Chemistry 155 Introduction to Instrumental Analytical Chemistry, Schemes and Mind Maps of Analytical Chemistry

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Chem 155 Unit 1 Page 1 of 316 Page 1 of 316 Chemistry 155 Introduction to Instrumental Analytical Chemistry Unit 1 Spring 2010 San Jose State University Roger Terrill Chem 155 Unit 1 Page 2 of 316 Page 2 of 316 1 Overview and Review ........................................................................................ 7 2 Propagation of Error ......................................................................................... 56 3 Introduction to Spectrometric Methods ............................................................ 65 4 Photometric Methods and Spectroscopic Instrumentation ............................... 86 5 Radiation Transducers (Light Detectors): ...................................................... 103 6 Monochromators for Atomic Spectroscopy: ................................................... 117 7 Photometric Issues in Atomic Spectroscopy .................................................. 138 8 Practical aspects of atomic spectroscopy: ..................................................... 152 9 Atomic Emission Spectroscopy ...................................................................... 163 10 Ultraviolet-Visible and Near Infrared Absorption .......................................... 178 11 UV-Visible Spectroscopy of Molecules ........................................................ 194 12 Intro to Fourier Transform Infrared Spectroscopy ........................................ 211 13 Infrared Spectrometry: ................................................................................. 234 14 Infrared Spectrometry - Applications ............................................................ 247 15 Raman Spectroscopy: .................................................................................. 259 16 Mass Spectrometry (MS) overview: ............................................................. 279 17 Chromatography .......................................................................................... 294 Chem 155 Unit 1 Page 5 of 316 Page 5 of 316 11.7 Lanthanide and Actinide Ions: .................................................... 206 11.8 Photometric Titration .................................................................. 207 11.9 Multi-component Analyses: ........................................................ 208 12 Intro to Fourier Transform Infrared Spectroscopy .................................. 211 12.1 Overview: ................................................................................... 212 1 molecular vibrations ............................................................................... 212 12.2 IR Spectroscopy is Difficult! ....................................................... 215 12.3 Monochromators Are Rarely Used in IR..................................... 216 12.4 Interferometers measure light field vs. time ............................... 217 12.5 The Michelson interferometer: ................................................... 218 12.6 How is interferometry performed? .............................................. 219 12.7 Signal Fluctuations for a Moving Mirror ...................................... 220 12.8 Mono and polychromatic response ............................................ 222 12.9 Interferograms are not informative: ............................................ 223 12.10 Transforming time  frequency domain signals: .................... 224 12.11 The Centerburst: ..................................................................... 225 12.12 Time vs. frequency domain signals: ........................................ 226 12.13 Advantages of Interferometry. ................................................ 227 12.14 Resolution in Interferometry .................................................... 228 12.15 Conclusions and Questions: ................................................... 232 12.16 Answers: ................................................................................. 233 13 Infrared Spectrometry: ........................................................................... 234 13.1 Absorbance Bands Seen in the Infrared: ................................... 235 13.2 IR Selection Rules ..................................................................... 236 13.3 Rotational Activity ...................................................................... 238 13.4 Normal Modes of Vibration: ........................................................ 239 13.5 Group frequencies: a pleasant fiction! ........................................ 242 13.6 Summary: ................................................................................... 246 14 Infrared Spectrometry - Applications ...................................................... 247 14.1 Strategies used to make IR spectrometry work - ....................... 248 14.2 Solvents for IR spectroscopy: .................................................... 249 14.3 Handling of neat (pure – no solvent) liquids: .............................. 249 14.4 Handling of solids: pelletizing: .................................................... 250 14.5 Handling of Solids: mulling: ........................................................ 250 14.6 A general problem with pellets and mulls: .................................. 251 14.7 Group Frequencies Examples .................................................... 