Chemistry 155 Introduction to Instrumental Analytical Chemistry

Chem 155 Unit 1 Page 1 of 316 Chemistry 155 Introduction to Instrumental Analytical Chemistry Unit 1 Spring 2010 San Jose State University Roger Terrill Page 1 of 316

Chem 155 Unit 1 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):... 102 6 Monochromators for Atomic Spectroscopy:... 116 7 Photometric Issues in Atomic Spectroscopy... 137 8 Practical aspects of atomic spectroscopy:... 151 9 Atomic Emission Spectroscopy... 162 10 Ultraviolet-Visible and Near Infrared Absorption... 177 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 Page 2 of 316

Chem 155 Unit 1 Page 3 of 316 1 Overview and Review... 7 1.1 Tools of Instrumental Analytical Chem.... 8 1.2 Instrumental vs. Classical Methods.... 12 1.3 Vocabulary: Basic Instrumental... 13 1.4 Vocabulary: Basic Statistics Review... 14 1.5 Statistics Review... 15 1.6 Calibration Curves and Sensitivity... 23 1.7 Vocabulary: Properties of Measurements... 24 1.8 Detection Limit... 25 1.9 Linear Regression... 31 1.10 Experimental Design:... 35 1.11 Validation Assurance of Accuracy:... 43 1.12 Spike Recovery Validates Sample Prep.... 45 1.13 Reagent Blanks for High Accuracy:... 46 1.14 Standard additions fix matrix effects:... 47 1.15 Internal Standards... 52 2 Propagation of Error... 56 3 Introduction to Spectrometric Methods... 65 3.1 Electromagnetic Radiation:... 66 3.2 Energy Nomogram... 67 3.3 Diffraction... 68 3.4 Properties of Electromagnetic Radiation:... 71 4 Photometric Methods and Spectroscopic Instrumentation... 86 4.1 General Photometric Designs for the Quantitation of Chemical Species... 87 4.2 Block Diagrams... 88 4.3 Optical Materials... 89 4.4 Optical Sources... 90 4.5 Continuum Sources of Light:... 91 4.6 Line Sources of Light:... 92 4.7 Laser Sources of Light:... 93 5 Radiation Transducers (Light Detectors):... 102 5.1 Desired Properties of a Detector:... 102 5.2 Photoelectric effect photometers... 103 5.3 Limitations to photoelectric detectors:... 105 5.4 Operation of the PMT detector:... 106 5.5 PMT Gain Equation:... 107 5.6 Noise in PMT s and Single Photon Counting:... 109 5.7 Semiconductor-Based Light Detectors:... 111 5.8 Charge Coupled Device Array Detectors:... 114 6 Monochromators for Atomic Spectroscopy:... 116 6.1 Adjustable Wavelength Selectors... 117 6.2 Monochromator Designs:... 118 6.3 The Grating Equation:... 119 6.4 Dispersion... 122 6.5 Angular dispersion:... 123 Page 3 of 316

