Session 2: Fundamentals and Classical methods of quantitative elemental analysis http://bcs.whfreeman.com/qca7e http://www.good-weighing-practice.com/gwp/proper-weighing
Measurement of Mass and Volume:Recognising random and systematic errors
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
Measuring Mass Classical two-pan balance Modern electronic analytical balance F = m x g Electroma-gnetic force to counter From: Harris, 6th edition
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
Specifications for balances • Capacity • Readability • Repeatability (standard deviation); larger than readability Capacity x readability: Analytical balances: tens to hundreds of g x 0.1 - 0.01 mg Ultra-micro balance: e.g. 6 g x 0.0001 mg
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 (0.0012 g/ml); dw = density of calibration weights (8.0 g/ml); d = density of weighed object
Correcting buoyancy errors Buoyancy correction in dependence on density of weighed object
Exercise: • A bottle weighed 7.6500 g empty and 9.9700 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.
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.)
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
Random errors in volume measurement:Range and precision of typical Eppendorf micropipettes
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 40.00 mL sample is taken from an aqueous solution at 5°C. What volume does it occupy at 20 °C?
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).
Volume occupied by 1.0000g water weighed in air against stainless steel weights • Exercise: • A 25 mL pipette has been measured to deliver 24.976 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.
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
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
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
Precipitate analyte using precipitating agent Examples • Convert analyte (usually ions) to its elemental form using reducing agents
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
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
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?
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 (2.0000 g ) was accurately weighed into a pre-weighed silica crucible and roasted in air (A reacts with H2O) to produce SnO2 (0.4810 g). A second sample of A (2.0000 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=2.9986 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)
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 =118.69 x a + 126.90 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?
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
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)
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 thetitration error • Can be determined with ablank 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
Typical titration curve Decrease in concentration of analyte Note: semi-log plot log c Equivalence point Volume/ amount of titrant added
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)
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¯] 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
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-]
Effect of solubility product Log [Ag+] Ksp≈10-12 Ksp≈10-18 The higher the solubility, the more difficult becomes the end point recognition
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 = 2.66 pK5 = 6.16 pK6 = 10.24 (n-4)+ [M(H2O)6]n+ + [H2(EDTA)]2- + 6 H2O + 2 H+ ISO 6059: Determination of Hardness in water
Stoichiometric formation constants for EDTA complexes [MY(n-4)+] [Mn+][Y4-] =KMY (Kf) Mn++Y4-⇌ MY(n-4)+
Titration curve shape depends on formation constant [MY(n-4)+] [Mn+][Y4-] Mn++Y4-⇌ MY(n-4)+ =KMY (or Kf) • Ca2+ has smallest formation constant (weakest EDTA complex) • Fe3+ has largest formation constant (strongest EDTA complex) Titration curves for 50 mL of 0.01 mol/L cation solutions at pH 6.0.
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 Y4- HY3- H2Y2- H3Y- Speciation curve
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.
Minimum pH needed for the satisfactory titration of various cations with EDTA
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
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
Exercise • Find and list gravimetric and/or volumetric methods that may be commonly used in a commercial Analytical Lab