nearly equal to give a color change to form I>A which helically complexes with starch’s amylose units o Used if formal ∆E between analyte & titrant is > 0.4 V pH Dependency o Example: ferroin; at 1.147 V, a color change from red to blue o Performed in weakly acidic to mildly alkaline (pH 8) solutions occurs (~1.088 to ~1.206 V) o Too basic: I@ disproportionates Auxiliary Reagents o Too acidic: starch is hydrolyzed and the oxidizing power of I@ is Pre-Reduction/Pre-Oxidation – ensures that the analyte is initially decreased present in a single oxidation state (e.g., a mixture containing Fe(II) Titration: direct and Fe(III) is Girst reduced to ensure that only Fe(II) is present) Analyte: oxidizable by iodine in acidic medium; reducing agents Auxiliary Reductants Auxiliary Oxidants Titrant: iodine Stannous chloride, SnCl& Medium: weakly acidic to mildly alkaline Peroxydisulfate,(NHD )& S& OF Chromous chloride, CrCl& Sodium bismuthate, NaBiOC Indicator: starch (can be added at the beginning of the titration) Jones Reductor (Zn coated with Zn amalgam) Endpoint: formation of a dark blue iodine-starch complex H& O& Walden Reductor (solid Ag and 1 M HCl) Iodometry Reduction of analyte (oxidant) with KI, yielding I@ which is titrated with standard Na@ S@ O> (reductant; standardized with KIO> ) Two redox reactions occur: iodine is oxidized and then reduced More common compared to iodimetry Titration: indirect Analyte: can reduce iodine in acidic medium; oxidizing agents !+!$'*! During Titration I& + 2S& O&I &I I C ⇌ SD O\ + 2I Titrant: S@ O@A > Medium: < pH 9 since I@ disproportionates to I A & HOI which oxidizes S@ O@A @A > to SO? © Y.S. Masuda (2024). NOT FOR PUBLIC DISTRIBUTION.  Indicator: starch (added only before the equivalence point because Part 4 the starch-triiodide complex decomposes in high I@ concentration) Endpoint: disappearance of the blue color Parts of an Electrochemical Cell Example. A 0.200-g sample containing Cu is analyzed by iodometry. Cu(II) is reduced to Cu(I) by iodide; CuI precipitates. What is the % Cu in the sample if 20.0 Anode Cathode mL of 0.100 N Na& S& OC is required for titration of the liberated I& ? Site Of Oxidation Reduction 31 Recall n = 1 for 𝐶𝑢 and n = 1 for𝑆3 𝑂43+. 31 At the EQP, 𝑒𝑞 𝐶𝑢 = 𝑒𝑞 𝑆3 𝑂43+ Electron Source Electron Sink 0.0200 L Na3 S3 O4 0.100 eq Na3 S3 O4 1 eq Cu31 63.55 g Cu 31 Voltaic Cell × × × × 100% Negative Terminal Positive Terminal 0.200 g sample 1 L Na3 S3 O4 1 eq Na3 S3 O4 1 eq Cu31 𝐠 Electron Sink Electron Source % 𝐂𝐮 = 𝟔𝟑. 𝟓𝟓% Electrolytic Cell 𝐠 Positive Terminal Negative Terminal Solution Anolyte Catholyte Wire Color Black Red Cerimetry Cell Placement Left Right Ce?< Salt Bridge – maintains electrical neutrality by supplying inert ions o Strong oxidant; yellow in acid Devices o Requires redox indicator such as ferroin. o Preparation: Current Potential Charge § From 1˚ STD diammonium hexanitratocerate(IV), galvanostat potentiostat (NH? )@ [Ce(NO> )P ] in 1 M H@ SO? Controls amperostat potentiometer § Standardization of other salts (such as Ce(OH)? ) with Fe(%) galvanometer potentiometer Measures electrometer or Na@ C@ O? ammeter voltmeter Titration: direct Titrant: Ce?< Types of Electrochemical Cells Medium: acidic Galvanic or Voltaic Cell ° ° ° Indicator: redox indicator (e.g., ferroin) o Harvests chemical potential ER$'' = ER=&!(-$ − E=+(-$ Endpoint: for ferroin, red to blue energy from spontaneous ° ° ° Example. A 0.1432-g sample was analyzed for KClOC content. The sample was redox reactions and ER$'' = EL$-*R&"(+ − E(S"-=&"(+ dissolved in 50.00 mL of 0.09101 M Fe(NOC )& and the solution was acidi`ied. The converts it to electrical excess Fe&1 was back titrated with 12.60 mL of 0.08362 M Ce(NOC )D solution. energy Calculate the percentage of KClOC (122.55 g/mol) in the sample. Hint: ClOI C will o Alessandro Volta (1793) be reduced to ClI in the titration. § Found that electricity is produced by placing different In the back-titration; Fe&1 + CeD1 ⇌ FeC1 + CeC1 metals on the opposite sides of a wet paper or cloth. n = 6 for 𝐶𝑙𝑂CI and n = 1 for 𝐶𝑒 D1 and 𝐹𝑒 &1. At the EQP, 𝑒𝑞 𝐶𝑙𝑂CI = 𝑒𝑞 𝐹𝑒 &1 § Made his Girst battery by placing Ag and Zn on opposite 0.09101 mol Fe&1 1 eq Fe&1 sides of a cloth moistened with salt or weak acid solution. ⎡ ž0.05000 L Fe&1 × × ⎤ ⎢ 1 L Fe&1 1 mol Fe&1 ⎥ Example. Daniell Cell ° ⎢ 0.08362 mol Ce D1 1 mol Fe &1 1 mol Fe &1 ⎥ Cathode: Cu&1 + 2eI → Cu (EQ%!" /Q% = +0.34 V) ⎢− ž0.01260 L Ce × D1 × × ⎥ ° ⎣ 1 L CeD1 1 mol CeD1 1 mol CeD1 ⎦ Anode: Zn → Zn&1 + 2eI (Eh* !" /h* = −0.76 V) 1 eq ClOIC 1 mol ClO I C 1 mol KClO C 122.55 g KClO C 100% ° E)"55 = (+ 0.34 V) − (−0.76 V) = +𝟏. 