Principles of Instrumental Analysis

CHM 2280SYLLABUSWINTER 2015

General Chemistry II

Professor C. F. Poole, 185 Chemistry

046 Deroy MW 4:30-5.50

Martin Luther King Holiday 1-19Spring Break 03-16 to 03-21First Class, Monday 01-12Last Class, Monday 04-27

Course Texts

RecommendedQuantitative Chemical Analysis, 8 th Edition, Daniel C. Harris, Freeman, 2010(e-book version available from Sapling)

OptionalSolution manual for Quantitative Chemical Analysis is available

Online HomeworkYou will need to register with Sapling Learning2COURSE OUTLINE

Module 1Introduction to Measurement ScienceModule 2Chemical EquilibriaModule 3Acid-Base Chemistry and Titration Module 4Compleximetric (EDTA) Titrations Module 5Fundamentals of Electrochemistry and Redox Titrations Module 6Fundamentals of Spectroscopy Module 7Atomic SpectroscopyModule 8Fundamentals of Separations

GRADING

3 Periodic Exams worth 200 points each = 600Comprehensive Final Examination = 400Homework (10 best scores)= 200Total = 1200

No makeup exams and no exam can be dropped. .Typical grade scale for this class: A, A-85-100%B+, B, B-84-59C+, C, C- 58-36D+, D 35-26F 0-25

This is not a grading guarantee. Grading scale used for Fall 2013 and should be a reasonable guide EXAM SCHEDULE: Tentative and subject to change with adequate notice 02-09 (M), 03-12 (W), and 04-22 (W). The final examination is 04-29 (W) from 4:30-7:00. All exams will be in 046 Deroy unless indicated otherwise. General Chemistry IIIntroduction to Measurement ScienceModule 1Goals of Chemical AnalysisDetermine the composition of SamplesIdentification of components (Qualitative Analysis)Relative composition (Quantitative Analysis)Different approaches for atoms and moleculesElemental composition (Atoms)Structural elucidation (molecules)Identification of the elemental composition and bond order

General ApproachesClassical Methods (wet chemistry)Isolation by precipitation, extraction, distillation, etc.Identification by converting to products identified from similarity of physical properties to a known standardQuantification by gravimetric or volumetric methods Instrumental MethodsIsolation by chromatographic methodsIdentification by spectrophotometryQuantification by physicochemical methods using special purpose instrumentsClassical MethodsSemimicro Qualitative AnalysisIdentification of ions by color formation, precipitation, gas production, selective solvationVisual detection of changesGravimetric AnalysisFormation of sparingly soluble salts (precipitates)Quantitative analysis based on weightTitrimetric AnalysisNeutralization (acid vs base)Precipitation (insoluble salt formation)Complex formationRedox reactionsInstrumental MethodsInteraction of Electromagnetic Radiation with Matter (Spectroscopy)ElectrochemistryMass SpectrometryThermal MethodsVacuum Spectroscopy (surface analysis)SensorsSeparation MethodsAnalytical WorkflowCollection of a Representative SampleSample PreparationIsolationConcentrationMatrix SimplificationChemical AnalysisClassical methodsInstrumental methodsData AnalysisScientific UnitsLengthmetermMasskilogramkgAmount of substancemole (mol)MTimesecondsTemperaturekelvinK ( 273.16+C)Electric currentampereA

Derived Scientific UnitsFrequencyhertzHzs-1ForcenewtonNm.kg.s-2PressurepascalPakg.m-1.s-2Energy jouleJm2.kg.s-2Electrical chargeCoulombCA.s-1Electrical potentialVoltVm2.kg.A-1.s-2Scientific NotationConsists of a number and a scale factor based on powers of 101.23 x 10nCommon non-numeric abbreviationstera T a = 1012pico p a = 10-12giga G a = 109nano n a = 10-9mega M a = 106micro a = 10-6kilo k a = 103milli m a = 10-3deca da a = 10centi c a = 10-2deci d a = 10-1Solutions A solution is a homogeneous mixture of two or more substances Major component: the solvent Minor components: the solutes

The concentration of the solute(s) is the amount of solute contained in a specified volume (mass) of solution (solvent) Molarity (M) = the number of moles of a solute per liter of solution. Concentrations are generally designated in terms of molarity [C]Chemical ConcentrationsThe atomic weight of an element is the weight in grams of 1 mole of atoms

Molecular Weight = (atomic weights of all atoms) MW is the weight in grams of 1 mol of moleculesMW of HCl = AW of H + AW of Cl = 1 + 35.5 = 36.5 g

