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Compulsory textbook

Fundamentals of Analytical Chemistry, D. A. Skoog, D. M. West, F. J. Holler and S. R. Crouch, Brooks/Cole 2004 8th EditionBrooks/Cole, 2004, 8th Edition

Recommended textbooks

Principles of Instrumental Analysis, D. A. Skoog, F. J. Holler and T. A. Nieman, Saunders College Publishing 1999Publishing, 1999.

Quantitative Analytical Chemsitry, J. S. Fritz and G. H. Schenk, Allin and Bacon, 1987.

Instrumental Methods of Analysis, H. H. Willard et al., Wadsworth Publ. Co., 1988.

Topics of the first semester

1. General introduction (1)2 Fundamental concepts in analytical chemsitry (1)2. Fundamental concepts in analytical chemsitry (1)3. Gravimetric methods in the analysis (1)4. Titrimetry – general principles and concepts (2)5. Precipitation titrations (argentometry) (1)6. Neutralization titrations (acidi-alkalimetry) (2)7 Complexometric titrations (chelatometry) (1)7. Complexometric titrations (chelatometry) (1)8. Redox titrations (oxidi-reductometry) (3)

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Analytical chemistryinvolves

separating,identifying andd t i i th l ti t f th determining the relative amounts of the

components (analytes) of the sample

Qualitative analysiswhat is present? – chemical identity of the species in the sample (preceeds quant. anal.)

Quantitative analysisQuantitative analysishow much is present? – percentage or mass of the analyte in the sample

Separation techniques (chromatographies)different components may interfere one with another

Analysis types

1. Complete analysis – each constituent is analysed

2. Ultimate (elemental) analysis – each element is ( ) yanalysed

3. Partial analysis – the amount of selected compounds/atoms/components

Exampleswater analysisblood sample analysisN,S,P,C-content in foodstuffsserial analysis of a pharmaceutical producthousehold gas analysisair analysisetc., etc., etc.

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Methods of analytical chemistry

Classical

i tgravimetryvolumetric methods or titrations

Instrumental

electroanalysisspectrometric analysismagnetic methodsmagnetic methodsthermal methodsmiscellaneous methods

To be considered1. accuracy & reliability required vs. economics2. no. of samples to be analysed3. complexity of the samples

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representative sampling –when the sample truly represents the object to be analysed

grinding (homogeneity)drying (deliquescence)

homogeneous sample: its constituents can be d h d ll distinguished visually or with the aid of a light microscope ( heterogeneous sample)

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replicate samples:portions of the material of (approximately) the same size that are same size that are carried through the analytical procedure

weighing (by an analytical balance –measurement of mass)f )

pipetting (by a pipette –measurement of volume)

preparing aqueous preparing aqueous solutions

solubilization (digestion)

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interference: species other than the analyte, which interferes with the results of the measurement, i.e.,measurement, i.e.,causes errors

The measured property, X has to vary in a known and reproducible way with the concenctration of the analyte, cAA

Ideally

cA = k×X

X – the signal k – characteristic to the method, s ll k ( x t usually unknown (except

gravimetry and coulometry)

calibration – the process of determining k

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For the calculations

1. experimental data2. stoichiometry3. instrumental data

are required

uncertaintiesassociated with the measurements must be known –errors in the chemical analysisanalysis

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Chapter 2.Chemicals, Apparatus and Unit Operations of Analytical Chemsitry

- dealt with in practical (compulsory)p ( mp y)

Chapter 3.Using Spreadsheets in Analytical Chemistry

- dealt with in practical (optional)

Calculations used in analytical chemistry

Atom –the smallest particle of an elementMolecule - the smallest particle of a compoundCompounds are combination of elements –

molecules are made up of atomsThe important thing for an (analytical) chemist is the number of atoms reacting (and not the mass)

Atomic mass (Ar): relative masses based on the 12C isotope

Molecular mass (Mr): the sum of the atomic masses of the atoms that make up the molecule

The chemical mass unit: the mole (1 mole = 6.022×1023 atoms of an element or molecules of a compound)

grams of material (m)Number of moles (n) = _____________________________

formula mass (Ar or Mr)

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Expressing concentration of solutions 1.

