prof. Viktor Kanický, Analytická chemie I
1
ANALYTICAL CHEMISTRY

prof. Viktor Kanický, Analytická chemie I
2
Analytical chemistry
nανάλυσις = analysis
nMaterial Þ decomposition Þ A, B, C Þ identification
nScience : Analytical Chemistry(ACH)
nMethodology: Chemical Analysis
nAnalytical chemistry is the science of creation and evaluation of analytical signals carrying
information about the chemical composition of the sample
nAnalytical Chemistry
qqualitativeÞ EVIDENCE (WHAT?)
qquantitativeÞ DETERMINATION? (HOW MUCH)

prof. Viktor Kanický, Analytická chemie I
3
History of Analytical Chemistry
nEgypt, China, Indie, Greece (Demokritos, Platon, Aristoteles, (5.-4. st. BC), Middle Ages–
alchemists
nanalysis
q„dry“ -  reaction in solid phase (heating of solids – metallurgy)
q„wet“ – in solution
nfundamentals
qR. Boyle 17. century
qJ. Dalton 18.-19. century
qA. L. Lavoisier 18. century
qFresenius (19. st.): separation and identification of cations using hydrogen sulphide
qInstrumental methods: spectral analysis, Bunsen a Kirchhoff (19.cent.)
qJ. Heyrovský: polarography, Nobel Prize1959

prof. Viktor Kanický, Analytická chemie I
4
Methodology of analytical chemistry
nAnalytical approach in Science and Humanities
qPartition of problem into particular simpler parts, solution of these partial tasks and combining
of individual information for understanding of the whole
nDecomposition of material  into chemical species Þ molecules, atoms, ions
n X
nAnalysis by physical methods– study of matter in solid state, without decomposition, dissolution
nComputer Based Analytical Chemistry (COBAC)
nACH is a scientific discipline that develops and applies methods, instruments and strategies to
gather information on the composition and nature of matter in space and time
n

prof. Viktor Kanický, Analytická chemie I
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Chemistry
Theory
Synthesis
Explanation
Characterisation
Analyses
Analytical chemist
Instrument

prof. Viktor Kanický, Analytická chemie I
6
Classification of analytical methods according to principle
nChemical methods (chemical reactions)
qGravimetry
qVolumetry (titrimetry)
q
nPhysico-chemical methods
qSpectroscopic (radiations, particles - electrons, ions)
qSeparation (separation of comonents in time and space between two phases)
qElectrochemical (electrode processes)
q
nBiochemical methods (enzymes, microorganisms)

prof. Viktor Kanický, Analytická chemie I
7
Classification of analytical methods according to object of analysis
nMaterial (examples)
qwater, geological, metallurgical, ceramics, building, environmental, pharmaceutical, foodstuff,
clinical
nDetermined component type - analyte (examples):
qElemental analysis of samples with inorganic and organic matrix
qAnalysis of organic compounds
qDetermination of radioactive isotopes
nAnalyte content
qTotal analysis (main constituents, S=100%)
qtrace(mg/g) and ultratrace(ng/g, pg/g) analysis
nSample size (g, mg, mg, ng, ml, nl)
n

prof. Viktor Kanický, Analytická chemie I
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Elemental analysis
nElemental analysis enables:
qverification of the presence of the element (qualitative analysis)
qdetermination of elemental concentration/content (quantitative  analysis)
qidentification of structure, in which the element is present (structural analysis)
qidentification of compound, in which the element is bound (speciation)
nWHOWHO analysis
qwhat (qualitative)
qhow much (quantitative)
qwhere (structure)
qhow bound (speciation)
nThe aim is to find structure vs properties relation
n
n

prof. Viktor Kanický, Analytická chemie I
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General procedure for analysis
nSampling
qRepresentative sample
qHomogeneous sample
nSample transfer to a form suitable for analysis
qDecomposition, dissolution, pressing of powdered samples
qSeparation of components (from matrix, separation of individual analytes), concentration of
constituents
nAnalytical signal measurement
qmass, volume, flow of electromagnetic radiation or ions, electrochemical potential, current,
charge, conductivity
nData evaluation
qMean value, standard deviation, error, uncertainties, validation
nConclusions, analytical report
n

prof. Viktor Kanický, Analytická chemie I
10
Analytical system
nAnalytical system is a subsystem of higher information system
nSampling system and analytical system
n
Sampling
 system
Laboratory
sample
Analytical
 statement
Analytical system

prof. Viktor Kanický, Analytická chemie I
11
Analytical system
nScheme of analytical process
Laboratory
 sample
Preparation
of sample
 for
measurement
measuring
Analytical
 signal
Signal
 evaluation
Analytical
 results

prof. Viktor Kanický, Analytická chemie I
12
Analytical signal
nAnalytical chemistry is the science of creation and evaluation of the analytical signal (AS),
carrying information about the chemical composition of the sample
nAS has two aspects - dimensions:
qPosition (wavelength of radiation, half-wave potential), corresponding to quality (WHAT?)
qMagnitude, intensity (radiant flux, limiting diffusion current, corresponding to quantity (HOW
MUCH?)
nAnalytical signal intensity is generally a function of concentration of determined analyte cA,
concentration of other components czi, and a number of variables pj (insrumental parameters,
reagents)
n S = S(cA, czi, pj)
n

