ADVANCED ANALYTICAL LAB TECH (Lecture) CHM 4130-0001 Spring 2013 Professor Andres D. Campiglia Textbook: “Principles of Instrumental Analysis” Skoog, Holler and Crouch, 5 th Edition, 6 th Edition or newest Edition 1
INTRODUCTION • A common challenge faced by an analytical chemist is the determination of target species in complex samples • Complex sample: sample with numerous species. Example of complex samples: physiological fluids (blood, urine, saliva), environmental samples (air, water, soil), etc. • Target species is the species of interest. It is also called analyte. Example: benzo[ a ]pyrene in soil sample, PSA (prostate specific antigen) in physiological fluid, etc. • Some possibilities: Analyte: Other species = concomitants: Analyte is the main Analyte is not the main Analyte is not the main component in the sample with component in the sample component in the sample only but and two types of species sample contains sample contains only two types of species several types of species 2
General Scheme Sample Collection Sample = Matrix Sample Preparation: Clean-up and/or Pre-concentration Analytical Sample Qualitative and Quantitative Analysis Statistical Analysis of Data 3
Quantitative and Qualitative Analysis • Classical and instrumental methods • Classical methods = wet-chemical methods Analyte separation: precipitation, extraction or distillation Qualitative analysis: chemical reactions yielding products of characteristic colors boiling or melting points solubility in a series of solvents odors, optical activities or refractive indexes Quantitative analysis: Gravimetric or volumetric analysis • Main disadvantages of classical methods: Time consuming Numerous manual steps, which make them prone to indeterminate (random) errors 4
Instrumental Methods • Most instrumental methods require a source of excitation to stimulate a measurable response from the analyte. See Figure 1-1. • The first six entries in Table 1-1 involve interactions of the analyte with electromagnetic radiation. • The first characteristic response involves radiant energy produced by the analyte. • The next five properties involve changes in electromagnetic radiation brought about by its interaction with the sample. • Four electrical properties and miscellaneous properties follow. • The name of the corresponding instrumental method is given in the second column of Table 1-1. 5
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Evaluation of Analytical Data (Appendix One) • Analytical chemists may be presented with two types of problems 1) Provide a qualitative answer Example: Does this distilled water contain any Boron? Is this soil sample contaminated with polycyclic aromatic hydrocarbons (PAH)? 2) Provide a quantitative answer Example: How much lead is in this water sample? This steel sample contains traces of chromium, tungsten and manganese; how much of each one? • Often, both types of questions are answered with quantitative methods Example: B, Pb, Cr, W, Mn in H 2 O: AAS or AES PAH in H 2 O: HPLC • In cases where a positive answer is obtained, the analyst will give the answer in terms of analyte concentration Example: This water sample contain 1 m g/mL of B Most certainly, if the analyst repeats the experiment with the same sample using the same method he/she will find a different result Why? Because of inherent experimental errors 7
Random and systematic errors • Example: Four students (A-D) each perform an analysis in which exactly 10.00mL of exactly 0.1M sodium hydroxide is titrated with exactly 10.00mL of exactly 0.1M hydrochloric acid. Each student performs five replicate titrations with the results shown in the following table Student Results (mL) A 10.08, 10.11, 10.09, 10.10, 10,12 B 9.88, 10,14, 10.02, 9.80, 10.21 C 10.19, 9.79, 9.69, 10.05, 9.78 D 10.04, 9.98, 10.02, 9.97, 10.04 A Results are all very close to each other (10.08-10.12) = highly reproducible All the results are too high (they are all higher than 10.00, which is the theoretical value) Two separate types of errors have occurred with this student: Random errors: these cause the individual results to fall on both sides of the average value (10.10mL) Systematic errors: these cause all the results to be in error in the same sense (too high) Random errors affect the reproducibility of an experiment or precision Systematic errors affect the proximity of the experimental value to the theoretical value or accuracy 8 8