252 14.8 Fingerprint Examples ................................................................. 253 14.9 Diffuse Reflectance Methods: .................................................... 254 14.10 Quantitation of Diffuse Reflectance Spectra: .......................... 255 14.11 Attenuated Total Reflection Spectra: ...................................... 256 15 Raman Spectroscopy: ............................................................................ 259 15.1 What a Raman Spectrum Looks Like ......................................... 261 15.2 Quantum View of Raman Scattering. ......................................... 262 15.3 Classical View of Raman Scattering .......................................... 263 15.4 The classical model of Raman: .................................................. 265 15.5 The classical model: catastrophe! .............................................. 266 Chem 155 Unit 1 Page 6 of 316 Page 6 of 316 15.6 Raman Activity: .......................................................................... 267 15.7 Some general points regarding Raman: .................................... 269 15.8 Resonance Raman .................................................................... 271 15.9 Raman Exercises ....................................................................... 272 16 Mass Spectrometry (MS) overview: ....................................................... 279 16.1 Example: of a GCMS instrument: ............................................... 279 16.2 Block diagram of MS instrument. ............................................... 280 16.3 Information from ion mass .......................................................... 281 16.4 Ionization Sources ..................................................................... 282 16.5 Mass Analyzers: ......................................................................... 287 16.6 Mass Spec Questions: ............................................................... 292 17 Chromatography – Chapter 26 ............................................................... 294 17.1 General Elution Problem / Gradient Elution ............................... 307 17.2 T-gradient example in GC of a complex mixture. ....................... 309 17.3 High Performance Liquid Chromatography ................................ 310 17.4 Types of Liquid Chromatography ............................................... 311 17.5 Normal Phase: ........................................................................... 311 17.6 HPLC System overview: ............................................................ 314 17.7 Example of Reverse-phase HPLC stationary phase: ................. 315 17.8 Ideal qualities of HPLC stationary phase: .................................. 316 Chem 155 Unit 1 Page 7 of 316 Page 7 of 316 1 Overview and Review Skoog Ch 1A,B,C (Lightly) 1D, 1E Emphasized Analytical Chemistry is Measurement Science. Simplistically, the Analytical Chemist answers the following questions: Additionally, Analytical Chemists are asked: What chemicals are present in a sample? • Where are the chemicals in the sample? • liver, kidney, brain • surface, bulk • What chemical forms are present? • Are metals complexed? • Are acids protonated? • Are polymers randomly coiled or crystalline? • Are aggregates present or are molecules in solution dissociate? • At what temperature does this chemical decompose? • Myriad questions about chemical states… QUALITATIVE ANALYSIS At what concentrations are they present? QUANTITATIVE ANALYSIS Chem 155 Unit 1 Page 10 of 316 Page 10 of 316 1.1.3 Mass Spectrometry Detection method where sample is: volatilized, injected into vacuum chamber, ionized, usually fragmented, accelerated, ions are „weighed‟ as M/z – mass charge. Often coupled to: chromatograph laser ablation atmospheric “sniffer”. Very sensitive (pg) quantitation Powerful identification tool Chem 155 Unit 1 Page 11 of 316 Page 11 of 316 1.1.4 Electrochemistry Simple, sensitive, limited to certain chemicals Ion selective electrodes (ISE‟s): e.g. pH, pCl, pO2 etc. ISE‟s measure voltage across a selectively permeable membrane (e.g. glass for pH) E α log[concentration] ISE‟s have incredible dynamic range! pH 4  pH 10 [H+] = 0.0001 0.0000000001 M Dynamic electrochemistry – measure current (i) resulting from redox reactions at an driven by a controlled voltage at an electrode surface i(E,t) α [concentration] 1.1.5 Gravimetry Precipitate and weigh products – very precise, very limited 1.1.6 Thermal Analysis Thermogravimetric Analysis TGA Mass loss during heating – loss of waters of hydration, or decomposition temperature Differential Scanning Calorimetry DSC Heat flow during heating or cooling Chem 155 Unit 1 Page 12 of 316 Page 12 of 316 1.2 Instrumental vs. Classical Methods. Methods of Analytical Chemistry Classical # Chemicals Isolated / hr and amount (g) Instrumental # Chemicals Isolated / hr and amount (g) Separation Extraction 1-2 g High Performance Liquid Chromatrography 10 ng Distillation 1-2 g Gas Chromatography 100 ng Precipitation 1-2 g Electrophoresis 50 pg Crystallization 1-2 g Estimated Number of uniquely identifiable molecules by method Qualitative Speciation Combination of Color / Smell Melt / Boiling Point, Solubility Wetting Density Hardness 100‟s UV-Vis 1,000‟s Infrared 100,000‟s Mass Spectrometry > 106 NMR Spectroscopy > 106 Best Quantitative Precision and Sensitivity Quantitation Precision