Analytical Methods and Techniques
Analytical Methods and Techniques CHE 221
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Henry Su December 12 2001 Chapter Notes Chemistry 221 Chapter 5 Dr Rahni Errors in Chemical Anal ses Assessin the ualit of Results It is impossible to perform a chemical analysis in such a way that the results are totally free of errors or uncertainties We can only hope to minimize these errors and estimate their size with acceptable accuracy Every measurement is in uenced by many uncertainties that combine to produce a scatter of results Measurement uncertainties can never be completely eliminated so the true value for any quantity is always unknown However the probable magnitude of the error in a measurement can o en be evaluated It is then possible to de ne limits within which the true value of a measured quantity lies at a given probability It is seldom easy to estimate the reliability of experimental data Nevertheless we must make such estimates whenever we collect laboratory results because data of unknown quality are worthless SA Defining Terms 5A 1 The Mean and the Median Mean arithmetic mean and average are synonyms for the quantity obtained by dividing the sum of replicate measurements by the number of measurements in the set The median is the middle result when replicated data are arranged in order of size EJIF39 I Example Calculate the mean and the median for this set of data 194 196 195 198 201 203 mean l94l95l96l9820l203 1978 6 median l96l98 197 6 5A 2 What is Precision Precisi0n describes the reproducibility of measurements or the closeness of the results that have been obtained in exactly the same way Three terms are widely used to describe the precision of a set of replicate data Standard Deviation Variance and Coefficient of Variation All above terms are a function of the deviation from the mean d1iXiXi 5A 3 What About Accuracy Accuracy indicates the closeness of the measurement to its true or accepted value and is expressed by the error Note that the basic difference between accuracy and precision is that accuracy measures agreement between a result and its true value while precision describes the agreement among several results that have been obtained in the same way We may determine precision just by replicating or repeating a measurement but we can never determine accuracy exactly because a true value of a measured quantity can never be known exactly Accuracy is expressed in terms of either absolute or relative error Absolute error The difference between the accepted and experimental results i Xt Relative Error Absolute error divided by the accepted value Er xiiL x100 X1 5A 4 Classifying Experimental Errors Random or indeterminate error causes data to be scattered more or less symmetrically around a mean value and affect the precision of measurement Systematic or determinate error causes the mean of a set of data to differ from the accepted value Gross error usually only occur occasionally are often large and may cause a result to be either high or low Lead to outliers results that appear to differ markedly from all other data SB Systematic Errors Systematic errors have a definite value an assignable cause and are of about the same magnitude for replicate measurements made in the same way Lead to bias in measurement technique Affects all the data in a set in approximately the same way and bears a sign 5B 1 How Do Systematic Errors Arise lInstrument errors are caused by imperfections in measuring devices and instabilities in their components differences in calibration distortion in container walls etc 2Method errors arise from nonideal chemical or physical behavior of analytical systems slowness or incompletion of reactions instability of certain species etc 3Personal errors result from the carelessness inattention or personal limitations of the experimenter estimation errors observation errors etc 5B 2 What Effects Do Systematic Errors Have on Analytical Results Systematic errors may either be constant or proportional The magnitude of a constant error does not depend on the size of the quantity measured Proportiona1 errors increase or decrease in proportion to the size of the sample taken for analysis A common source of proportional errors is the presence of interfering contaminants in the sample Example Suppose that 050 mg of precipitate is lost as a result of being washed with 200 mL of wash liquid If the precipitate weighs 500 mg the relative error due to solubility loss is 050500 x 100 0l Loss of the same quantity from 50 mg of precipitate results in a relative error of 701 5B 3 Detecting Systematic Instrument and Person Errors Systematic errors are usually found and corrected by calibration Most personal errors can be minimized by care and selfdiscipline 5B 4 Detecting Systematic Method Errors Bias in method is particularly difficult to detect Use the following steps to help 1 Analyzing Standard Samples The best way to estimate the bias of an analytical method is by analyzing standard reference materials materials that contain one or more analytes at wellknown or certi ed concentration levels 2 Using an Independent Analytical Method The independent method should differ as much as possible from the one under study to minimize the possibility that some common factor in the sample has the same effect on both methods 3 Performing Blank Determinations B1ank determinations are useful in detecting certain types of constant errors In a blank all steps of the analysis are performed in the absence of a sample The results from the blank are then applied as a correction to the sample measurements Revea1 errors due to interfering contaminants from the reagents and vessels employed in analysis 4 Varying the Sample Size As the size of a measurement increases the effect of a constant error decreases Thus constant errors can often be detected by varying the sample size Henry Su December 12 2001 Chapter Notes Chemistry 221 Chapter 13 Dr Rahni Titrating Polyfunctional Acids and Bases 13A Polyfuncti0nal Acids Phosphoric Acid is a typical polyfunctional acid H3PO4 H20 cgt H2P0439 H30 Ka1 igi gi 7lle3 H3PO4 H2PO439 H20 cgt HPO4392 H30 K32 m giu i 632e8 H2P0439 HPO4392 H20 cgt 1304393 H30 K33 319i Po L 45el3 HPO439Z Ka1gt Ka2gt Ka3 13B Describing Polyfunctional Bases C03392 H20 cgt HCO339 OHquot Kbl HCOf OH EL 213e4 0034 Kill HCO339 H20 cgt HzCO3 OHquot sz 132 OH ELL 67e4 HCOg39 Kaz 13C Findin2 the pH of n 39 quot 0f 39 39 quot Salts Amphiprotic salts are formed during neutralization titration of polyfunctional acids and bases An amphiprotic salt is a species that can act as an acid and as a base when dissolved in a suitable solvent HA39 H20 cgt A392 H30 acidic HA39 H20 cgt HzA OH39 basic H30 K31 K32 approx eq 134 Example Calculate the hydronium ion concentration of a 0100 M NaHC03 solution We first examine the assumptions leading to Equation 134 The dissociation constants for H2c03 are Kal l5e4 and Kaz 469ell H3015c 4 x 469e11 84e8 M 13D Constructing Titration Curves for Polyfunctional Acids Compounds with two or more acid functional groups yield multiple endpoints in a titration provided the functional groups differ sufficiently in strengths as acids Included in a titration curve for a weak diprotic acid and strong base are the following lInitial pH Initially only the first dissociation makes an appreciable contribution to H301 2First Buffer Region The addition of minimal base results in the formation of a buffer consisting of the weak acid HZM and its conjugate base HM39 The solution can be treated as a simple buffer system 3First Equivalence Point 4Second Buffer Region Further additions of base to the solution create a new buffer system consisting of HM39 and M39z 5Second Equivalence Point 6pH Beyond the Second Equivalence Point pH is determined by the concentration of the excess OH39 13E Drawing Titration Curves for Polyfunctional Bases The construction of a titration curve for a polyfunctional base is pretty much the same issue as with a polyfunctional acid only with a negative slope like a 1800 horizontally ipped polyfunctional acid titration curve 13F The Composition of Polyprotic Acid Solutions as a Function of pH Alpha values can be calculated for polyfunctional acids and bases in the following equation V0 3le c c Hle HM Ml V1 HMll Ct v21Mi1 V0V1Vzl ct sum of alpha values must equal unity Note that the denominator is the same for each expression Note also that the fractional amount of each species is fixed at any pH and is independent of the total concentration ct
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