B The average of the five results (10.01mL) is very close to the theoretical value = data is accurate, without substantial systematic error The spread of the results is very large (9.80 – 10.21) = data is imprecise, with the presence of substantial random errors Comparing A and B A: precise and inaccurate B: poor precision and accurate Random and systematic errors can occur independently of one another C His work is neither precise (range 9.69 – 10.19mL) nor accurate (average = 9.90mL) D Precise results (9.97 – 10.04mL) and accurate (average = 10.01mL) 9 9
Distinction between random and systematic errors, and precision and accuracy Student Results A Precise but inaccurate B Accurate but imprecise C Inaccurate and imprecise D Accurate and precise 10 10
Terms used to describe accuracy and precision of a set of replicate data • Accuracy (systematic errors): absolute error or relative error #1 • Precision (random errors) : standard deviation, variance or coefficient of variation 11
Random Errors • Whenever analytical measurements are repeated on the same sample, a distribution of data similar to that in Table a1-1 is obtained. • The variations among the individual results are due to the presence of random (indeterminate) errors. • The data can be organized into equal-sized, adjacent groups or cells, as shown in Table a1- 2. • Figure a1-1A shows the histogram of the data, i.e. the relative frequency of occurrence of results in each cell. • As the number of measurements increases, the histogram approaches the shape of the Table a1-1 continuous curve shown as plot B in Figure a1- 1. • Plot B shows a Gaussian curve , or normal error curve , which applies to an infinitely large set of data. Figure a1-1 12 Table a1-2
Systematic Errors and the Gaussian Curve • Systematic errors have a definite value and an assignable cause and are of the same magnitude for replicate measurements made in the same way. Figure a1-2 • Systematic errors lead to bias in measurement results. • Figure a1-2 shows the frequency distribution of replicate measurements in the analysis of identical samples by two methods that have random errors of identical size. • Method A has no bias so that the mean ( m A ) corresponds to the true value. Method B has a bias that is given by: bias = m B – m A • The analyst should be able to identify systematic errors and remove them from the method of analysis. 13
Statistical Treatment of Random Errors • Random errors can not be completely eliminated from experiments. • Statistical treatment of random errors provide the means to evaluate their contribution to final results. • Definition of some terms: Population Mean ( m ) #2 Sample Mean #3 Population Standard Deviation ( s ) and Population Variance ( s 2 ) #4 Sample Standard Deviation (s) and Sample Variance (s 2 ) #5 Relative Standard Deviation (RSD) and Coefficient of Variation (CV) #6 14
The Normal Error Law • In Gaussian statistics, the results of replicate measurements arising from indeterminate Figure a1-3a (random) errors distribute according to the normal error law, which states that the fraction of a population of observations, dN/N, whose values lie in the region x to (x+dx) is given by: #7 • The two plots in Figure a1-3a are plots of the equation above. The standard deviation for the data in curve B is twice that for the data in curve A. (x – m ) is the absolute deviation of the individual • values of x from the mean. • Figure a1-3b plots the deviations from the mean in terms of the variable z: z = x – m / s when x – m = s z = 1 x – m = 2 s z = 2 x – m = 3 s z = 3 and so forth. • The distribution of dN/N in terms of the single variable z is given by: #8 15 Figure a1-3b
Characteristic Properties of the Normal Error Curve • Zero deviation from the mean occurring with maximum frequency. • Symmetrical distribution of positive and negative deviations about this maximum • Exponential decrease in frequency as the magnitude of the deviation increases. Thus, small random errors are much more common than large random errors. • The area under the curve in figure a1-3b is the integral of equation #8, which is given by: #9 • The fraction of the population between any specified limits is given by the area under the Figure a1-3b curve between these limits. Examples: -1 z 1 D N/N = 0.683 = 68.3% of a population of data lie within 1 s. -2 z 2 D N/N = 0.954 = 95.4% of a population of data lie within 2 s. -3 z 3 D N/N = 0.997 = 99.7% of a population of data lie within 3 s. 16
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