prof. Viktor Kanický, Analytická chemie I
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Generating of analytical signal in optical atomic emission spectrometry (OES) and mass spectrometry
(MS)
Solid sample
Solid
particles
molecules
solution
nebulizations
atoms
ions
+
photons
vaporization
dissociation
desolvation
Gaseous sample
ionization
excitation
OES
MS

prof. Viktor Kanický, Analytická chemie I
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Atomic (optical) emission spectromety in inductively coupled plasma ICP-AES, ICP-OES
nAtomic (line) emission spectrum  of chlorine and  oxygen in UV region

prof. Viktor Kanický, Analytická chemie I
15
Mass spectrometry ICP-TOF-MS
nResolution m/z: 137Ba+ a 138Ba+
nMass spectrum
137Ba+
∆m = 0.312 amu
138Ba+
Signal position

prof. Viktor Kanický, Analytická chemie I
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Analytical process scheme
ANALYZER
Signal
 generating
Signal
isolation
Signal
 detection
Sample
 introduction
into
analyzer
Sample pretreatment
Sample preparation
Sample storage
Sampling
chemik
Signal
treatment
Analytical
result
Statistics
Algorithms
Software

prof. Viktor Kanický, Analytická chemie I
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Inductively coupled plasma
Sample solution
Carrier gas
       Ar
Nebuliser
Sample introduction
Aerosol
hν
Signal
isolation
Spectrometer
polychromator
SiO2
hn
Doped  Si
electrodes
electrode
hole-electron
storage
Inversion  zone
integration)
substrate
gate
0 V
Signal detection
Atomic line spectrum

prof. Viktor Kanický, Analytická chemie I
18
Mass (inorganic) spectrometry in inductively coupled plasma source ICP-MS
ICP-MS

prof. Viktor Kanický, Analytická chemie I
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Analytical method
nSampling and sample storage, preservation of representative material
nProcessing of the part of the sample for quantitative analysis
nDetermination
nCalculation of results
n
nDEFINITION (ISO 3534)
n
qrandom error = component of measurement error, which changes in the course of repeated
measurements in an unpredictable way
qsystematic error, bias = component of measurement error, which does not change in the course of
repeated measurements or changes in a predictable way
n

prof. Viktor Kanický, Analytická chemie I
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Analytická metoda
nDEFINICE (ISO 3534)
n
nprecision = tightness of agreement between the results obtained with the repeated use of the same
experimental procedure under defined conditions (random error)
qRepeatability
qReproducibility
q
ntrueness = tightness of agreement between the „true (actual) value“ and the mean value of measured
results (systematic error, bias)
naccuracy = method is accurate if it is satisfied at the same time precision and trueness of the
results

prof. Viktor Kanický, Analytická chemie I
21
Repeatability
nRepeatability represents random fluctuations of the measured values of the analytical signal (or
results) around the mean value within one experiment (a series of replicates)
n
nCause of fluctuations is noise: in case of emission spectrometry – example:
qshot noise (photons)
qflicker noise (sample introduction noise)
qdetector noise
q
nRepeatability is usually expressed as standard deviation (SD) or relative standard deviation (RSD)

prof. Viktor Kanický, Analytická chemie I
22
bias
accepted
value
Recommended,
Certified value
experimental
value
repeatability
precision
concentration

prof. Viktor Kanický, Analytická chemie I
23
Standard deviation and fluctuation peak - peak
n5 s includes 99% of the population
nFor mean value 100 and standard deviation 1 are fluctuations between 97.5 and 102.5
n
5s
s

prof. Viktor Kanický, Analytická chemie I
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Reproducibility
nPrinciple as in the case of repeatability, in addition, one other parameter changes
n
nReproducibility may be:
qBetween laboratories
qBetween operators in one laboratory
qBetween analyzers
qIn different days
qetc…
n

prof. Viktor Kanický, Analytická chemie I
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Repeatability x Trueness
repeatability
good
poor
good
trueness
good
good
poor

prof. Viktor Kanický, Analytická chemie I
26
Parameters of data sets
nArithmetic mean = mean value of Gaussian = normal distribution, n values
n
nSample standard deviation = dispersion parameter of the sample set, for n > 7
n
nmedian = mean value insensitive to outliers
qFor odd n the median of a set of values arranged by size X1, … X(n+1)/2, … Xn is equal to the
middle value of the series:
q
qFor even n the median is equal to arithmetic mean of the central pair
n
n
n
n

prof. Viktor Kanický, Analytická chemie I
27
Parameters of data sets - Span
nStandard deviation sR of data set for
n is calculated from the span of values:
n
n

prof. Viktor Kanický, Analytická chemie I
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Level of significance and confidence interval of mean
nA level of significance indicates the probability that the true parameter value does not lie
within the 100(1- α)% interval
nConfidence interval L1,2 of the mean X on the level of significance α is an interval, in which the
true value μ lies with probability (1- α)
npro α = 0,05 je ± 2σ
n    P (X)
n

prof. Viktor Kanický, Analytická chemie I
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Trueness
nStandard deviation s is estimate of σ
n