1 mol of HCl weighs 36.5 g 1 mol solution of [HCl] contains 36.5 g HCl in 1 liter of solventIonic SolutionsAn electrolyte is a substance that dissociates into ions in solution. Strong electrolytes are mostly dissociated in solution NaCl Na+ + Cl- Weak electrolytes are mostly undissociated in solution

Ionic SolutionsThe molecular weight of a strong electrolyte is called the formula weight (FW) because it is the (AW of the atoms in the formula), even though there are very few molecules with that formula present in solutionFW (or F) of NaCl = 22.99 + 35.45 = 58.44[NaCl] = 58.44 g of NaCl in 1 L of solutionMolalityMolality (m) is the number of moles of a substance per kilogram of solvent (not total solution)Molality is independent of temperature

Molarity depends upon temperature because the solution volume depends on temperatureRelative Composition

For very small quantities parts per million (ppm) and parts per Billion (ppb) are used1 ppm = 1 g of substance per 106 g of total solution1 ppb = 1 g of substance per 109 g of total solutionFor gases. Volume is used instead of massTo prepare a solution with a desired molarityTo prepare solutions with a d Calculate the correct mass of solute needed (molecular weight x volume in L) Weigh out the correct mass of the solute. Dissolve solute in solvent so that the total volume after mixing is the desired volume.Dilute solutions can be prepared from concentrated solutions.

Example CalculationThe molarity of concentrated HCl is 12.1 M. How many mililiters of this reagent should be diluted to 1.000 liters to make 0.100M HClMconc = 12.1Vconc = xMdil = 0.100Vdil = 1000 x = (0.100 M) x (1000 ml) = 8.26 ml (12.1 M)

StoichiometryThe calculation of quantities of substances involved in a chemical reactionMater can neither be created nor destroyed(all reactant atoms) = (all product atoms)Electrical neutrality is conserved(all reactant charges) = (all product charges)

How many Tablets Should We Analyze?Each tablet contains 15 mg of ironHow many tablets should we analyze to provide 0.25 g of Fe2O3?

How many g of Fe are in 0.25 g of Fe2O3First calculate the moles of Fe2O3 (x) in 0.25 gx = 0.25/159.69 = 1.6 x 10-3 moles1 mol Fe2O3 = 159.69 g

Since 1 mol of Fe2O3 contains 2 moles of Fe2x = 2 x 1.5 x 10-3 = 3.2 x 10-3 moles

Convert to g of Fe= 3.2 x 10-3 x 58.845 = 0.18 g Fe1 mol Fe = 55.845 g

If each tablet contains 15 mg FeNumber of tablets required = 0.18 g/0.015 g = 12 tablets Significant FiguresThose digits in a number which are known with certainty plus the first uncertain digit

Significant FiguresOnly significant figures should be used in recording a resultBalance1.234 5 gBurette1.23 mlWhen not stated explicitly uncertainty is 1Otherwise always stated 5.34 0.04 (unit)Particular Problem with ZerosZeros which appear between other digits are always significantInitial zeros are never significant (only indicate the position of the decimal point)0.0724 g of 72.4 mg (3 significant figures)Exception: initial zeros to the right of the decimal point in logs are significant0.079 is the log 1.20 (3 significant figures)Terminal zeros are generally considered significant30,200 (5 significant figures)Particular Problem with ZerosTerminal zeros in a number without a decimal point may or may not be significant900 cm may have 1, 2 or 3 significant figures900. cm has three significant figuresUncertainty can be removed through the use of scientific notation9.0 x 102 has two significant figures9 x 102 has one significant figure9 x 106 has one significant figureSignificant FiguresAddition and Subtraction

1.362 x 10-45.345 7.26 x 1014+ 3.111 x 10-4 + 6.728 - 6.69 x 1014 4.473 x 10-4 12.073 0.57 x 1014Number of digits = Number of significant figuresThis number can be greater or less than the number of significant figures in the original dataSignificant FiguresAddition and SubtractionFor numbers with different numbers of digits the result is governed by the number with the fewest digitsMolecular weight of KF2 18.998 4032 (F) 18.998 4032 (F) 83.798 (Kr)121.794 8064 (not significant)Significant FiguresAddition and Subtraction scientific notation: express the numbers with the same exponent 1.632 x 105 + 4.107 x 103 + 0.984 x 106 1.632 x 105+ 0.04107 x 105+ 9.84 x 105 11.51x 1051.151 x 106Significant FiguresRounding numbers to obtain the correct number of digitsWhen the first insignificant digit is 5 round last significant digit up by +1When the first insignificant digit is < 5 leave the last significant digit unchanged (round number down)1.794 846 to four significant figures 1.7951.794846 to five significant figures 1.7948Significant FiguresMultiplication and DivisionLimited to the number of digits contained in the number with the fewest significant figuresThe number of digits retained is independent of the power for exponentials3.26 x 10-54.3179 x 1012 34.60 x 1.78 x 3.6 x 10-19 2.46287 5.80 x 10-51.6 x 10-7 14.05Significant FiguresLogarithms and Antilogarithms