Titration 0.1 % 1 ppm Optical Spectroscopy 0.1% 10-23 M Gravimetry 0.01 % 1 ppm Mass Spectrometry 0.1% amount 10-13 M 10-4% mass Colorimetry 10% 1 ppm NMR Spectroscopy 1% 100 pppm What are the more precise measurements that you have made and what were they? Relax, you don‟t need to memorize this table – just humor Dr. Terrill while he talks about it. Chem 155 Unit 1 Page 15 of 316 Page 15 of 316 Population Standard Deviation: x N N xN 2 N lim Mean : N N xNlim N Sample Standard Deviation: xavg N xN N sx N xN xavg 2 N 1Average: Bias or absolute systematic error = xavg Relative standard deviation = s xavg 1.5 Statistics Review 1.5.1 Precision and Accuracy a 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 2.781 2.66 2.763 2.524 2.157 3.022 2.94 3.278 4.096 3.404 3.493 3.431 3.458 .337 2.478 3.035 0 1 2 3 4 5 6 0 20 40 60 80 Histogram of normally distributed events Value observed N um b er o f ti m e s it w a s o b se rv e d His togram of 1024 events 1.5.2 Basic Formulae Mean Mean + one standard deviation Mean - one standard deviation Chem 155 Unit 1 Page 16 of 316 Page 16 of 316 When you make real measurements of things you generally don’t know the „true‟ value of the thing that you are measuring. (Call this the true mean, , for now. For the purposes of this discussion let us assume that there is no systematic (accuracy) error (i.e. no bias). 1.5.3 Confidence Interval WHAT DO YOU DO TO ENSURE THAT YOUR ANSWER IS AS CLOSE AS POSSIBLE TO THE TRUTH? But, you still don‟t know the exact answer… SO WHAT DO YOU REALLY WANT TO SAY? How do you calculate what that interval is? You need to know: The average of the data set: x The standard deviation: or s The number of measurements (observations) made: N This interval is called a confidence interval (CI). Which is better,a bigger or a smaller CI? How can you improve your CI? TAKE THE AVERAGE xAVG I am highly confident that the true mean lies within this interval (e.g between 92 and 94 grams). In fact, there is only a 1 in 20 chance that I am wrong! Smaller is better… Make more measurements (N) Chem 155 Unit 1 Page 17 of 316 Page 17 of 316 Confidence Interval (continued). If you know the standard deviation, , (less common case), then: If you don‟t know the standard deviation, , (more commonly the case), then: This leaves only z and t – what are they? These numbers represent the multiple of one standard deviation ( or s) that correspond to the confidence interval. In the second case, s is only an estimate of , so the error in s needs to be taken into account, so t is a function of the “number of degrees of freedom”. For our purposes, i.e. averaging multiple identical measurements, the number of degrees of freedom is simply N-1. The x% confidence interval for = xAVG ± z / N ½ The x% confidence interval for = xAVG ± ts / N ½ In this case t is a function of N If you have only a rough estimate of xAVG, then you are less confident that it is close to , hence you divide by N½. Chem 155 Unit 1 Page 20 of 316 Page 20 of 316 1.5.5 CI PROBLEM: This imperfect camera thermometer is going to be used to screen passengers boarding an airliner. Passengers with a high temperature may have avian flu. Our criterion is this: if there is more than a 90% probability that a given passenger‟s temperature exceeds 102°, then we will take him aside and test him for bird flu. We have only moments to acquire three measurements per passenger, so precision is low. Also, the precision is not the same each time. For three passengers we get the following results: Passenger 1: 100.3°, 101.1°, 103.0°. Passenger 2: 98.8°, 98.5°, 98.4° Passenger 3: 104.0°, 103.9°, 103.9° How do we answer the question: does this person‟s temperature exceed our 90% / 102° criterion? To answer this, we must accept the following: Assuming that measurements are unbiased (accurate) we can state, for the 80% CI, that there is a 10% probability that the true mean lies below the lower limit of the CI, an 80% probability that the true mean lies within this CI, and a 10% probability that the true mean lies above this CI. So, there is a 90% probability that the true mean lies within or above the 80% CI. For example, if we took some measurements and then computed the 80% CI to be 101.8° to 102.6° then we could say that the probability that the true temperature is 101.4° or higher is 90%. 10% chance is 101.8° or lower 101° 102° 103° 80% chance 101.8° < < 102.6° 10% chance is 102.6° or higher Chem 155 Unit 1 Page 21 of 316 Page 21 of 316 Use this table: Use this formula: % confidence interval °freedom 50 80 95 99 1 1.00 3.08 12.71 63.66 2 0.82 1.89 4.30 9.92 3 0.76 1.64 3.18 5.84 4 0.74 1.53 2.78 4.60 5 0.73 1.48 2.57 4.03 6 0.72 1.44 2.45 3.71 7 0.71 1.41 2.36 3.50 8 0.71 1.40 2.31 3.36 9 0.70 1.38 2.26 3.25 10 0.70 1.37 2.23 3.17 20 0.69 1.33 2.09 2.85 50 0.68 1.30 2.01 2.68 100 0.68 1.29 1.98 2.63 Complete the following table: Lower boundary of 80% CI Upper boundary of 80% CI Is the probability that the passenger‟s Temp is > 102° 90% or more? Passenger TAVG(°F) St dev (°F) 1 101.5 1.1 2 98.57 0.17 3 103.93 0.047 What is another way to word the conclusion above? Assuming our equipment is accurate, then averaged over many passengers, and using this criterion, our conclusion that the person’s temperature is > 102° will be wrong less than 10% of the time! CI ± t s N Note the following: For a straight average of N points, the number of degrees of freedom is N-1. Chem 155 Unit 1 Page 22 of 316 