𝟏𝟎 𝐕 × × × × × 1 eq Fe&1 6 eq ClOIC 1 mol ClOIC 1 mol KClOC 0.1432 g sample Electrolytic Cell – applies electrical energy to drive forth a chemical 𝐠 % 𝐊𝐂𝐥𝐎𝟑 = 𝟒𝟗. 𝟖𝟖% process 𝐠 Example. Electrolysis of aqueous NaCl ° Cathode: 2H& O + 2eI → H& + 2OH I (EO ! i/O! = −0.83 V) Dichrometry Anode: 2ClI → Cl& + 2eI (EQ5° /Q5( = −1.36 V) ! K @ Cr@ OO ° E)"55 = (−1.36 V) − (−0.83 V) = −𝟎. 𝟓𝟑 𝐕 o Weaker compared to MnOA ? and Ce ?< o Red-orange; available as a 1˚ STD; long-term stability Electrolysis of Aqueous Salt Solutions o Limited use; only for analytes that are highly oxidizable At the Cathode – more positive EL$- ° gets reduced here Titration: direct o Reduced: cations of less active metals (e.g., Au, Ag, Cu, Cr, Pt, Cd, Titrant: K @ Cr@ OO etc.) Medium: acidic o Not Reduced: cations of more active metals (Groups 1, 2, & Al) Indicator: redox indicators (diphenylamine & diphenylamine At the Anode – more negative EL$- ° gets oxidized here sulfonic acid) o By Default: O@ & H < Endpoint: green to violet o Oxidized: X A (except F A & dil. ClA ) Redox Titration of a Mixture o Not Oxidized: F A , common oxyanions (SO@A @A A @A ? , CO> , NO> , PO? ) Possible if standard state potentials differ by at least 200 mV Faraday’s Law of Electrolysis ° First to be titrated: stronger reducing agent (lowest EL$- ) First Law: amount of the substance deposited or Q = It Reduction Potential liberated at an electrode is directly proportional to the Measures the tendency of a half cell to be reduced quantity of electricity passed through an electrolyte More positive – easily reduced, stronger oxidant (F is the strongest Second Law : when the same quantity of electricity m4 eq 4 oxidant and the weakest reductant) is passed through different electrolytes, the = amounts of the products obtained at the electrodes mT eq T More negative – easily oxidized, strong reductant (Li is the weakest oxidant and the strongest reductant) are directly proportional to their chemical Cell voltage depends only on ∆E not absolute potentials equivalents or equivalent weights Nernst Equation Electroanalytical Methods Named after Walther Nernst RT Relates reduction potential of an E = E° − ln Q Interfacial Methods nF Dynamic electrochemical reaction to standard Bulk Method Static Controlled Controlled electrode potential, T, and activities 0.05916 Potential Current (concentrations) of the chemical E = E° − log Q n Potentiostatic Coul. Amperostatic Coul. species undergoing redox. Potentiometry Voltammetry Conductometry Higher electron transfer, higher [reactant], lower T, and lower product Electrogravimetry Amperometry concentration increases E and makes: o Reaction more spontaneous Technique Measures At Constant o Reactants more reducible/stronger oxidant Potentiometry Potential Current o Products more oxidizable/stronger reductant Potentiostatic Potential Redox Titration Coulometry Charge Quantity Equation Amperostatic Current 0.05916 [analyte]6X Coulometry ˚ Electrode Potential before 𝐕𝐄𝐐𝐏 E'*'5_!" − log ž Voltammetry Current Scan Rate n [analyte]$"7 ˚ ˚ Conductometry Conductivity Temperature n'*'5_!" E'*'5_!" + n!+!$'*! E!+!$'*! Electrode Potential at 𝐕𝐄𝐐𝐏 n'*'5_!" + n!+!$'*! Reference Electrodes 0.05916 [titrant]6X Electrode Potential after 𝐕𝐄𝐐𝐏 ˚ E!+!$'*! − log ž Standard Hydrogen Electrode ( EL$F = n [titrant]$"7 0.00 V) 2H < + eA ⇌ H@ o Electrode: Pt wire o Electrolyte solution: 1 M HCl (outside) o H@ (#) bubbled continuously at 1 atm Standard Calomel Electrode Hg @ Cl@ + 2eA ⇌ 2Hg + 2ClA (EL$F = 0.244 V) o Electrode: Pt wire © Y.S. Masuda (2024). NOT FOR PUBLIC DISTRIBUTION.  o Electrolyte solution Potentiometry Inside Outside Potential measured under static conditions sat KCl/Hg & Cl& sat. KCl Components Ag/AgCl Electrode (EL$F = 0.197 V) o Reference Electrode – ER$'' = (E"+- − EL$F ) + E[ o