Fundamentals of Analytical Chemistry, D. A. Skoog, D. M. West, F. J. Holler and S. R. Crouch,

Compulsory textbook

Fundamentals of Analytical Chemistry, D. A. Skoog, D. M. West, F. J. Holler and S. R. Crouch,

Brooks/Cole 2004 8th Edition Brooks/Cole, 2004, 8th Edition

Recommended textbooks

Principles of Instrumental Analysis, D. A. Skoog, F.

J. Holler and T. A. Nieman, Saunders College Publishing 1999

Publishing, 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)

Analytical chemistry involves

separating, identifying and

d t i i th l ti t f th determining the relative amounts of the components (analytes) of the sample

Qualitative analysis

what is present? – chemical identity of the species in the sample (preceeds quant. anal.) Quantitative analysis

Quantitative analysis

how 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 y analysed

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

Examples

water analysis blood sample analysis

N,S,P,C-content in foodstuffs

serial analysis of a pharmaceutical product household gas analysis

air analysis etc., etc., etc.

Methods of analytical chemistry

Classical

i t gravimetry

volumetric methods or titrations Instrumental

electroanalysis

spectrometric analysis magnetic methods magnetic methods thermal methods miscellaneous methods

To be considered

1. accuracy & reliability required vs. economics

2. no. of samples to be analysed

3. complexity of the samples

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)

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)

interference:

species other than the analyte, which

interferes with the results of the measurement, i.e., measurement, i.e., causes errors

The measured property, Xhas to vary in a knownand

reproducibleway with the concenctration of the analyte, c_AA

Ideally

c_A = k×X X– the signal

k – characteristic to the method, s ll k ( x t

usually unknown (except gravimetryand coulometry) calibration – the process of determining k

For the calculations 1. experimental data 2. stoichiometry 3. instrumental data are required

uncertainties

associated with the measurements must be known –

errors in the chemical analysis

analysis

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 element Molecule- the smallest particle of a compound Compoundsare combination of elements –

molecules are made up of atoms

The important thing for an (analytical) chemist is the number of atomsreacting (and not the mass)

Atomic mass (A_r):relative masses based on the ¹²C isotope Molecular mass (M_r): the sum of the atomic masses of the atoms that make up the molecule

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

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

formula mass(A_ror M_r)

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 solute c = volume of solution

unit: mole/litre or mole/dm

or M unit 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 solute

number of moles of solute m =

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

Expressing concentration of solutions 3.

Mole fraction –

number of moles of solute X =

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 solution unit: 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 mg mass of solute in mg concentration 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 µg concentration in ppb =

volume of solution in litre Unit: ppb, part(s) per billion

Expressing concentration of solutions 5.

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

mass percent = x100 mass 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 t volume of solute

vol% = 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 c_T

Equilibrium molarity– the concentration of ions or molecules actually present in solution, taking into account the possible dissociation of the solute into ions

Symbol: […]

The analytical concentrationis equal to the sum of the equilibrium concentrationsof the various forms of the solute

concentrationsof the various forms of the solute

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 x x₁, x₂, x₃, …, x_N

Mean(median, arithmetic mean, average), x

∑

= ^N

i

xi

x N

1

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 = x_true - x_i

Types of errors

Random (indeterminate) error – causes data to be scattered symmetrically around the mean value; associated with the y y precision(or the reproducibility) of the measurement Systematic(determinate) error – (for example instrumental,

methodor personalerror); causes the mean of the data set to differ from the true value; associated with the accuracy of the measurement

Gross error– they occur occasionally and lead to outliers

Characterization of random errors, i.e., the pre cision of the measurement

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

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

( )

1

1

2

−

−

=

∑

=

N x x s

N i

i

d_i = x – x_i– the deviationof the i-th result, x_ifrom the mean;

N- the total number of the measurements;

N-1– number of degrees of freedom N 1 number of degrees of freedom s– standard deviation

s²– sample variance

Significant figures

The significant figuresin a number are all the certaindigits plus the first uncertaindigit

– most important example: reporting a burette reading l t th t th b tt i f 25 L it let us say, that the burette is of 25 mL capacity smallest division is 0.1 mL

12.24 mL

the first three digits are certain

the last digit is estimated, i.e., uncertain

if 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 balance 0,9668 g

the sample weighed must be at least 100 mg (to keep error at

≤1% level)