Molar concentration (molarity) the number of moles of solute present in 1 L of solution

number of moles of the solutec =

volume of solution

unit: mole/litre or mole/dm3 or Munit mole/litre or mole/dm or M

(equal to mmol/mL!!!)

Expressing concentration of solutions 2.

Molal concentration (molality or Raoult’s- concentration) –

number of moles of solutenumber of moles of solutem =

mass of solvent

unit: mole/kg

Advantage of m over c: m is independent of Advantage of m over c: m is independent of temperature

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Expressing concentration of solutions 3.

Mole fraction –

number of moles of soluteX = X =

the moles of solvent + the moles of solute

unit: -

Grams per volume – the mass of the solute divided by the volume of solution

mass of solute

volume of solutionunit: g/L

Expressing concentration of solutions 4.

ppm – the mass of the solute in mg divided by the volume of the solution in litre

mass of solute in mgmass of solute in mgconcentration in ppm =

volume of solution in litre

The mass of 1 litre of water equals to 1000g

Unit: ppm – part(s) per million,

ppb – the mass of the solute in µg divided by the volume of the solution in litre

mass of solute in µgconcentration in ppb =

volume of solution in litre

Unit: ppb, part(s) per billion

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Expressing concentration of solutions 5.

Mass percent – the mass of solute divided by the mass of solution

mass of solutemass percent = x100mass percent x100

mass of solution

Unit : g/100g or m/m%

Volume percent - the volume of solute divided by the volume of solvent

l f l tvolume of solutevol% = x100

volume of solution

Unit : mL/100mL or V/V%

Expressing concentration of solutions 6.

Analytical molarity – the total number of moles of solute present in a given volume of solution (it says nothing about the actual state of the solute, whether it ionizes or not, etc.)S b l Symbol: c or cT

Equilibrium molarity – the concentration of ions or molecules actually present in solution, taking into account the possible dissociation of the solute into ionsSymbol: […]The analytical concentration is equal to the sum of the equilibrium concentrations of the various forms of the soluteconcentrations of the various forms of the soluteExample:

HAc H+ + Ac-

cHAc = [Ac-] + [HAc] – this is a mass balance equation

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Errors in chemical analysis –how certain can we be about the results we obtain?

Obtained values (results) for a given quantity from N replicates:x x x xx1, x2, x3, …, xN

Mean (median, arithmetic mean, average), x

∑=

=N

iixN

x1

1

Precision – the reproducibility of the measurements, or the closeness of results that have been obtained exactly in the same way; can be b i d b i h obtained by repeating the measurements

(MEMO-technique: pre=rep)

Accuracy – the closeness of our measurements to the true or accepted values; cannot be obtained by repeating the measurements; expressed in terms of the absolute error: E = xtrue - xi

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Types of errors

Random (indeterminate) error – causes data to be scattered symmetrically around the mean value; associated with the y yprecision (or the reproducibility) of the measurement

Systematic (determinate) error – (for example instrumental, method or personal error); causes the mean of the data set to differ from the true value; associated with the accuracyof the measurement

Gross error – they occur occasionally and lead to outliers

Characterization of random errors, i.e., the precision of the measurement

Gaussian (normal error) curve shows the symmetrical distribution of data around the mean of an infinite set of data

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Sample standard deviation, s –the measure of precision of a measurement

( )

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2

−

−=∑=

N

xxs

N

ii

di = x – xi – the deviation of the i-th result, xi from the mean;N - the total number of the measurements;N-1 – number of degrees of freedomN 1 number of degrees of freedoms – standard deviations2 – sample variance

Significant figuresThe significant figures in a number are all the certain digits plus

the first uncertain digit

– most important example: reporting a burette readingl t th t th b tt i f 25 L itlet us say, that the burette is of 25 mL capacitysmallest division is 0.1 mL12.24 mLthe first three digits are certainthe last digit is estimated, i.e., uncertainif you report 12 mL – rounding off error (ca. 1.8 %)if you report 12.24478 mL – nobody believes you (rightly so)if you try to read < 0.1 mL on the same burette –

meaningless result

- another very important example: reading an analytical balance0,9668 gthe sample weighed must be at least 100 mg (to keep error at ≤1% level)