prof. Viktor Kanický, Analytická chemie I
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Statistical testing
nComparison of results of analyses
nnull hypothesis: the assumption that between the compared values ​​is no other difference than
that which can be explained by the presence of random errors
nnull hypothesis H0 is rejected if the actual difference exceeds a critical value that corresponds
to the pre-selected significance level α
nrisk that we reject the correct null hypothesis is called the error of the 1st kind and is given
by the significance level α
qPI = 1 – α is the probability that we accept the correct null hypothesis

prof. Viktor Kanický, Analytická chemie I
31
Test of Trueness
nStudent test (Gosset), trueness:
n
n
n    if                                 n > 7
n
n
nfor the number of degrees of freedom ν = n-1 and the chosen significance level α, e.g. α = 0.05
for P = 95%, then the difference is statistically significant
n

prof. Viktor Kanický, Analytická chemie I
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Test of Trueness using span
nLord test
n
n
n
n
n →   statistically significant difference

prof. Viktor Kanický, Analytická chemie I
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Correspondence of results
nMoore test of outliers
nLord test of outliers
rozdíl statisticky významný

prof. Viktor Kanický, Analytická chemie I
34
Correspondence of results
ntest of averages (Student test)
qIf the value t is greater than the critical value tkrit, the difference in averages is
statistically significant:

prof. Viktor Kanický, Analytická chemie I
35
Correspondence of results
ntest of averages (Studentův test)
qIf t is greater than the critical value, then the difference is statistically significant

prof. Viktor Kanický, Analytická chemie I
36
Exclusion of outliers
nT-test; Grubbs test for n > 7
Þ extreme values are outliers

prof. Viktor Kanický, Analytická chemie I
37
Exclusion of outliers
nQ-test; Dean-Dixon test for
if
Then are Q1 a Qn outliers

prof. Viktor Kanický, Analytická chemie I
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Types of analytical methods
nISO Guide 32 proposal classifies methods of chemical analysis according to  calibration procedure:
qAbsolute methods (calculable methods) – result can be calculated on the basis of relations
resulting from chemical and physical laws, using measured values (titrimetry, gravimetry,
coulometry)
qRelative methods – analyzed sample is compared with a set of calibration samples with known
contents using the detection system, which has a linear response to the concentration of fixed
components
ndifferences between calibration and analyzed samples do not affect the signal in comparison with
the magnitude of uncertainty
nsamples before measurement can be adjusted (adjustment of the matrix of calibration samples to the
matrix of analyzed samples, elimination of interferences)
n
n

prof. Viktor Kanický, Analytická chemie I
39
Types of analytical methods
qComparative methods - analyzed sample is compared with a set of calibration samples with known
contents using the detection system, which responds not only to the fixed component, but also to
change the composition of the matrix
ncalibration of such a method requires use of certified reference materials (CRM)
nit is a quick method to control technological processes (wave-dispersive X-ray fluorescence
spectrometry in the production of steel, alloys, oxide powder, ceramic materials, etc.)
n

prof. Viktor Kanický, Analytická chemie I
40
Analytical chemist
n80% in industrial laboratories, the analytical chemist is a solver of problems and issues
ngood theoretical knowledge of the methods used and the ability to develop experimental techniques
and to select relevant, the optimal method
ndevelopment of specialized analytical procedures for analysis of routine and unique, unusual
samples, communication with experts from other disciplines to obtain information about analyzed
materials, the ability to choose a compromise between the cost analysis and its accuracy
n
n

prof. Viktor Kanický, Analytická chemie I
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Industrial analytical laboratory environment
Communication
Statistical uncertainty
Accuracy of analysis
Duration of analysis
Price of analysis

prof. Viktor Kanický, Analytická chemie I
42
Method of analytical problem solving
nknowledge of chemistry of the problem
nknowledge of sampling and sample processing
nuse of suitable separation methods
nuse of proper calibration and standards
nselection of the best methods for measuring the analytical signal
n

prof. Viktor Kanický, Analytická chemie I
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Theoretical Foundations of Analytical Chemistry
nDissolving of substances and solutions
qsolution: solid, liquid, gaseous
qAnalytical chemistry– liquid solvents
qdissolution = overcoming of intermolecular forces between particles
qDissolution of A = dispersion of A in a solvent B
n
B
B
DEB> 0
DEA> 0
A
A
DEAB< 0
B
A
DEA+ DEB+ DEAB < 0 Þ DEAB > DEA+ DEB

prof. Viktor Kanický, Analytická chemie I
44
Nature of intermolecular forces and dissolution
Substance to be dissoleved
solvent
Nature of intermolecular forces
solubility
electrolyte
polar
similar
electrolyte
nonpolar
diffrenet
nonelectrolyte
polar
diferent
nonelectrolyte
nonpolar
similar
+
-
+
-

prof. Viktor Kanický, Analytická chemie I
45
Dissolution
nRelative permitivity » eR dielectric constant
dipole momentD
n
nNonpolar solvents
qvan der Waals forces
qSolid nonelectrolytes:
nSolubility is given (to10-3 mol/l) DHt= latent heat of melting » increasing of distances between
particles, dispersion
qLiquids: miscibility according to eR
qGases- nonpolar molecules: O2, N2, H2, CH4 better soluble in n-pentane and n-hexane than in water

