1. Session 2: Fundamentals and Classical methods of quantitative elemental analysis

2. Measurement of Mass and Volume: Recognising random and systematic errors

3. Recap: Quantitative Analysis - Principles
Define sample amount (mass or volume)
Measure quantity proportional to analyte concentration
Measured property must vary in a defined way: calibration with known standards necessary
Analysis must be specific: Interferences must be known and if possible be eliminated
Accuracy: Proximity of measured value to accepted (or "true") value: must be determined
Precision: Closeness of measured values to one another: must be defined and reported

4. Classical two-pan balance
Measuring Mass
Classical two-pan balance
Modern electronic analytical balance
F = m x g
Electroma-gnetic force to counter
From: Harris, 6th edition

5. Random errors in weight measurements: tolerances of analytical balances and weights for calibration
Analytical balances need to be calibrated regularly
Typically use stainless steel weights (d = 8.0 g/ml)
From: Harris, 6th edition

6. Specifications for balances
Capacity
Readability
Repeatability (standard deviation); larger than readability
Capacity x readability:
Analytical balances: tens to hundreds of g x mg
Ultra-micro balance: e.g. 6 g x mg

7. Avoiding systematic error in weight measurements: buoyancy
Any object displaces a certain amount of air
This reduces the apparent mass that a balance measures
If density of the object being weighed is significantly different from calibration weights, buoyancy correction is necessary:
m = true mass; m’ = measured mass; da = density of air ( g/ml); dw = density of calibration weights (8.0 g/ml); d = density of weighed object

8. Correcting buoyancy errors
Buoyancy correction in dependence on density of weighed object

9. Exercise:
A bottle weighed g empty and g after introduction of an organic liquid with a density of 0.92 g cm-3. The balance was equipped with stainless steel weights having a density of 8.0 g cm-3. Correct the weight of the sample for the effects of buoyancy.

10. Avoiding systematic errors in weight measurements
Temperature effects
Convection air currents
Warm air in balance weighs less
Measured mass of object appears lower
Essential to weigh at room temperature
Prevent object from picking up moisture:
Do not touch with bare fingers
Let cool in desiccator
If weighing substances that are kept in fridge or freezer, let warm up before weighing
Be aware of hygroscopic substances
Absolute error in weight as a function of time after object was removed from a 110°C oven (A: porcelain filtering crucible, B: weighing bottle containing 7.5 g of KCl.)

11. Measuring Volume Apparatus for volume measurement
Pipettes, Burettes, Volumetric flasks
Calibrated either for containment (flasks) or delivery (pipettes, burettes) of specified volume
Typical pipettes: (a) volumetric (transfer pipette); (b) Mohr; (c) serological; (d) Eppendorf micropipette

12. Characteristics of pipettes
Name
Function
Capacity (cm3)
Type of drainage
Volumetric
Delivery of fixed volume
1-200
Free
Mohr
Delivery of variable volume
1-25
To lower calibration line
Serological
0.1-10
Blow out last drop
Eppendorf
Delivery of fixed or variable vol.
Empty tip by air displacement

13. Random errors in volume measurements: Tolerances of Class A Pipettes
Capacity (cm3)
Tolerances (cm3)
0.5
 0.006 1 2 5
 0.01 10
 0.02 20
 0.03 25 50
 0.05
100
 0.08

14. Random errors in volume measurement: Range and precision of typical Eppendorf micropipettes
Volume range (mL)
Standard dev. (mL)
1-20
2 mL
20 mL
10-100
15 mL
100 mL
20-200
25 mL
200 mL
250 mL mL mL mL

15. Tolerances of Class A burettes and volumetric flasks
Burette Vol. (mL)
Tolerance (mL)
Volumetric flask vol. (mL) 5
 0.01
 0.02 10 25
 0.03 50
 0.05
100
 0.20
 0.08
250
 0.12
500
1000
 0.30
2000
 0.50

16. Avoiding systematic errors in volume measurements: Temperature effects
Volume occupied by a given mass of liquid, as well as the device that holds the liquid, varies with temperature
For dilute aqueous solution:
Coefficient of expansion = 0.025% / °C
1°C increase in temp. yields 0.025% increase in volume.
Refer volumetric measurements to temperature at which they were made (standard temperature is 20 °C).
Exercise:
A mL sample is taken from an aqueous solution at 5°C. What volume does it occupy at 20 °C?