Page 22 of 316 1.5.6 tEXP PROBLEM: Another way of approaching this type of problem is to calculate an experimental value of „t‟ called tEXP. In the example below, we will compare a measured result with an exact one. The question one answers with tEXP is this: Am I confident that the observed value (x) differs from the expected value ( )? Our threshold temperature, exactly 102° was tested, so we can make measurements and test the hypothesis that „the true temperature is greater than 102°‟. Given the following three measurements of a passenger‟s temperature: 103.76°, 102.11°, 105.38° – calculate an experimental value of the „t‟ statistic for this population relative to the true value of 102°. Average = 103.75, std dev = 1.34 % confidence interval °freedom 50 80 95 99 1 1.00 3.08 12.71 63.66 2 0.82 1.89 4.30 9.92 3 0.76 1.64 3.18 5.84 texp 103.76 102( ) 3 1.34 texp 2.275 Can you state with the given confidence that this person‟s temperature differs from the expected value of 102°? 99%? No 95%? No 80%? Yes 50%? Yes texp xav N s = test value Chem 155 Unit 1 Page 25 of 316 Page 25 of 316 1.8 Detection Limit The detection limit is denoted “CM” CM is the minimum concentration that can be “detected,” or distinguished confidently from a blank. Let us define the minimum detectable signal change as: SM Therefore: SM = mCM must be a multiple (n) of the noise level in the blank: ( b). By convention, m=3. Derive a formula for CM based on B and m: Derive a formula for CM based on : 1.8.1 SM ≡ 3 b = mCM Minimum Detectable Signal Signal due to blank Minimum detectable concentration Chem 155 Unit 1 Page 26 of 316 Page 26 of 316 A Graphical Look at Detection Limit (CMIN) Consider the minimum detectable signal in the context of the confidence interval: SMIN = 3 b + Sb To what confidence interval does 3 correspond? Assume N=2 (two replicate measurements of Sb) Another way of saying this (crudely) is that we consider a signal „detected‟ when it falls outside of the boundaries corresponding to the 99% confidence interval for the blank signal. Chem 155 Unit 1 Page 27 of 316 Page 27 of 316 1.8.2 Minimum Detectable Temperature Change? Using the thinking that we developed for the general case of signals with random error – what do you think is the probability that the following signal change is due to random fluctuations? Chem 155 Unit 1 Page 30 of 316 Page 30 of 316 1.8.4 Direct Interference In order to measure a concentration directly, without corrections, kB,A, kC,A must be approximately: If there is interference, it is necessary to know both: and before one can determine the desired quantity CA! Chem 155 Unit 1 Page 31 of 316 Page 31 of 316 1.9 Linear Regression Least-Squares Regression or Linear Regression Assuming that a set of x,y data pairs are well described by the linear function y = a+bx, and assuming that most error is in y (x is more precisely known) and the errors in y are not a function of x, then the coefficients that minimize the residual function: 2 = (yI – (a + bxI)) 2 can be found from the following equations: from Data Reduction and Error Analysis for the Physical Sciences, Philip R. Bevington, cw. 1969 Mc Graw Hill. Non-linear Regression Methods for fitting arbitrary curves to data sets. Standard Additions Plot A nearly matrix-effect free form of analysis. A standard additions plot is a linear plot of instrument signal versus quantity of a standard analyte solution „spiked‟ or added to the unknown analyte sample. The unknown analyte concentration is derived from the concentration axis-intercept of this plot. Sample Matrix / Standards Matrix The matrix is the solution, including solvent(s) and all other solutes in which an analyte is dissolved or mixed Matrix Effect A matrix effect refers to the case where the instrumental sensitivity is different for the sample and standards because of differences in the matrix. Internal Standards A calibration method in which fluctuation in the instrument signals due to matrix effects are, ideally, cancelled out by monitoring the fluctuations in the instrument sensitivity to chemicals, internal standards, that are chemically similar to the analyte. Chem 155 Unit 1 Page 32 of 316 Page 32 of 316 0 2 4 6 8 10 0 0.5 1 1.5 Analyte Concentration (C) In st ru m en t S ig n al ( S ) 1.5 0 S i S i F i F i 100 C i 1.9.1 Linear Least Squares Calibration The most common method for determining the concentration of an unknown analyte is the simple calibration curve. In the calibration curve method, one measures the instrument signal for a range of analyte concentrations (called standards) and develops an approximate relationship (mathematically or graphically) between some signal „S‟ and analyte concentration „C‟. If the signal-concentration relationship is linear, then: But, one can not just draw the line between any two points because all the points have some error. So, one mathematically attempts to minimize the residuals. 2 = (yi – (a + bxi)) 2 S = SB + mC y = a + bx Chem 155 Unit 1 Page 35 of 316 Page 35 of 316 1.10 Experimental Design: Designing an experiment involves planning how you will: make calibration and validation standards; prepare the sample for analysis; and perform the measurements. 1.10.1 Making a set of calibration standards. 1. You need to know the dynamic range of your instrument. 2. You need to know the sample size requirement of your instrument. 3. You need to know the estimated expected concentration of your sample. 