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Sampling

The analytical method of choice depends on the sample size and constituent type

sample size type of analysis> 0.1 g macro0.01-0.1 g semimicro0.0001 g – 0.01 g micro< 0.0001 g ultramicro

l l l f analyte level type of constituent1% - 100% major0.01%(100 ppm) -1% minor100 ppm – 1 ppb trace< 1 ppb ultratrace

Minimizing errors in analytical procedures

1. Choosing the correct blank solution2. Application of separation techniques – elimination of

i t f sinterferences3. Saturation – deliberate addition of large amount of

interfering components to all samples and standards (this may degrade sensitivity and detectability)

4. Matrix modification – a non-interfering component is added to modify the response, to make it independent of the presence of the interfering species

5. Adding of a masking agent – it selectively reacts with the g g g yinterfering component and makes it „invisible”

6. Dilution method7. Matrix matching method – for example, synthetic

seawater

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Classical methods of chemical analysis

includesincludesgravimetrytitrimetry

argentometryacidi-alkalimetrycomplexometrycomplexometryredox titrations

Gravimetric methods

are quantitative methods that are based on determining the mass of the pure compound to which the analyte is chemically related

The mass is always measured on an (accurate) analytical balanceT p f im t i m th dsTypes of gravimetric methods

precipitation gravimetryvolatilazation gravimetryelectrogravimetrythermogravimetrygravimetric titrimetry

Steps of precipitation gravimetry:1 an excess precipitating reagent added to the sample thus the 1. an excess precipitating reagent added to the sample, thus the

analyte converted into sparingly soluble product (precipitate)2. precipitate is filtered 3. precipitate is washed from impurities4. precipitate is dried or ignited (to convert it to a product with

known composition)5. precipitate is weighed

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Precipitation gravimetry

A successfull gravimetric determination meets the following criteria

1 h l b l l ( l ) d 1. The analyite must be completely (quantitatively) precipitated 2. The precipitating agent reacts selectively or, at least, specifically with

the analyte• Selective reagent reacts only with a single chemical species (rare)• Specific reagent reacts with several, but limited number of

chemical species (more common)3 The precipitate must easily filtered and washed free from 3. The precipitate must easily filtered and washed free from

contaminants4. Must be of sufficiently low solubility (to avoid loss of the analyte)5. Must be unreactive with constituents of the atmosphere6. Its weighed form must be of known composition (gravimetric factors)

Solubility of precipitates

Precipitate – it is formed from a solution which is supersaturated with respect to the solute; when no more precipitate is ible to form, the remaining solution is called saturated solution

Types of electrolyte solutions:

1. Non-saturated (or undersaturated)2. Saturated3. Supersaturated

1 2 31 2 3

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Solubility of precipitates

Solubility (or equilibrium solubility,S): the concentration of a saturated solution in molarity at a given temperature; characteristic to the given salt (depends on solvent and temperature)

MA M+ + A-

MxAy xMy+ + yAx-

S = [My+ ]/x = [Ax-]/y

Solubility product (L, Ksp) : the equilibrium constant for the y p sp qcomponents of the precipitate in a saturated solution (i.e., in a solution, which contains some precipitate)

Ksp = [M+ ][A-]

Ksp = [My+ ]x[yAx-]y

Solubility and solubility product

[ ] [ ] yxyxxy SySxAMK )()(== −+

E l l l t l bilit f

[ ] [ ]sp SySxAMK )()(

yxyx

sp

yxK

S +=

Examples: calculate solubility for

AgCl in water, at 25 oC Ksp = 1.0.10-10

Ag2CrO4 in water, at 25 oC Ksp = 1.1.10-12

Bi2S3 in water, at 25 oC Ksp = 1.0.10-72

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Factors influencing the solubility of a precipitate

1. Common ion effect – common ion will reduce the concentration of the other ion (and therefore the solubility) of ppt(unless the common ion forms complex compound with the ppt)the ppt)

2. Effect of pH –• if the anion gets protonated, decrease of pH

increases solubility• if the cation hydrolyses, increase of pH increases

solubility

3. Effect of complexation – complexation always increases solubility

4. Effect of foreign ions – foreign ions in small quantities increase, while in large quantities decrease solubility (latter is called salting-out)

…now back to gravimetry…Steps of precipitation gravimetry:1. Precipitation: an excess precipitating reagent

added to the sample thus the analyte converted added to the sample, thus the analyte converted into precipitate