Sampling

The analytical method of choicedepends on the sample sizeand constituent type

sample size type of analysis

> 0.1 g macro

0.01-0.1 g semimicro

0.0001 g – 0.01 g micro

< 0.0001 g ultramicro

l l l f

analyte level type of constituent

1% - 100% major

0.01%(100 ppm) -1% minor

100 ppm – 1 ppb trace

< 1 ppb ultratrace

Minimizing errors in analytical procedures

1. Choosing the correct blanksolution

2. Application of separationtechniques –eliminationof

i t f s

interferences

3. Saturation– deliberate additionof 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 agentg g g – it selectively reacts with the y interfering component and makes it „invisible”

Classical methods of chemical analysis includes

includes

gravimetry titrimetry

argentometry acidi-alkalimetry complexometry complexometry redox titrations

Gravimetric methods

are quantitative methods that are based on determining the massof the pure compoundto which the analyte is chemically related The mass is always measured on an (accurate) analytical balance T p f im t i m th ds

Types of gravimetric methods precipitationgravimetry volatilazationgravimetry electrogravimetry thermogravimetry gravimetric titrimetry

Steps of precipitation gravimetry:

1 an excess precipitating reagentadded to the sample thus the 1. an excess precipitating reagentadded to the sample, thus the analyte converted into sparingly solubleproduct (precipitate) 2. precipitate is filtered

3. precipitate is washedfrom impurities

4. precipitate is dried or ignited (to convert it to a product with known composition)

5. precipitate is weighed

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 selectivelyor, at least, specificallywith the analyte

• Selective reagentreacts only with a singlechemical species (rare)

• Specific reagentreacts with several, but limited numberof chemical species (more common)

3 The precipitate must easily filtered and washed free from 3. The precipitate must easily filtered and washed free from

contaminants

4. Must be of sufficiently low solubility (to avoid loss of the analyte) 5. Must be unreactivewith constituents of the atmosphere

6. Its weighed formmust be of known composition(gravimetric factors)

Solubility of precipitates

Precipitate – it is formed from a solution which is

supersaturatedwith 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. Saturated

3. Supersaturated

1 2 3 1 2 3

Solubility of precipitates

Solubility (or equilibrium solubility,S):the concentration of a saturated solutionin molarity at a given temperature;

characteristicto the given salt (dependson solvent and temperature)

MA M⁺+ A^- M_xA_y xM^y++ yA^x- S = [M^y+]/x = [A^x-]/y

Solubility producty p (L, K_spsp) : the equilibrium constantq for the components of the precipitate in a saturated solution (i.e., in a solution, which contains some precipitate)

K_sp= [M⁺][A^-] K_sp= [M^y+]^x[yA^x-]^y

Solubility and solubility product

[ ] [ ] ^M

^A

^Sx

^Sy

K =

= ( ) ( )

E l l l t l bilit f

[ ] [ ]

sp

M A Sx Sy

K ( ) ( )

y

x x y

sp

y x S =

K

Examples: calculate solubility for AgCl in water, at 25 ^oC K_sp= 1.0^.10^-10 Ag₂CrO₄in water, at 25 ^oC K_sp= 1.1^.10^-12 Bi₂S₃in water, at 25 ^oC K_sp= 1.0^.10^-72

Factors influencing the solubility of a precipitate

1. Common ion effect– common ion will reducethe 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 decreasesolubility (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 impurities 4. Drying: precipitate is dried or ignited (to

convert it to a product with known composition)

1. Precipitation

• Particle sizeand 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 filteror 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

Drying and weighing

• Drying/ignitionis necessary to obtain constant mass for the precipitate

• Drying/ignitionleads 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, ignitioncan be done, if glass filteris used, only dryingis 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: SO₄^2-ions in the form of BaSO₄

Ca

ions in the form of Ca(COO)

.H

O

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 fast

4. completion of the reaction can be indicated

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 tothe 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 – E_t = V_ep – V_eq, where V_epis the actual volume of reagent required to reach the end pointand V_eq is the theoretical volume to reach the equivalence point

Perfect titration - V_ep = V_eq,

Terms used in titrimetry

Titration curves – plot the reagent volumeon 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 sigmoidalor linear segmentcurve.

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 purity

atmospheric stability absence of hydrate waterf y reasonable cost

reasonable solubility large 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

Terms used in titrimetry

Preparation 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