4. You need to prepare and dilute your sample until it is a. within the dynamic range of your instrument and b. such that there is enough solution to measure. 5. You need to choose target standard concentrations that bracket the expected sample concentration generously – e.g. by a factor of 2 to 3. For example, if your expected concentration is 5.3 ppm, you may wish to make a calibration set that consists of standards that are about 2,4,8,10 and 12 ppm. Chem 155 Unit 1 Page 36 of 316 Page 36 of 316 6. You need to make a primary stock solution, the concentration of which you know accurately and precisely. This solution will usually be more than twice as concentrated as your most concentrated calibration standard. You will dilute this primary stock solution to make the calibration standards. You need to have enough to make all of your calibration standards. 7. You need to choose the pipets and volumetric flasks that you will use to perform the dilutions. This means that you plan the preparation of each standard. This takes some planning and compromising and many choices – there are many ways to do this correctly – there is more than one right answer! 8. Decide on and record a labeling system in your notebook, collect the glassware, and do the work. I have a labeling system for your caffeine, benzoic acid, iron and zinc standards – I need you to use these labels so that we can sort things out in the class. Chem 155 Unit 1 Page 37 of 316 Page 37 of 316 1.10.2 Exercise in planning an analysis: Assume that you will be analyzing sucrose in corn syrup sweetened ketchup packets. The packets are thought (i.e. expected) to contain about 0.8 grams of corn syrup that is about 70% sucrose by weight. The HPLC instrument that you will be using can detect sucrose by refractive index in the 0.1-20 parts per thousand (ppth) range (this is the instrument‟s dynamic range for sucrose). You have pure sucrose for standards, and will be making five calibration standard solutions. The instrument requires between 250 and 1000 L of sample. You have the following glassware at your disposal: Pipets Volumetric Flasks Volume Relative Precision Volume Relative Precision 20-200 L 5-1% 1 mL 1% 1 mL 1% 5 mL 1% 5 mL 1% 10 mL 1% 10 mL 1% 25 mL 1% 15 mL 1% 50 mL 1% 20 mL 1% 100 mL 0.5% 25 mL 0.5% 250 mL 0.5% 50 mL 0.5% 1000 mL 0.25% Chem 155 Unit 1 Page 40 of 316 Page 40 of 316 4. What concentrations „bracket‟ the 5.6 ppth target? For example: 5.2, 5.4, 5.6, 5.8, 6.0 ppth --- or --- 1, 2, 4, 6, 8 ppth --- or --- 1, 2, 5, 10, 15 ppth --- or --- 0.050, 0.50, 5.0, 50, 500 ppth 5. What volumes of standards should you prepare? How much is needed by the instrument? What is the smallest volume that you can conveniently and precisely measure? How expensive is the analyte and solvent? How expensive is it to dispose of the waste? 0.1 or 1 or 10 or 100 or 1000 mL Do you need to make standards on an even spacing? Does the analyte have to fall right in the middle of the calibration standards? No, but it minimizes error! No – but calibration points above and below the std. are needed. Chem 155 Unit 1 Page 41 of 316 Page 41 of 316 6. How do you prepare the calibration series from the primary stock solution? Primary Stock (1) is diluted to make  Calibration Standard (2) C1V1 = C2V2 First calibration standard: Make 10 mL of 1 ppth sucrose from 100 ppth stock solution. C1 = 100 ppth C2 = 1 ppth V2 = 10.0 mL V1 = ? = volume to pipet over V1 = C2V2/C1 Chem 155 Unit 1 Page 42 of 316 Page 42 of 316 7. How to plan a set of standard preparations in the MS Excel spreadsheet program: Calibration Standard Preparation: Target Conc: Stock Conc: Final Volume: Volume to Pipet: C2 / ppt C1 / ppt V2 / mL V1=C2*V2/C1 1.00 100.0 10.00 0.100 mL 2.00 100.0 10.00 0.200 mL 5.00 100.0 10.00 0.500 mL 10.00 100.0 10.00 1.000 mL 15.00 100.0 10.00 1.500 mL Calibration Standard Preparation: Target Conc: Stock Conc: Final Volume: Volume to Pipet: C2 / ppt C1 / ppt V2 / mL V1=C2*V2/C1 1 100 10 =A4*C4/B4 mL 2 100 10 =A5*C5/B5 mL 5 100 10 =A6*C6/B6 mL 10 100 10 =A7*C7/B7 mL 15 100 10 =A8*C8/B8 mL These are formulas that you type into Excel – normally only the result of the formula calculation is displayed. Chem 155 Unit 1 Page 45 of 316 Page 45 of 316 1.12 Spike Recovery Validates Sample Prep. To do a spike recovery analysis, one takes replicate samples and to a subset of them adds a spike of analyte before the sample prep begins. So, for example, one could take four vitamin tablets, and divide them into two groups of two. To one group one could add some Fe, say half the amount originally expected. For example, if there is supposed to be 15 mg of iron in the tablet, one could spike two samples each with 5 mg of iron and leave two unspiked. digest filter Dilute to 100 mL volume Sample Sample+ 5.00 mg spike Analyze  140 ppm 14.0 mg found digest filter Dilute to 100 mL volume Analyze  187 ppm 18.7 mg found 18.7-14.0 = 4.7 mg of spike found: spike recovery percent = 4.7 / 5.00  94% Acids etc. What does this say about our sample preparation method? We may be losing about 6% of the analyte during sample prep. Chem 155 Unit 1 Page 46 of 316 Page 46 of 316 1.13 Reagent Blanks for High Accuracy: A reagent blank is a blank that is made by doing everything for the sample prep etc. but without the sample: In this example the reagent blank is analyzed against ultrapure water. The 0.23 mg Fe found in the reagent blank may be due to Fe impurities in the acids, but it also may be a matrix effect. In either case, it suggests that we should do what in order to arrive at a more accurate result? digest filter Dilute to 100 mL volume “No Sample” sample. Ultrapure water blank Analyze  2.3 ppm 0.23 mg Fe found Acids etc used in sample prep. Either: a. analyze all standards and samples against reagent blanks or b. obtain higher purity acids c. subtract the signal from the reagent blank (with regulatory approval…) Chem 155 Unit 1 Page 47 of 316 Page 47 of 316 1.14 Standard additions fix matrix effects: Use the method of standard additions when matrix effects degrade the accuracy of the calibration curves. There is one important assumption built into the calibration curve idea. That assumption is the following: Why would the sensitivity be different? 