17. Avoiding systematic errors in volume measurement: Calibration of Volumetric Ware
Measure mass of liquid of known density and temperature contained in or delivered by a stated volume
Buoyancy correction must be made (see Table)
Divide corrected mass by density of liquid
Express results at standard temperature (20°C).

18. Volume occupied by 1.0000g water weighed in air against stainless steel weights
Volume (mL/g) at T
Temperature T (°C)
Corrected for buoyancy
Corrected for buoyancy and change in container volume = 20°C 10
1.0013
1.0016 12
1.0015
1.0017 14
1.0018
1.0019 16
1.0021
1.0022 18
1.0024
1.0025 20
1.0028 22
1.0033
1.0032 25
1.0040
1.0036 26
1.0043
1.0041 28
1.0048
1.0046 30
1.0054
1.0052
Exercise:
A 25 mL pipette has been measured to deliver g of water weighed against stainless steel mass at 25°C. Use the data in the Table to determine the volume delivered by this pipette at 25°C and 20 °C.

19. Treatment of glassware
Need to ensure that containers are clean and not contaminated
Important that liquids interact in defined way with glass surfaces: use detergents
For trace analysis, it is common to use an “acid wash”
If possible, use polypropylene or teflon rather than glass

20. Summary All measurements carry errors/uncertainty
Systematic errors can be corrected
Accuracy of methods can be improved
Random errors cannot be corrected
Precision of method can be determined and must be known
All quantitative data must be reported with error
Methods to solve a given analytical question can be selected according to their performance characteristics
Analysts must be aware of the performance characteristics of their tools

21. Classical analytical methods: Gravimetric and volumetric analyses

22. Gravimetric analysis
Analyte is converted to a solid product of known (pure) composition and weighed
Conversion of the analyte can be accomplished in several ways:
Reduction of an ion to its elemental form (e.g. by electrolysis)
Roasting (hydrolysis/oxidation) of a compound
Precipitation of an ion with a counterion
Precipitation of an organic molecule
Methods exist for most inorganic anions and cations, H2O, SO2, CO2, and iodine
Organic compounds can also be quantified

23. Examples Precipitate analyte using precipitating agent
Convert analyte (usually ions) to its elemental form using reducing agents
Reducing agent
Analyte
SO2
Se, Au
SO2 + H2NOH Te
H2NOH Se
H2C2O4 Au H2
Re, Ir
HCOOH Pt
NaNO2
SnCl2 Hg
Precipitate analyte using precipitating agent
Precipitating agent
Ion precipitated (Precipitate)
AgNO3
Cl- (AgCl), Br- (AgBr), I- (AgI)
HCl
Ag+ (AgCl), Hg+ (Hg2Cl2),
Na+ (NaCl)
HNO3
Sn4+ (SnO2)
H2SO4
Li+, Mn2+, Sr2+, Cd2+, Pb2+, Ba2+ (all as sulfates)
H2C2O4 (oxalate)
Ca2+, Sr2+, Th4+ (as oxalates or oxides)

24. Gravimetric analysis: precipitation of insoluble salts or complexes
Involves precipitation, filtration, drying, weighing
e.g.: Sulfate with BaCl2
Ni(II) with dimethylglyoxime
8-hydroxyquinoline (oxine): range of metal ions. Forms sparingly soluble complexes
For accuracy, certain conditions must be fulfilled:
The ion of interest must precipitate completely (=quantitatively). The formed salt must have a very low solubility product
Precipitate must be a pure compound (avoid co-precipitation)
Precipitate must be easy to filter

25. Why gravimetry is still in use, although time-consuming and challenging:
Accurate and precise (if done properly)
Absolute method: No calibration required
Apparatus required is relatively inexpensive

26. Exercise:
Lead (as Pb2+) can be determined by precipitation with sodium iodide
Write down the stoichiometric reaction formula
What mass of NaI is needed to convert 1.00 g of Pb(NO3)2 to PbI2?
What mass of PbI2 will be formed?