Chem 155 Unit 1 Page 4 of 316 6.6 Effective bandwidth... 125 6.7 Bandwith and Atomic Spectroscopy... 126 6.8 Factors That Control Δλ EFF... 127 6.9 Resolution Defined... 128 6.10 Grating Resolution... 129 6.11 Grating Resolution Exercise:... 130 6.12 High Resolution and Echelle Monochromators... 132 7 Photometric Issues in Atomic Spectroscopy... 137 8 Practical aspects of atomic spectroscopy:... 151 8.1 Nebulization (sample introduction):... 152 8.2 Atomization... 156 8.3 Flame Chemistry and Matrix Effects... 157 8.4 Flame as sample holder :... 158 8.5 Optimal observation height:... 159 8.6 Flame Chemistry and Interferences:... 160 8.7 Matrix adjustments in atomic spectroscopy:... 161 9 Atomic Emission Spectroscopy... 162 9.1 AAS / AES Review:... 163 9.2 Types of AES:... 164 9.3 Inert-Gas Plasma Properties (ICP,DCP)... 165 9.4 Predominant Species are Ar, Ar +, and electrons... 165 9.5 Inductively Coupled Plasma AES: ICP-AES... 166 9.6 ICP Torches... 167 9.7 Atomization in Ar-ICP... 168 9.8 Direct Current Plasma AES: DCP-AES... 169 9.9 Advantages of Emission Methods... 170 9.10 Accuracy and Precision in AES... 172 10 Ultraviolet-Visible and Near Infrared Absorption... 177 10.1 Overview... 177 10.2... 177 10.3 The Blank... 178 10.4 Theory of light absorbance:... 180 10.5 Extinction Cross Section Exercise:... 181 10.6 Limitations to Beer s Law:... 182 10.7 Noise in Absorbance Calculations:... 184 10.8 Deviations due to Shifting Equilibria:... 185 10.9 Monochromator Slit Convolution in UV-Vis:... 188 10.10 UV-Vis Instrumentation:... 190 10.11 Single vs. double-beam instruments:... 191 11 UV-Visible Spectroscopy of Molecules... 194 11.1 Spectral Assignments... 195 11.2 Classification of Electronic Transitions... 196 11.3 Spectral Peak Broadening... 197 11.4 Aromatic UV-Visible absorptions:... 201 11.5 UV-Visible Bands of Aqeuous Transition Metal Ions... 202 11.6 Charge-Transfer Complexes... 205 Page 4 of 316

Chem 155 Unit 1 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 Page 5 of 316

Chem 155 Unit 1 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 Page 6 of 316

Chem 155 Unit 1 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: What chemicals are present in a sample? QUALITATIVE ANALYSIS At what concentrations are they present? QUANTITATIVE ANALYSIS Additionally, Analytical Chemists are asked: 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 Page 7 of 316

Chem 1555 Unit 1 Page 8 of 316 1.1 Tools of Instrumental Analytical Chem. 1.1.1 Spectros scopy w/ Electromagnetic (EM) Radiation Name of EM regime: Gamma ray Wavelength 0.1 nm Predominant Excitation Nuclear Name of Spectroscopy Mossbauer X-Ray 0. 1 to 10 nm Vacuum 10-180 nm Ultraviolet Ultraviolet 180-400 Visible 400-800 Near Infrared 800-2,500 Infrared 2.5-40 μm Microwave 40 μm 1 mm Microwave 30 mm Radiowave 11 m Core electron Valence electron Valence electron Valence electron Vibration (overtones) Vibration rotations Electron spin in mag field Nuclear spin in mag field x-ray absorption, fluorescence, xps Vuv Uv or uv-vis Vis or uv-vis Near IR or NIR IR or FTIR Rotational or microwave ESR or EPR NMR Page 8 of 316

Chem 155 Unit 1 Page 9 of 316 1.1.2 Chromatography Chemical Separations Different chemicals flow through separation medium (column or capillary) at different speeds plug of mixture goes in chemicals come out of column one-by-one (ideally) Gas Chromatography GC Powerful but Suitable for Volatile chemicals only Liquid Chromatography High Performance (pressure), HPLC in it s many forms Electrophoresis -Liquids, pump with electric current, capillary, gel, etc. Chromatogram absorbance time / s Page 9 of 316

Chem 1555 Unit 1 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 e (pg) quantitation Powerful identification tool Page 10 of 316

Chem 155 Unit 1 Page 11 of 316 1.1.4 Electrochemistry Simple, sensitive, limited to certain chemicals Ion selective electrodes (ISE s): e.g. ph, pcl, po 2 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 Page 11 of 316