prof. Viktor Kanický, Analytická chemie I
46
Dissolution
nPolar solvents
qElectrostatic forces
qH2O: D = 1,84; eR= 80
nshielding of attractive forces between ions in solution
qIonic compounds : dissociation
q M+A-® M(H2O)+x + A(H2O)-y
nDegree of dissociation a, conductivity, strong electrolytes, conc. ´ activity
qPolar compounds: ionization+ dissociation:
q H(+)-Cl(-) + H(+)-O(-)-H(+)  ® H3O+Cl- ®H3O++ Cl-
n

prof. Viktor Kanický, Analytická chemie I
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Solubility of electrolytes in water
nSolid electrolyte
qIons in crystal lattice
qPolar molecules
nEnergy necessary for disruption of chemical bond
qGain by hydration of ions Þ solubility » DE (bond strength, hydration)
nBond strength in ionic compounds
qLattice energy U = f(z, r, k),    z = charge, r = ion radius, k = coordination number
nU = const´z2/r0 for similar ions, r0 = rK + rA
n     rK, rA- crystallographic values Þ influence of particular ions
n     (dU/dr) = const ´(z2/r02) = const ´(z/r0)2 square of ionic potential, changes in series of
similar compounds
nHydration energy of ions EH – is proportional to:
qbond strength between ion and water molecule (dipole) » z2/r
qnumber of coordinated water molecules
nIons bound molecules of H2O the stronger, the greater is z and  smaller r
nChange of  EH » const ´(z2/r2) » z/r

prof. Viktor Kanický, Analytická chemie I
48
Solubility of electrolytes in water
nIonic potential z/r decreases (z decreases, r increases) Þ U, EH decrease, hydration energy
decreases slower, because at higher r number of coordinated water molecules increases (compensation
of the decrease)
nSolubility of ionic compounds depends on balance EH + U
qionization (dissociation) = endothermal process, U > 0
qhydration = exothermal process, EH < 0
nCompound dissolve:
qwell, if EH + U < 0,  (U < | EH| )
qwith difficulty, if EH + U > 0, (U > | EH| )
nSolubility of fluorides of alkali metals increases LiF Þ CsF, because U decreases from Li ® Cs
steeper than EH (decrese of EH is hindered by  growth of coordinated molecules H2O (Li+ 4 H2O,
Cs+ 8 H2O)

prof. Viktor Kanický, Analytická chemie I
49
Solubility of electrolytes in water
nSolubility of salts of  small ion (Li+, Na+, F-) increases with decrease of z/r of counterion:
qLiF < LiCl = LiBr < LiI
qNaF < NaCl < NaBr < NaI
qLiF < NaF < KF < CsF
nSolubility of salts of big ion (Cs+, I-) diminishes with decrease of z/r of counterion
qCsF > CsCl > CsBr > CsI
qLiI > NaI > KI > RbI > CsI
nSolubility of salts of medium-size ion (K+, Rb+, Cl-, Br-) at first                        with
decrease of z/r diminishes and then slightly increases or remains constant:
qKF > KCl > KBr > KI
qRbF > RbCl > RbBr < RbI
qLiCl > NaCl > KCl < RbCl < CsCl
nOH- = small ion Þ Mg(OH)2 < Ca(OH)2 < Sr(OH)2 < Ba(OH)2
nIonic potential:         3,08           2,02           1,77            1,48
nBig ions: PO43-, SO42-, S2O32-, SiF62-, CrO42-, IO3-, NO3- : Þ
qMg2+ > Ca2+ > Sr2+ > Ba2+ (in this sense decreases z/r of cations)

prof. Viktor Kanický, Analytická chemie I
50
Solubility of electrolytes in water
nEffect of electron shell – example Pb2+ a Tl+:
n
n
n
nSimilarity of Rb+ s Tl+
qSoluble hydroxides RbOH, TlOH and  carbonates Rb2CO3, Tl2CO3
qLittle soluble Rb2[ PtCl6], Tl2[ PtCl6]
nexception: F-: CaF2 < SrF2 < MgF2 < BaF2 (small ion)
nexception: CO32-: Mg2+ >Ca2+ > Ba2+ > Sr2+ (big ion)
nexception: C2O42-: Ca2+ > Sr2+ > Ba2+ > Mg2+ (big ion)
nEffect of z/r on solubility of salts of cations of transition elements is limited
qPrevails influence of unoccupied d-orbitals (ligand field, stabilization energy)
n
Pb2+
2
8
18
32
2
PbS
PbCrO4
PbI2
PbCl2
Tl+
2
8
18
32
2
Tl2S
Tl2CrO4
TlI2
TlCl
Little soluble salts

prof. Viktor Kanický, Analytická chemie I
51
Solubility of electrolytes in water
nElectrolytes with polar covalent bound
nStrength is higher then corresponds to ionic attraction
nThe smaller the difference of electronegativities the stronger the bond and lower solubility
n
nexample: according to z/r the AgCl solubility should be comparable with that of KCl, generally of
halogenides, but AgF only is well soluble
n