1. Many Instruments are sensitive to things like: 2. Sometimes other chemicals (interferants) can change the calibration sensitivity by: These two things are examples of: the sensitivity of the instrument to the analyte in the standards is the sensitivity of the instrument to the analyte in the sample matrix EQUAL TO 1. pH 2. ionic strength 3.organic components of the solvent matrix chemically binding to or interacting with the analyte atom/molecule Matrix Effects Chem 155 Unit 1 Page 50 of 316 Page 50 of 316 1.14.3 Calculating Conc. w/ Standard Additions: One way of analyzing this uses similar triangles: a / b = The y-axis absorbance signal (S) is proportional to the moles of analyte (VXCX) and standard (VSCS). The x-axis is simply the standard „spike‟ volume. The x-intercept is the hypothetical spike volume (VS)0 containing the same amount of analyte as the sample. a is proportional to moles of analyte in the sample = VXCX a‟ is proportional to moles of std added = VSCS b is (VS)0 – the x-intercept of the graph b‟ is VS – the spike volume Substitute for a,a‟,b,b‟: Solve for CX: a b a' b' (VS)0 CX = CS(VS)0/VX a‟/b‟ VSCS = VXCX VS Chem 155 Unit 1 Page 51 of 316 Page 51 of 316 1.14.4 Standard Additions by Linear Regression: Let: VX = volume of unknown analyte solution added to each flask CX = concentration of unknown solution VT = final, diluted volume VS = volume of „spike‟ added to unknown soln. before dilution CS = concentration of analyte in spike solution Dilution Calc 1: (V1C1 = VTCT  CT = V1C1/VT) Contribution to concentration of analyte from sample: Dilution Calc 2: Contribution to concentration of analyte from spike: Total Signal (sensitivity = k) given that „x‟ variable is VS. S = k + k Slope = m = intercept = b = we can get b and m from linear regression and we want CX … so … b/m = = so : CX = VXCX/VT VSCS/VT VXCX/VT VSCS/VT kCS/VT kVXCX/VT kVXCX/VT kCS/VT VXCX/CS bCS mVX Chem 155 Unit 1 Page 52 of 316 Page 52 of 316 1.15 Internal Standards Internal standards can correct for sampling, injection, optical path length and other instrument sensitivity variations. An internal standard is a substance added (or simply present) in constant concentration in all samples, and standards. When something unexpected decreases the sensitivity of the instrument (m) so the signal drops (S = mC + SB) – it can be impossible to distinguish this from a change in analyte concentration without an internal standard. Consider the ratio of the blank corrected analyte ( BANAN sSS ' ) to the internal standard (IS) signals (S): IS AN ISIS ANAN IS AN C C k Cm Cm S S ' ' Assumes for the moment that k is a constant, i.e. invariant to factors affecting overall instrumental sensitivity. As an example, let‟s consider k to be a correction for injection volume in a chromatographic system. It is perfectly reasonable to assume that an accidentally low or high injection volume would affect the internal standard and analyte signals identically – e.g. if a given injection were 6% high, then both analyte and internal standard peaks would be 6% larger than expected. If k is invariant to instrument fluctuations, then the true analyte concentration can always be derived from the ratio of the corrected signals so long as the internal standard concentration remains constant. kS CS C IS ISAN AN ' ' where k CIS is easily derived from a previously measured calibration standard for which the analyte signal ( STDAS ' ) and concentration ( STDAC ) of the analyte and internal standard ( STDISSTDIS CS ,' ) are known: IS AN STDASTDIS STDISSTDA m m CS CS k ' ' From a calibration standard. Anlalyte conc. in a sample. Chem 155 Unit 1 Page 55 of 316 Page 55 of 316 1.15.1 Internal Standards Calculation How about calculating the actual concentration of the sample in 3 above? Standard STDAS ' 530 mAu . s STDAC 25 ppm STDISS ' 480 mAu . s STDISC 100 ppm IS AN STDASTDIS STDISSTDA m m CS CS k ' ' 530 100 480 25 4.417 unitless Sample ANS ' 630 mAu . s ISS ' 520 mAu . s ISC 100 ppm kS CS C IS ISAN AN ' ' 630 100 520 4.417 27.4 ppm Chem 155 Unit 2 Page 56 of 316 Page 56 of 316 2 Propagation of Error Skoog Chapters Covered: Appendix a1B-4 a1B-5 and – eqn. a1-28 table a1-5 There is a general problem in experimental science and engineering: How to estimate the error in calculated results that are based on measurements that have error? Let‟s consider the sum of two measurements a and b that both have some fluctuation sa = 0.5 lb and sb = 0.5 lb. Let‟s also pretend that we know the true values of a and b. True value of: a = 5.0 lb b = 5.0 lb Let‟s say that we are weighing a and b and putting them into a box for shipment. We need to know the total weight. Our