Chem 155 Unit 1 Page 12 of 316 1.2 Instrumental vs. Classical Methods. Separation Classical Methods of Analytical Chemistry # Chemicals Isolated / hr and amount (g) Extraction 1-2 g Distillation 1-2 g Precipitation 1-2 g Crystallization 1-2 g Instrumental High Performance Liquid Chromatrography Gas Chromatography Relax, you don t need to memorize this table just humor Dr. Terrill while he talks about it. # Chemicals Isolated / hr and amount (g) 10 ng 100 ng Electrophoresis 50 pg Qualitative Speciation Estimated Number of uniquely identifiable molecules by method Combination of Color / Smell Melt / Boiling Point, Solubility Wetting Density Hardness 100 s UV-Vis Infrared 1,000 s 100,000 s Mass Spectrometry > 10 6 NMR Spectroscopy Best Quantitative Precision and Sensitivity Titration 0.1 % 1 ppm > 10 6 Optical Spectroscopy 0.1% 10-23 M Quantitation Precision Gravimetry 0.01 % 1 ppm Mass Spectrometry 0.1% amount 10-4 % mass 10-13 M Colorimetry 10% 1 ppm NMR Spectroscopy 1% 100 pppm What are the more precise measurements that you have made and what were they? Page 12 of 316

Chem 155 Unit 1 Page 13 of 316 1.3 Vocabulary: Basic Instrumental Analyte The chemical species that is being measured. Matrix The liquid, solid or mixed material in which the analyte must be determined. Detector Device that records physical or chemical quantity. Transducer The sensitive part of a detector that converts the chemical or physical signal into an electrical signal. Sensor Device that reversibly monitors a particular chemical e.g. ph electrode Analog signal A transducer output such as a voltage, current or light intensity. Digital signal When an analog signal has been converted to a number, such 3022, it is referred to as a digital signal. Analog signals are susceptible to distortion, and so are usually converted into digital signals (numbers) promptly for storage, transmission or readout. Page 13 of 316

Chem 155 Unit 1 Page 14 of 316 1.4 Vocabulary: Basic Statistics Review Precision Random Error Accuracy Systematic Error (bias) Histogram Probability Distribution If repeated measurements of the same thing are all very close to one another, then a measurement is precise. Note that precise measurements may not be accurate (see below). Random error is a measure of precision. Random differences between sequential measurements reflect the random error. If a measurement of something is correct, i.e. close to the true value, then that measurement is accurate. Systematic error is the difference between the mean of a population of measurements and the true value. A graph of the number or frequency of occurences of a certain measurement versus the measurement value. A theoretical curve of the probability of a certain measured value occurring versus the measured value. A histogram of a set of data will often look like a Gaussian probability distribution. Average The sum of the measured. x values divided by the number n n of measurements. Median Variance (σ 2 ) Standard Deviation (σ) Relative Standard Deviation Propagaion of Error x MEAN Half of the measurements fall above the median value, and half fall below. A measurement of precision. The sum of the squares of the random σ 2 n measurement errors. n 1 A widely accepted standard measurement of precision. The square root n σ of the variance. n 1 The standard deviation divided by the mean, and often expressed as : %RSD=σ/x MEAN 100%. When the mean of a set of measurement (x) has a random error (σ x ), it is reported as x±σ x. If we wish to report the result of a calculation y=f(x) based on x, we propagate the error through the calculation using a mathematical method. n x MEAN x n 2 x MEAN x n 2 Page 14 of 316

Chem 155 Unit 1 Page 15 of 316 1.5 Statistics Review 1.5.1 Precision and Accuracy Histogram of normally distributed events 80 Mean Number of times it was observed 60 40 20 Mean - one standard deviation Mean + one standard deviation 0 0 1 2 3 4 5 6 Value observed Histogram of 1024 events 1.5.2 Basic Formulae Mean : μ lim N N x N N Population Standard Deviation: σ x lim N x N μ ( )2 N N Average: x avg x N N N Sample Standard Deviation: s x x N x ( avg )2 N N 1 Bias or absolute systematic error = x avg μ Relative standard deviation = s x avg Page 15 of 316