27. Exercise: A sample of metallic tin (2.00 g) was reacted with iodine (8.80 g) in a refluxing organic solvent, and an orange-yellow solid (A) (8.62 g) was isolated. A qualitative elemental analysis of A showed it contained only tin and iodide. A sample of A ( g ) was accurately weighed into a pre-weighed silica crucible and roasted in air (A reacts with H2O) to produce SnO2 ( g). A second sample of A ( g) was dissolved in a small excess of nitric acid, and excess silver nitrate added dropwise to precipitate silver iodide, which was collected in a weighed sinter crucible, dried in an oven at 110°C, and then cooled and weighed (mass of AgI obtained= g). When a sample of A was exposed to air for several months, it became hydrated as shown by a second analysis of the impure product, B, which showed Sn=17.92%, I=76.64%, and H=0.61%. (Sn=118.69, I=126.90, O=16.00, Ag=107.87, H=1.008)

28. Exercise (continued):
From the amount of SnO2 obtained in the original analysis, calculate the percentage of tin in A
From the amount of AgI obtained, calculate the percentage of iodide in A.
Assuming a molecular formula for A of SnaIb, the molecular weight of A is therefore = x a x b. Percentage tin X (1) Percentage iodide Y (2) Use equations (1) and (2) and your calculated values for X and Y to estimate the ratio b/a and determine the empirical formula of A.
A mass spectrum of A showed a cluster of peaks centred at a charge/mass ratio m/z=626, and no other peaks at higher m/z. Assuming the observed m/z corresponds to the approximate molar mass, M, what is the molecular formula of A?
What is the percentage purity of the exposed sample, B, compared with A (regard A as pure), and how many water molecules are there in B?

29. Volumetric analysis
Amount of analyte determined by measurement of volume of a reagent needed to react with analyte
Titrimetry: Determining the quantity of a reagent of known concentration that is required to react completely with the analyte
Titration: Adding standard solution (titrant) to solution of the analyte until reaction is complete. Solution dispensed from burette to determine volume of reagent required for reaction
Requires that
Reaction has a large equilibrium constant
Reaction proceeds rapidly

30. Titrimetric methods Acid-base titrations Precipitation titrations
Volhard (Ag+ directly or Cl- via back titration)
Complexometric titrations
Cations with EDTA
Redox titrations
Manganometry, iodometry
Spectrophotometric titrations
Measures changes in UV-Vis spectra
Potentiometric titrations
Measures changes in potential (e.g. with pH electrodes or Ion-selective electrodes)

31. General terminology
Equivalence point: Point in a titration when quantity of added titrant is the exact amount necessary for stoichiometric reaction with analyte. This is the “ideal” point sought in a titration. In reality, we find the
End point: Point reached when a (ideally sudden) physical change in the solution occurs, which indicates the absence of unreacted analyte. End points are often detected through an indicator
Ideally, there is very little difference between the volumes for the equivalence and end points. This difference is the titration error
Can be determined with a blank titration
Back titration: Excess of a standard solution added to consume analyte is determined by addition of second standard. Required when direct reaction is slow or unstable

32. Typical titration curve
Decrease in concentration of analyte
Note: semi-log plot
log c
Equivalence point
Volume/ amount of titrant added

33. General terminology: Standardisation
Titrations require standard solutions: Reagent of known concentration used to carry out titration
Primary standard: Solution of a highly purified compound (>99.9%) that can be accurately weighed
Serves as a reference material in a given volumetric titration method. The accuracy of such methods is critically dependent on the properties of this compound
Must be stable (not decomposed during storage)
Must be a compound that can be dried to remove residue water
Standard reference materials commercially available (SRMs)
Secondary standard: Solution of titrant that has been standardised by titrating a known amount of primary standard (also commercially available)

34. Precipitation Titrations
Based on reactions that give products of low solubility
One of the oldest analytical techniques (mid 1800s)
E.g. Volhard method for silver(I) titrations
For direct analysis of silver ions or indirect detn. of halides
Titrant: NaSCN
Fe(III) acts as the indicator
Red colour observed at [Fe(SCN)2+] = 6.4×10-6 M
Reaction 1: Ag+ + SCN¯ ⇌ AgSCN(s)
Ksp=[Ag+][SCN¯]=1.1 ×10-12
Reaction 2: Fe3+ + SCN¯ ⇌ [Fe(SCN)]2+ (red)
Kf= [Fe(SCN)]2+ =1.4 ×102
[Fe3+][SCN¯]