scale is really bad (poor precision, lots of fluctuation), and it can‟t weigh both a and b at the same time because it has a limited capacity. So, we have to first weigh a, then b and then calculate the total weight. But we know that there is a problem with fluctuations, so we repeatedly weigh the same items a and b and do the following experiment: Characteristics of numbers in sum „a‟ and „b‟ Characteristics of sum „c‟ Trial # Weight of: Deviation: Total weight: Deviation from avg: a b da db 1 4.5 4.5 -0.5 -0.5 9.0 -1 2 5.5 4.5 +0.5 -0.5 10.0 0 3 4.5 5.5 -0.5 +0.5 10.0 0 4 5.5 5.5 +0.5 +0.5 11.0 +1 average 5.0 5.0 0.5 0.5 10 0.5 This is somewhat artificial and is not quite right, but it gives you the general idea. Errors in a and b propagate into c. Chem 155 Unit 2 Page 57 of 316 Page 57 of 316 From this example above, one would conclude that the fluctuation in the sum is equal to the fluctuation in the numbers summed – but this is not right. Which is bigger? a. the fluctuations in the individual numbers summed b. the fluctuations in the sum Graphically we consider here a similar case, for clarity we let a have a slightly larger fluctuation than b. a = 5 2, b = 3 1 “R e a l” d is tr ib u ti o n th e o re ti c a l th e o re ti c a l c a+sa a-sa a+sa+b+sb a+sa+b-sb a-sa+b+sb a-sa+b-sb a Chem 155 Unit 2 Page 60 of 316 Page 60 of 316 For a simple example – if you construct a simple calibration curve of instrument signal versus concentration, and then use a real (i.e. noisy) signal to determine concentration. Errors propagate from S to C according to the sensitivity. Chem 155 Unit 2 Page 61 of 316 Page 61 of 316 Let‟s consider an example wherein the relationship between the measured signal and the desired quantity is non-linear : Obviously – the same error in P can give rise to different errors in A! This is a propagation of error problem. How can you calculate the error in A that should result from a particular error in P? Absorbance Absorbance is a nonlinear function of light power - the measured quantity in a spectrophotometric experiment. A log P P l 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.5 1 1.5 2 A i P i A = -log (P/Po) Chem 155 Unit 2 Page 62 of 316 Page 62 of 316 Obviously, the answer has to do with the way that the dependent variable (A) in this case changes as a function of the independent variable (P). Consider a calculated value „S‟ that depends on the measured quantites, e.g. instrument signals, a,b,c… S = f(a,b,c…) In fact – the variance in S is proportional to the variance in a,b,c – and the proportionality is the partial derivative squared: (Skoog appendix a1B-4 has a derivation if you are curious) So – let‟s take an example: S = a+b-c find S = f(S,a, a, b, b,c, c) Note that the larger terms dominate! S f a± a b± b c± cfor: S 2 S a 2 a 2 S b 2 b 2 S c 2 c 2 Chem 155 Unit 3 Page 65 of 316 Page 65 of 316 3 Introduction to Spectrometric Methods Skoog Chapter 6 all sections Electromagnetic Radiation (EMR) is: EMR described as a classical, electromagnetic wave: In vacuum (air): n=1 In matter: n>1 Note: When the refractive index ( ) changes ___________ ___________ Light! = c = wavelength = frequency c = light speed MEDIUM = cMEDIUM MEDIUM = VAC / cMEDIUM = cVAC / distance Stays same changes Chem 155 Unit 3 Page 66 of 316 Page 66 of 316 3.1 Electromagnetic Radiation: A vast range of energies covers many physical processes. These processes are the basis of spectroscopy. Chem 155 Unit 3 Page 67 of 316 Page 67 of 316 Energy Nomogram 106 105 104 103 102 1012 1013 1014 1015 101 102 103 104 105 10-3 10-2 10-1 100 101 10-1 100 101 102 10-1 100 101 102 103 101 102 103 104 105 nm cm-1 s E / eV E / kCal /mol T / KE / kJ /mol Energy nomogram - Hard UV 100 nm to Far IR 1mm Chem 155 Unit 3 Page 70 of 316 Page 70 of 316 Diagram for deriving a formula for the path length difference between diffracted rays: Chem 155 Unit 3 Page 71 of 316 Page 71 of 316 3.3 Properties of Electromagnetic Radiation: Most EM Radiation is polychromatic, i.e. the beam is a mixture of rays of different: E.g. incandescent light sources are polychromatic. Another term for polychromatic light: is white light. EM Radiation is monochromatic if all rays have identical: E.g. Na-atomic emission lamps are nearly monochromatic because nearly all of the light is from a single atomic transition that emits at 590nm. White light can be filtered so that it is nearly monochromatic. Coherence: EM Radiation is coherent if all rays have identical: Coherent radiation comes from lasers and exotic light sources called synchrotrons. frequency phase frequencies phases frequency Chem 155 Unit 3 Page 72 of 316 Page 72 of 316 3.3.1 Polarization: Most light is unpolarized Special filters, called polarizers, can remove all E-field components except those falling in a given plane. The result is plane polarized light: Elliptically polarized light: Electric vector randomly oriented All E-field lies in one plane E-field vector rotates around direction of propagation. Chem 155 Unit 3 Page 75 of 316 Page 75 of 316 3.3.4 Reflection: Calculate the total reflection loss due to the two reflections (air | glass and glass | water) when a light beam passes through one side of a cuvette ( = 1.5), containing water ( = 1.3). Fresnel Equation for a special case: Normal Incidence No Absorption Incident beam Reflected beam Transmitted beam Chem 155 Unit 3 Page 76 of 316 Page 76 of 316 3.3.5 Scattering: Scattering Process Scatterer