2. Filtration: precipitate is separated from the solution via filtration

3. Washing: precipitate is washed from impurities4. Drying: precipitate is dried or ignited (to

convert it to a product with known composition)5. Weighing: precipitate is weighed

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1. Precipitation

• Particle size and filterability/washability – the larger the better

• The factor determining the particle size:The factor determining the particle size:relative supersaturation = (Q-S)/S (where Q is the

concentration of the supersaturated solution)• Nucleation -• Particle growth -• At large relative supersaturation the rate of nucleation is

large – large naumber of small particles are formed • At small relative supersaturation the particle growth At small relative supersaturation the particle growth

dominates, large particles are formed ☺• In practice: elevate temperature to increase solubility, use

dilute solution (to decrease Q) and add the precipitating agent slowly and under vigorous stirring

Filtration and washing

• Filtration may happen on paper filter or on glass filter• Mother liquor – is the liquid from which the precipitate is

formed• Washing liquids – distilled water or water saturated with the

precipitate• Peptization – is a process by which the precipitate returns to

it dispersed state (behaves as a solution again)• Coprecipitation – soluble components other than the analyte

are removed from the solution together with the precipitateg p p– surface adsorption– mixed crystal formation– occlusion and mechanical entrapment

• Precipitation from homogeneous solution

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Drying and weighing

• Drying/ignition is necessary to obtain constant mass for the precipitate

• Drying/ignition leads to the weighing form – the form of the analyte with accurately known composition (or stoichiometry)

• Drying: t < 200 oC• Ignition: t = 6-800 oC• If the filtration is done with filter paper, ignition can be done,

if glass filter is used, only drying is allowed• Weighing is always done by using an analytical balance Weighing is always done by using an analytical balance • The weighed mass must always be larger than 100 mg (to have

accuracy better than 1%)

• Examples: SO42- ions in the form of BaSO4

Ca2+ ions in the form of Ca(COO)2.H2O

Fundamentals of titrimetry

A chemical reaction between the titrant solution and the analyte is suitable for titrimetry if the analyte is suitable for titrimetry, if

1. it takes place according to one kind of known stoichiometry

2. it is quantitative (conversion is > 99.9%, no excess of reactant is needed)

3. it isreasonably fast4. completion of the reaction can be indicated

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Terms used in titrimetry

Standard solution – is a reagent of exactly known concentration that is used in the titrimetric analysis

Titration – is a process in which the standard solution is added to the analyte until the reaction between the analyte and the reagent is complete

Equivalence point – the point in the titration, when the amount of reagennt added to thge solution is exactly equivalent to the amount of the analyte (theoretical value)

End point – the point in the titration, when a physical change occurs that is associated with the chemical equivalenceq(practical value, this is what we obsrerve)

Titration error – Et = Vep – Veq, where Vep is the actual volume of reagent required to reach the end point and Veq is the theoretical volume to reach the equivalence point

Perfect titration - Vep = Veq,

Terms used in titrimetryTitration curves – plot the reagent volume on the horizontal axis

and some function of the analyte on the vertical axis; the equivalence point can be read off the titration curve; it can either be sigmoidal or linear segment curve.

Indicators they are added to the analyte solution to produce a Indicators – they are added to the analyte solution to produce a visually observable physical change (usually colour change) at or very near to the equivalence point

Primary standard – is an ultrapure compound that serves as a reference material for titrimetric method of analysis

high purityatmospheric stabilityabsence of hydrate waterf yreasonable costreasonable solubilitylarge molar mass

Secondary standard – a compound, whose purity has been established by chemical analysis and serves as a reference material for titrimetric method of analysis

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Terms used in titrimetryPreparation of standard solutions:

1 Direct method – includes (i) accurate weighing of a 1. Direct method includes (i) accurate weighing of a primary standard which is then (ii) dissolved in a suitable solvent and (iii) diluted to exactly known volume in a volumetric flask

2. Indirect method – includes preparation of the tatrant solution by approximate weighing and dilution to an approximately known volume, followed by standardization, which means (i) titrating a weighed quantity of a primary which means (i) titrating a weighed quantity of a primary or a secondary standard or (ii) titrating a known volume of a standard solution