prof. Viktor Kanický, Analytická chemie I
52
Theoretical fundamentals of analytical chemistry
nAnalytical reactions:
qSample treatment (decomposition)
qSeparation and preconcentration of analytes in solution
qdetermination
nEvaluation of chemical reation:
qThermodynamic criterion
qKinetic criterion
qChemical  thermodynamics – change of energy
qChemical kinetics – reaction path, mechanism, reaction rate
nAnalytical reaction occurs (in solutions)
qAt constant pressure
qAt constant temperature
nChange of energy content = change of Gibbs energy
nkinetics:
qIon reactions
qRadical reactions

prof. Viktor Kanický, Analytická chemie I
53
Requirements for analytical reactions
1.Fast reactions - během promíchání (titrace)
2.Unambiguous reactions  - without byproducts
3.Completness of conversion – equilibrium ® products
n
nChemical equilibrium
nCollision theory of chemical reactions
nA + B Þ AB (activated complex) Þ products
nNA NB – number of particles in a given volume
nNumber of collisions AB is given by combinatorial number:
n(NA + NB)!/[2!(NA + NB – 2)!] – NA!/[2!(NA – 2)!] – NB!/[2!(NB – 2)!]= NA·NB
nSimilarly for aA + bB Û AaBb the number of possible groupings reads =
n= (NA)a·(NB)b/a! ·b!
nInstant reaction rate
n v=k[A]a · [B]b
n

prof. Viktor Kanický, Analytická chemie I
54
Requirements for analytical reactions
qStandard thermodynamic  quantities DG°, DH°, DS°
qDG°= DH°-T DS° = -RT ln Ka      T, p = const.
qD = final – initial state, R = 8,314 J K-1mol-1
qDG°= 5,708·103 log Ka, DG°» J mol-1
qMolar concentration of substance cA= nA/V
q nA – number of moles, V – volume
n
aA + bB Û cC + dD
v=k[A]a · [B]b   v´=k´[C]c · [D]d    K = k/k´
nTheromodynamic equilibrium constant
n

prof. Viktor Kanický, Analytická chemie I
55
Requirements for analytical reactions
nActivity aA = [A] yA    [A] – equilibrium concentration
nyA – activity coefficient, expresses diffrences in behaviour:
qsolvation, electrostatic effects between ions
nConcentration ´ thermodynamic constant
n
nActivity coefficients, theory Debye-Hückel:
qMolal  activity coefficients g
qMolar activity coefficients y
qMolar fraction, activity coefficients f

prof. Viktor Kanický, Analytická chemie I
56
Requirements for analytical reactions
nStrong electrolytes
qDebye-Hückel:
q    - log g = 0.5115 · zi2Ö(I)/[1+Ö(I)]   25°C, zi – ion charge,
q    I = ½Σcizi2 ionic strength
q    valid for c< 10-3 mol/l
q    limit D-H relation:   - log yi = 0.5115 zi2Ö(I)
nWeak electrolytes (in the absence of strong electrolytes)
qActivity = molar concentration, valid for molecules without charge up to  c < 0,1 mol/l
(non-dissociated weak electrolytes)
nNonelectrolytes (in presence of strong electrolytes)
qFor concentrations c0< 0,5 mol/l and I < 5 je
q log y0 = k·I
qActivity of nonelectrolytes increases in presence of ions Þ their solubility decreases (salting
out of solutions)
n

prof. Viktor Kanický, Analytická chemie I
57
Thermodynamic and concentration equilibrium constants
nKa = lim (log K) for I ® 0
nlog K = log (Ka) + Dlog K
nDlog K = log K - log (Ka) = Dzi2(Ö(I)/[1+Ö(I)] – 0,3I)
nDzi2 =  algebraic sum of charges, Dzi2 of products >0, Dzi2 of reactants < 0
n
2
0,1         I
1
-Dlog K
K depends most steeply
at ionic strength I <0,1

prof. Viktor Kanický, Analytická chemie I
58
Completness of reaction from equilibrium constant
nposun rovnováhy nadbytkem činidla
n (fotometrie, gravimetrie, extrakce) ´ rušení, vedlejší reakce
aA + bB Û cC + dD
cA, cB initial concentrations of reactants, conversion to 99,90 %
at equilibrium [A] = [B] = 0,001cA , [C] = [D] = 0,999cA
je-li K = 106 Þ 99,9%
conversion to products
K= x2/(1-x)2

prof. Viktor Kanický, Analytická chemie I
59
Effect of reaction kinetics
nHalftime of reaction < 10 s, titration, redox processes at n1 ¹ n2 are slow
n
nExploitation in kinetic methods – determination of concentrations from time dependences
n
nIncrease in the reaction rate: heating, transfer to reaction complex using catalyst
n

prof. Viktor Kanický, Analytická chemie I
60
Types of chemical equilibria
Protolytic
reactions
Complex
forming
reactions
Redox
reactions
Homogeneous
Precipitation
reactions
Distribution
equilibria
Liquid-
liquid
Ion-exchanger
equilibria
Heterogeneous
System