Chem 155 Unit 1 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, μ, 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? TAKE THE AVERAGE x AVG But, you still don t know the exact answer SO WHAT DO YOU REALLY WANT TO SAY? 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! How do you calculate what that interval is? You need to know: The average of the data set: x The standard deviation: σ 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? Smaller is better How can you improve your CI? Make more measurements (N) Page 16 of 316

Chem 155 Unit 1 Page 17 of 316 Confidence Interval (continued). If you know the standard deviation, σ, (less common case), then: The x% confidence interval for μ = x AVG ± zσ / N ½ If you don t know the standard deviation, σ, (more commonly the case), then: If you have only a rough estimate of x AVG, then you are less confident that it is close to μ, hence you divide by N ½. The x% confidence interval for μ = x AVG ± ts / N ½ In this case t is a function of N This leaves only z and t what are they? These numbers represent the multiple of one standard deviation (σ or s) that correspond to the confidence interval. In the second case, s is only an estimate of σ, 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. Page 17 of 316

Chem 155 Unit 1 Page 18 of 316 An example: Assume that we do our best to measure the concentration of basic amines in a fish tank. Our answers are 4.2, 4.6, 4.0. N = 3 X AVG = (4.2+4.6+4.0) / 3 = 4.27 s = (4.2-4.27) 2 +(4.6-4.27) 2 +(4.0-4.27) 2 3-1 = 0.31 Number of degrees of freedom for confidence interval = 3-1=2 95% confidence limits for μ = 5.4 5.0 4.27± (4.3*0.31) / (3 1/2 ) = 4.27±0.93 or = 4.3 ± 0.9 or = 3.4 to 5.2 4.5 3.5 Page 18 of 316

Chem 155 Unit 1 Page 19 of 316 1.5.4 Confidence Interval (CI) in Words Consider this experiment. You have a camera device that measures the temperature of objects from a distance by measuring their infrared light emission. It is very convenient but somewhat 97.5, 96.0, 99.1 97.323 98.055 99.051 imprecise. Assume for the moment that the camera is perfectly accurate that is, if you measure the same object with it many times the average temperature result will equal the true temperature. In order to evaluate the precision of your camera thermometer, you measure the temperature of each item three times. In each case you get an average and a standard deviation. PROBLEM: The average camera reading is sometimes higher than the true value, and sometimes lower, but you don t know how to evaluate this fluctuation. In just a few words, how can you characterize this fluctuation? SOLUTION: Calculate the sample standard deviation. QUESTION: A series of experiments, each of three measurements each yields a set of sample standard deviations that also different each time! If you repeat the whole experiment, but this time you measure each sample ten times, then the standard deviations are much closer, but still not equal each time. Why does the sample standard deviation calculation give a different result each time? Assume for the moment that the camera performance (precision) is not changing. ANSWER: Realize this fact: Sample standard deviations are only estimates. Page 19 of 316

Chem 155 Unit 1 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%. 101 102 103 10% chance μ is 101.8 or lower 80% chance 101.8 < μ < 102.6 10% chance μ is 102.6 or higher Page 20 of 316

Chem 155 Unit 1 Page 21 of 316 Use this table: % 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 Use this formula: CI μ± ts N Note the following: For a straight average of N points, the number of degrees of freedom is N-1. Complete the following table: Passenger T AVG ( F) St dev ( F) 1 101.5 1.1 2 98.57 0.17 3 103.93 0.047 Lower boundary of 80% CI Upper boundary of 80% CI Is the probability that the passenger s Temp is > 102 90% or more? 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! Page 21 of 316

Chem 155 Unit 1 Page 22 of 316 1.5.6 t EXP PROBLEM: Another way of approaching this type of problem is to calculate an experimental value of t called t EXP. In the example below, we will compare a measured result with an exact one. The question one answers with t EXP is this: Am I confident that the observed value (x) differs from the expected value (μ)? 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 ( x av μ) N t exp s μ = test value ( 103.76 102) 3 t exp := 1.34 t exp = 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 Page 22 of 316