35. Volhard method for Ag+ Exercise:
Titrate 50 mL of 0.05 M Ag+ with 0.1 M KSCN
What concentration of Fe3+ should be used to reduce titration error to zero?
Note: For zero titration error, the Fe(SCN)2+ colour should appear when [Ag+] = [SCN-]

36. Effect of solubility product
Log [Ag+]
Ksp≈10-12
Ksp≈10-18
 The higher the solubility, the more difficult becomes the end point recognition

37. Compleximetric titration
Metal ion determination
Metal ion reacts with ligand to form complex
Can form soluble complexes or precipitates
Equivalence point determined by indicator
EDTA: Ethylenediamine tetraacetic acid; is a hexadentate ligand
pK1 = 0.0
pK2 = 1.5
pK3 = 2.0
pK4 =
pK5 =
pK6 = 10.24
(n-4)+
[M(H2O)6]n+ + [H2(EDTA)]2-
+ 6 H2O + 2 H+
ISO 6059: Determination of Hardness in water

38. Stoichiometric formation constants for EDTA complexes
[MY(n-4)+]
[Mn+][Y4-]
=KMY (Kf)
Mn++Y4- ⇌ MY(n-4)+
Cation
KMY
log KMY
Ag+
2.1×107
7.32
Cu2+
6.3×1018
18.80
Mg2+
4.9×108
8.69
Zn2+
3.2×1016
16.50
Ca2+
5.0×1010
10.70
Cd2+
2.9×1016
16.46
Sr2+
4.3×108
8.63
Hg2+
6.3×1021
21.80
Ba2+
5.8×107
7.76
Pb2+
1.1×1018
18.04
Mn2+
6.2×1013
13.79
Al3+
1.3×1016
16.13
Fe2+
2.1×1014
14.33
Fe3+
1.3×1025
25.10
Co2+
2.0×1016
16.31
V3+
7.9×1025
25.90
Ni2+
4.2×1018
18.62
Th4+
1.6×1023
23.20

39. Titration curve shape depends on formation constant
[MY(n-4)+]
[Mn+][Y4-]
Mn++Y4- ⇌ MY(n-4)+
=KMY (or Kf)
Titration curves for 50 mL of 0.01 mol/L cation solutions at pH 6.0.
Ca2+ has smallest formation constant (weakest EDTA complex)
Fe3+ has largest formation constant (strongest EDTA complex)

40. Effect of pH
Depending on pH, only a certain portion of EDTA is present as Y4-: [Y4-] = aY4- [EDTA]total
The value of aY4- decreases with pH pH
aY4- at 20°C
1.3×10-23 1
1.9×10-18 2
3.3×10-14 3
2.6×10-11 4
3.8×10-9 5
3.7×10-7 6
2.3×10-5 7
5.0×10-4 8
5.6×10-3 9
5.4×10-2 10
0.36 11
0.85 12
0.98 13
1.00 14
Y4-
HY3-
H2Y2-
H3Y-
Speciation curve

41. Effect of pH This leads to an apparent reduction in stability:
Significant for complexes with small K values:
Influence of pH on the titration of 0.01 mol/L Ca2+ (50 mL) with 0.01 mol/L EDTA.

42. Minimum pH needed for the satisfactory titration of various cations with EDTA

43. Endpoint recognition in Titrations with EDTA
Indicator for EDTA titrations: Eriochrome Black T
Different forms of indicator ( -, 2-, 3- ) have different colours
n-3 M
+ Mn+
+ 2H+
(red)
H2O + H2In- ⇌ HIn2- + H3O Ka1 = 5×10-7; pKa = 6.3
(red) (blue)
H2O + HIn2- ⇌ In3- + H3O+ Ka2 = 2.8×10-12; pKa = 11.6
(orange)
Kf for M(In) < Kf for M(EDTA): Solution stays red until no more M is left for complexation with ET
pH must be > 6.3 to see colour change to blue

44. Summary
Both gravimetric and volumetric methods require an understanding of the underlying Chemistry
Gravimetry: absolute method, no standardisation required (but accuracy of a given method must be tested)
Titrimetry: careful standardisation is required to achieve satisfactory accuracy

45. Exercise
Find and list gravimetric and/or volumetric methods that may be commonly used in a commercial Analytical Lab