prof. Viktor Kanický, Analytická chemie I
61
Protolytic equilibria
npolyprotic acid HnB
nHnB Û Hn-1B- + H+
nconsecutive eqilibria
nStepwise = consecutive
n
nHn-1B- Û Hn-2B2- + H+
nHB1-n Û Bn- + H+
n
noverall equilibrium
nHnB Û nH+ + Bn-
n
n
stepwise dissociation constant
stepwise protonization
constant
overall constant

prof. Viktor Kanický, Analytická chemie I
62
Protolytic equilibria
nDistribution diagram of H4B acid
d(H4B)
d(H3B-)
d(H2B2-)
d(HB3-)
d(B4-)

prof. Viktor Kanický, Analytická chemie I
63
Protolytic equilibria
n2 conjugated acid-base pairs
nAcid-base equilibrium of amphiprotic solvent= autoprotolysis
q2 SH Û SH2++ S-   KSH= [SH2+][S-]
nProtolytic equilibrium of acid
qHB + SH Û SH2+ + B-
q[SH] >> [HB], [B-], [SH2+]
q
nDissociation constant of base
qNH4OH Û NH4+ + OH-
q
nAcidic dissociation constant of base
qNH4+ Û NH3 + H+
q
n KaKb=Kw= [H+][OH-]  - ion product of water (self-ionization)
n

prof. Viktor Kanický, Analytická chemie I
64
Complex (forming) equilibria
nComplex:
qCoordination compound– association equilibrium:
q m M + n L Û MmLn , M - centr. ion, L - ligand
nCumulative (overall) stability (formation)
nConstant bnm
nConsecutive stability constants K:
qM + L Û ML
qML + L Û ML2
qbnm = K1 K2…Kn
nBjerrum formation function    :
qAverage number of particles of ligand L bound to the central ion M at the overall composition of
the complex forming system
n

prof. Viktor Kanický, Analytická chemie I
65
Complex (forming) equilibria
nBjerrum formation function
n
n
n
n
n
ncM and cL – total (analytical) concentrations of metal (ion) and ligand [L]
n
n cL - [L] = [ML] + 2 [ML2] + ….+ n [MLn] =
n b1[M][L] + 2 b2[M][L]2 + …+ n bn [M][L]n =
n
n

prof. Viktor Kanický, Analytická chemie I
66
Complex (forming) equilibria
ncM = [M] + [ML] +…+ [MLn] = [M] + [M] b1 [L] + …+ [M] bn [L]n =               = [M] {1 + b1 [L]
+…+ bn [L]n } =
n= [M] {1 +                     }, [M] in the nominator and denominator reduces Þ relation for
nFormation f.           = f { log [L] }
n
1,0
1
2
3
1) K1= K2=104
2) K1= 105
K2 = 103
    -6       -4      -2
log [L]
3) K1= 106
K2 = 102
2,0

prof. Viktor Kanický, Analytická chemie I
67
Complex (forming) equilibria
nDistribution coefficient indicates the relative share of individual complexes
n dk = [MLk]/cM
n
n aM(L) = side reaction coefficient
n
nConditional stability constant
n conditioned concentration (asterisk)
q
n
n
[ML*] = [ML] + [MHL] + … = aML [ML]
[M*] = cM - [ML*] = [M] + [MOH] + … = aM[M]
[L*] = cL- [ML*] = [L]  + [HL] + … = aL[L]
aML= side reaction coefficient

prof. Viktor Kanický, Analytická chemie I
68
Complex (forming) equilibria
ndistribution diagram of complex ML (1:1),  log K = 3,0
dM
dML
50% ML
50% M
K=103 = [ML]/([M][L])
[ML]=[M]Þ[L]=10-3

prof. Viktor Kanický, Analytická chemie I
69
Complex (forming) equilibria
ndistribution diagram of complexes  ML a ML2,  log K1= log K2= 3,0
dM
dML2
dML
33,3% M
33,3% ML
33,3% ML2
K1=103 = [ML]/([M][L])
[ML]=[M]Þ[L]=10-3
K2=103 = [ML2]/([ML][L])
[ML2]=[ML]Þ[L]=10-3

prof. Viktor Kanický, Analytická chemie I
70
Complex (forming) equilibria
ndistribution diagram of complexes ML and ML2,  log K1= 3 log K2= 6,0
dM
dML2
dML
K1=103 = [ML]/([M][L])
K2=106 = [ML2]/([ML][L])
[ML2] = [M] Þ [L] = 10-4,5
[ML2] + [ML] + [M] = 1 Þ
[ML2] = [M] = 0,484 [ML] = 0,016

prof. Viktor Kanický, Analytická chemie I
71
Solubility equilibria
nMmNn (s) Û MmNn Û mMn+ + nNm-
n         I                  II                  III
nStrong electrolytes:
qIn polar solvent I + III
qIn non-polar solvent I + II
nWeak electrolytes: in polar solvent I + II + III
nChemical potential
n
n
n
nIsothermal-isobaric process
qG = U + pV - TS = H – TS
qmi= mi0 + RT ln ai     mi- mi0 = RT ln ai
q is work associated with the transfer of 1 mole of solute from the state of unit activity to
activity ai
n
n
Gibbs energy
Partial molar free enthalpy