Features Raleigh (elastic) atoms and molecules weak, favors blue Tyndall (Mie) Elastic normally Colloids (bigger / nm) Strong (easy to image) Raman (visible) Molecules – vibrational spec very weak, inelastic Incident Scattered Transmitted Chem 155 Unit 3 Page 77 of 316 Page 77 of 316 3.3.6 The Photoelectric Effect and the Photon: Max Planck and Albert Einstein discovered that Kinetic energy of the emitted electrons depends on: and Kinetic energy of emitted electrons is independent of: Metal Light electrons current Light Frequency E le c tr o n E n e rg y (K E ) 0 EF Free e- Slope = “h” Electrons are emitted from metal surfaces that are irradiated with light of sufficiently high frequency. Light frequency Type of Metal Light intensity - more intensity means more electrons, but not more energetic electrons! Chem 155 Unit 3 Page 80 of 316 Page 80 of 316 3.3.7 Spectra typical of gas, liquid and solid. Absorber Phase Notes / transition types Atom Gas Extremely narrow lines / electronic Molecule Gas Fine structure due to electronic+ rotational+ vibrational Molecule / small Solution Broad bands + some fine structure / electronic + vibrational Molecule / larger Solution Broad bands electronic only resolved Chem 155 Unit 3 Page 81 of 316 Page 81 of 316 3.3.8 Energy levels and photon absorption and emission. Chem 155 Unit 3 Page 82 of 316 Page 82 of 316 3.3.9 Typical fluorphore Jablonski Diagram. 3.3.10 Photophysical Processes Chem 155 Unit 3 Page 85 of 316 Page 85 of 316 Quantitation by interaction with light: Chem. 155 Unit 4 Page 86 of 316 Page 86 of 316 4 Photometric Methods and Spectroscopic Instrumentation Skoog Chapters Covered: Review: Quantitation in Absorbance and Emission 7A Optical Designs – Absorbance Emission 7A Optical Materials (lightly!) 7B Light Sources Continuum and Line 7B Lasers! Chem. 155 Unit 4 Page 87 of 316 Page 87 of 316 4.1 General Photometric Designs for the Quantitation of Chemical Species 4.1.1 Generalized Detector Response: S = kP + SDARK 4.1.2 Absorbance More Analyte 4.1.3 Quantitation 4.1.4 Emission and Fluorescence More Analyte 4.1.5 Quantitation Less Signal A = bc = -log(P/P0) More Signal P = PO + mC = molar absorptivity b = pathlength (cm) c = concentration in moles/L P = Light Power at Detector PO = Light Power for Blank c = concentration in moles/L P = Light Power at Detector PO = Light Power for Blank c = concentration in any unit S = Signal k = proportionality P = light power SDARK = detector response in absence of light All absorbance methods! IR, VIS, UV, Xray! All light emission methods! Fluorescence (Xray - UV), Scattering, Luminescence, even NMR! Chem. 155 Unit 4 Page 90 of 316 Page 90 of 316 4.4 Optical Sources Cost Trade Off $$ VUV Only? $$ Short Lifetimes $$ Popular UV-source – used with W-Halogen for UV-Vis $ W-Halogen Visible only, long lifetimes $$ NIR and IR Only $ IR only $ IR Only $$ Low intensity, limited ‟s $$- $$$$ Exellent Intensity, limited ‟s $ - $$ very high resolution, poor dynamic range $$-$$$ PMT v. fast, v.v. sensitive, delicate, limited in IR $-$$ low sensitvity, limited in IR but cheap $ - $$$ sensitive and fast, much tougher than PMT $$-$$$$ v. sensitive, slow, tough, $$-$$$ detector of choice most IR More exotic „energy detectors‟ – don‟t know much about these Chem. 155 Unit 4 Page 91 of 316 Page 91 of 316 4.5 Continuum Sources of Light: Also called: 1. Simplest Design: a. Tungsten b. Quartz-Tungsten-Halogen c. Nernst Glower 2. Gas Emission Designs: a. H2 / D2 Kinetic Energy of H atoms = Therefore h can be: b. Ar, Xe, Hg Heavy (High-Z) atoms  Many atomic states + High Pressure (extensive broadening of lines) Broadband or White Light Sources Blackbody Sources Visible / Near IR / IR IR / Far IR H2 + e -  H2*  H + H + h Continuum Continuum Quasi-Continuum UV-Vis-Near IR UV Only Chem. 155 Unit 4 Page 92 of 316 Page 92 of 316 4.6 Line Sources of Light: 1. Low Pressure Gas Emission a. Hg b. Ar c. Xe d. Na 2. Hollow Cathode Lamps: a. Metals (Cathode!) b. Used in atomic spectroscopy (absorbance and fluorescence) Many Lines – can be filtered to emit only one predominant line. Na-D Line Predominates – 589.00 and 589.59 nm doublet 300V DC  Electrical Discharge Ne + Ne + Fe Metal Cathode Fe* + Fe + h Sputtering Atomic Emission Chem. 155 Unit 4 Page 95 of 316 Page 95 of 316 4.7.1 A laser is a light amplifier – Some of the above processes degrade the light in the cavity Spontaneous Emission Absorption Some of the above processes amplify the light in the cavity Pumping Stimulated Emission Pump Fast Decay Lasing! losses – absorption, spontaneous emission pump power in gain! – stimulated emission beam out 0 1 2 Pump Fast Decay Lasing! 0 2 3 Fast Decay 1 Two common laser configurations: 3-state 4-state (or more) Chem. 155 Unit 4 Page 96 of 316 Page 96 of 316 4.7.2 Polulation Inversion and laser amplification Roughly speaking lasing is possible when: lasing amplification population in state Ey absorption population in state Ex population in upper state 1 is greater than the population in lower state 2 This is called a population inversion. Chem. 155 Unit 4 Page 97 of 316 Page 97 of 316 4.7.3 Necessity of 3 or more states Why are three or more levels (states) necessary for lasing? N EXCITED N GROUND e E kTrecall: E = ENERGY DIFFERENCE us-ls k = Boltzmann const. 1.3x10-23 J/K T = temperature (K) NEXCITED = population (concentration) US NGROUND = population (concentration) LS What happens when T  infinity? NEXCITED  NGROUND