n is the antilogarithm of aLogarithm has a characteristic and a mantissaLog 339 = 2.530Characteristic = 2 (integer part)Mantissa = 530 (decimal part)logarithm to numberNumber of digits in the mantissa = number of significant figures

logarithm to antilogarithmNumber of significant figures in the antilogarithm = number of digits in the mantissa

Significant FiguresLogarithms and Antilogarithms

log 0.001237 = -2.9076log 1237 = 3.0924log 3.2 = 0.51antilog 4.37 = 2.3 x 104104.37 = 2.3 x 104Sources of ErrorsGross errorsMistakes (transcription errors, missing reagent, etc)Recognized by outlier testsSystematic errorsCause all results to be in error in the same sense (same sign and magnitude)May go undetected unless a true value is knownAccuracy effected without loss of precisionRandom errorsIndividual results fall on both sides of the average valueVary in sign and magnitude and are unpredictableAverage out and approach zero with sufficient measurementsPrecision affected without loss of accuracyAccuracyAccuracy is an indication of the closeness of a measurement to the true value for the sampleDetermined by the absolute error or relative error the sum of the contribution of systematic and random errors to the measurementGross errors also affect accuracy but results known to contain gross errors are not used for analytical measurementsBias (Systematic Error)PrecisionThe closeness of a set of results to each otherWith sufficient replication of a measurement the contribution of random errors can be removedRandom errors have different signs and magnitudes but their sum tends to zero as the number of measurements increasesRandom errors in experimental measurements can often be described by a Gaussian modelNo number of replications can account for systematic errors

Gaussian Distribution

Gaussian Model

Measure of Central Tendency(Average of all values)An indication of the true valueMeasure of the spread of the results(Standard deviation of all values)An indication of the precision of the measurements Accuracy and Precision are Independent Quantities

Uncertainty is a property of all measurementsThe uncertainty of a result is a parameter that describes a range within which the values of the quantities being measured is expected to lie, taking into account all sources of errorUncertainty is associated with all individual steps of an analytical procedure and an accumulated uncertainty with a single measurementUncertainty is sum of method errorsGross errors (must be identified and rejected)Systematic errors (bias)Random errorsProblem HighlightMeasurement uncertainty must be expressed as a single numerical valueSources of errorserrors of methodinstrument errorspersonal errorsIt contains two types of contributionsBias errors = xi - Random errors = standard deviationNot a true value (estimate)Not independent of the measurements made

Absolute and Relative Uncertainty

Absolute uncertainty = uncertainty associated with a measurement ( error)For a single measurement it is the experimental uncertainty for that measurement0.02 ml in reading a burette 0.0001 g in weighing a sampleRelative uncertainty scales theabsolute uncertainty to thequantity measuredSometimes expressed as a percentage(percent relative uncertainty)(or 0.2 %)Combining Individual UncertaintiesAddition or subtraction of random errors( y = x1 + x2) or ( y = x1 - x2)v = (e12 + e22)Multiplication or division of random errors ( y = x1.x2) or ( y = x1/x2)%v = (%e12 + %e22)%e = percent relative error (100ei/xi)Absolute uncertainty in v = %e.x

Propagation of Uncertainty from Random Errors

e4 = [(0.03)2 + (0.02)2 + (0.02)2] e4 = 0.043.06 0.04 (absolute uncertainty)(0.04/3.06 x 100) = 1%3.06 1% (relative uncertainty)

Addition and SubtractionPropagation of Uncertainty from Random ErrorsMultiplication and DivisionFirst convert all uncertainties to percent relative uncertainty and proceed as for subtraction and addition

Combining Individual UncertaintiesAddition or subtraction of systematic errors( y = x1 + x2) or ( y = x1 - x2)y = (1 + 2) with retention of signMultiplication or division of systematic errors ( y = x1.x2) or ( y = x1/x2)y = (1/x1 + 2/x2) with retention of sign

Combining Uncertainties from Systematic and random ErrorsThe usual method of tackling systematic errors is to treat them as coming from a rectangular distributionContribution to standard uncertainty is obtained by dividing the error by 3Combine uncertainty from systematic errors (/3) as if it came from a source of random error