prof. Viktor Kanický, Analytická chemie I
72
Solubility equilibria
nEquilibrium between solid phase and saturated solution DG = 0
qmI = mIII = mmM0 + mRT · ln aM + nmN0 + nRT · ln aN
nActivities are constant and unit in solid phase
qmI0 = mIII0 + RT·ln aMm · aNn
nSolubility product constant (Ks)a= aMm · aNn , const. at const. T
naM = [Mn+] · yM     aN = [Nm-] · yN
n Ks= [Mn+]m [Nm-]n  = (Ks)a/(yM · yN)
n Þ for a certain value of ionic strenght
nConditional solubility product KS* = KS · (aM(L))m (aN(H) )n
nElectrolyte solubility: c [mol/l]
qStoichiometry of precipitate:
q n(MmNn) : nM : nN = 1 : m : n Þ [Mn+] = m·c , [Nm-] = n·c
n
n      Þ
n

prof. Viktor Kanický, Analytická chemie I
73
Redox equilibria
nRedox processes– electric work is exerted ´ protolytic and complex forming equilibria
n
nElectric work is associated with transfer of n = nAnB electrons from reduced form of substance B
onto oxidized form of substance A:
n-DG = nA nB F E°
n where nA, nB are amounts of substances, F is Faraday constant    (96 484 C mol-1) and E° is
standard cell voltage
n
nRedox pairs = partial reactions:
nAox + nAe- Û Ared                  EA°
nBox + nBe- Û Bred                  EB°
n
nNernst-Peters equation:
n EA = EA° + [RT/(nAF)]ln(aAox/aAred)
n standard H-electrode, p = 101,32 kPa, aH+ = 1, c = 1,18 mol/l HCl, Pt black, H2 gaseous
n          2H+ + 2e- Û H2 (g)
n

prof. Viktor Kanický, Analytická chemie I
74
Redox equilibria
nE0H+/H2 = 0; EAº > 0; Aox is stronger oxidant than H+
n            EAº < 0; Ared is stroger reductant than H2
n
n- DG0 = RT ln (Ka) Þ log (Ka) = -DG0/(2,303RT) =
n = nA· nB · F·Eº/(2,303 RT); Eº = EAº-EBº:
n „total conversion“ (99,9 %) at nA= nB is at Ka=106
n
nT = 25 °C

prof. Viktor Kanický, Analytická chemie I
75
Sampling and sample preparation for analysis
ncomposition of the analyzed sample must correspond to the composition of the examined substances
qSampling of solids ČSN 650611, liquids  ČSN 650512
q
nSampling involves two operations
qgross sample collection from analyzed substance
ngross sample – sample portion taken from analyzed substance; from solid material – it is processed
by mechanical mixing, quartering, splitting, grinding, sieving and gradual  sample reduction
qanalytical sample collection from gross sample
nanalytický vzorek – must have identical composition with analyzed material

prof. Viktor Kanický, Analytická chemie I
76
Transferring the sample into a solution
nA) Dissolution in
1) water
2)acids
3)hydroxides
n„Wet“ decomposition:
qHCl, HNO3, H2SO4, HClO4, HF
qBeakers, dishes, pressurized autoclaves: glass, quartz, porcelain, PTFE
qheating: gas burner, hotplate, microwave oven
nB) Fusion
1)acid
2)alkaline
n „Dry“ decomposition:
qSodium carbonate, potassium carbonate, borax, disulphate, hydroxides– conversion  to salts
dissoluble in acids and in H2O
qCrucibles Pt, Ni, Fe, glassy graphite
qBurner, muffle furnace
q
q
n

prof. Viktor Kanický, Analytická chemie I
77
Transferring the sample into a solution
nDissolution
nspontaneous process in which particles are released from the range of forces, which bind them in
solid phase by the effect of solvation forces that stabilize the particles in solution
q
nSolvent
qLiquid capable of dissolving gases, liquids or solids, without chemically reacting with them
qMost important - water

prof. Viktor Kanický, Analytická chemie I
78
Transferring the sample into a solution
nDecomposition in acids
qHCl, diluted 1+1 (6 mol/l), without the effect of oxidation
ndissolves:
1)Metal with negative reduction potential
2)Alloys Fe s Cr, Co, Ni, Ti
3)Salts of weak acids
4)Carbonate ores
5)Oxidic ores (Zn, Mn, Fe)
6)Hydrolytic products (BiOCl)
ndoes not dissolve:
1)Bauxite, corindum
2)spinels MIIO . MIII2O3

prof. Viktor Kanický, Analytická chemie I
79
Transferring the sample into a solution
qHNO3, diluted1+1 (cca 4,6 mol/l, 30%), conc. too, oxidation effects, nitrates - soluble
ndissloves:
1)Most of metals with exception of Au and platinum group metals
2)alloys: Bi, Cd, Cu, Pb, Fe-Mn, Fe-P
3)ores: Cu, Mo, Co, Ni
nMII + 2 NO3- + 8 H+ Û 3 M2+ + 2 NO + 4 H2O
nAs, Sb transferred into solution (H3AsO3)
nSn – precipitates stannic acid:
n Sn + 4 NO3-  + 4 H+ + (x-2) H2O Û SnO2· x H2O + 4NO2-
nConcentrated HNO3
qPassivation Al, Cr, Fe
qOxidation of organic compounds
n

prof. Viktor Kanický, Analytická chemie I
80
Transferring the sample into a solution
qHCl + HNO3 (3+1) aqua regia
ndissolves:
1)PGM and Au
2)Ores and some silicates
3)phosphides, arsenides, antimonides, sulphides Þ acids: phosphoric, arsenic, chloroantimonic
q
nActive component Cl2 a NOCl
n             HNO3 + 3 HCl Þ NOCl + Cl2 + 2H2O
n             2 NOCl Þ 2 NO + Cl2
n 2 NO + O2 Þ 2 NO2
n         Hg + 2 NOCl Þ HgCl2 + 2 NO
nAu + 3/2 Cl2 + HCl Þ [AuCl4]- +  H+
n
n

prof. Viktor Kanický, Analytická chemie I
81
Transferring the sample into a solution
qHF conc.
nDecomposes all silicates:
q SiO2 + 4 HF Û SiF4 + 2 H2O
qRocks, ores (Nb, Ta, W), glasses, ceramics, alloys
qUsed in mixture with H2SO4 orHClO4 (increased boiling point), H2SO4 binds water and prevents thus
hydrolysis, perchloric acid exhibits oxidative effects
qH2SO4
nDiluted behaves as HCl:
qalone – limited use, sulphates less soluble than chlorides
nConcentrated
qOxidative effects, diss. Sb:
q 2 Sb +  6 H2SO4 Þ 2 Sb3++ 3 SO42- + 3 SO2 + 6 H2O
qphosphides, arsenides Þ phosphoric and arsenic acids
qKjeldalization – mineralization of organic nitrogen containing substances
n
q
q

prof. Viktor Kanický, Analytická chemie I
82
Transferring the sample into a solution
qHClO4 conc. (72%) exhibits oxidative effects at  elevated temperature
ndissolves:
1)steels(Cr, Si, V, P)
2)carbides
3)In mixture with HF for decomposition of silicates
nadvantage: soluble salts
ndisadvantage: explosive with organic compunds
n
qH3PO4
1)alloys
2)ferrovanadium, ferrosilicium, ferrochromium, ferroboron
n

prof. Viktor Kanický, Analytická chemie I
83
Transferring the sample into a solution
nDecomposition in hydroxides
qNaOH, KOH (35%)
ndissolves:
1)Light alloys (Al, Zn, Si, Mg), resulting aluminates, zincates, silicates:
n 2 Al + 2 OH- + 6 H2O Û 2 [Al(OH)4]- + 3 H2
n                Mg + 2 H2O Û Mg(OH)2 + H2
q
1)
n

prof. Viktor Kanický, Analytická chemie I
84
Transferring the sample into a solution
nFusion
nprocess, where high-temperature heated material changes from solid to liquid
qResulting products are dissoluble in water or dissolved acids
qAccording to fusion agent: alkaline and acidic fusion
nAlkaline fusion: transfer of acidic components (silicates, sulphates) in a solution by melting,
flux is anhydrous sodium carbonate or a mixture of sodium carbonate and potassium
nAcidic fusion: conversion of base-forming oxides to soluble salts (metal oxides, etc.). Transfer
into solution by fusion with potassium sulphate, or sodium tetraborate.
n
nFusion agents
qReagents used for decomposition by fusion
qAlkaline fusion: sodium carbonate, alkaline hydroxide, mixture of sodium carbonate and sulphur;
for acidic fusion: potassium disulphate, boron oxid, boric acid, sodium tetraborate

prof. Viktor Kanický, Analytická chemie I
85
Převádění vzorku do roztoku
nAlkaline fusion
ndecomposed: quartz, glass, porcelain, enamels, cement, aluminosilicates
qNa2CO3
1)Aluminosilicates are converted into soluble alkaline aluminates and silicates
2)Other oxides are converted to carbonates or depolymerize and in HCl are converted  into soluble
chlorides
qNaOH, KOH
q
n fusion in crucibles Ag, Ni or Fe
n
ndecomposed: ores W, Sn, Cr, Ti, Sb, Zr, corindum, bauxit, partially silicates
qLi2B4O7, LiBO2
1)Formation of borate glasses soluble in diluted acids –Si retained in solution

prof. Viktor Kanický, Analytická chemie I
86
Převádění vzorku do roztoku
nSintration
qReaction i solid phase at increased temperature but below the melting point of sintration reagent
(Na2O2)
qPt crucibles, sintered material soluble in water
q
n

prof. Viktor Kanický, Analytická chemie I
87
Převádění vzorku do roztoku
nAcidic fusion
qKHSO4, K2S2O7
q           2 KHSO4 Û K2S2O7 + H2O
q TiO2 + 2 K2S2O7 Û Ti(SO4)2 + 2 K2SO4
ndecomposed: aluminates, spinels, ores Cu, Sb, Ni, Ti
nLeaching of sulphates Zr a Ti at cold by addition of H2SO4
n
nActive constituent is SO3
n                  S2O72- Û SO42- + SO3
n Al2O3 + 3 SO3 Û 2 Al3+ + 3 SO42-
n TiO2 + 2 SO3  Û Ti4+ + 2 SO42-
n
n