PROBLEMS IN ANALYTICAL CHEMISTRYCHEM 824, Spring 2015

MWF 9:30-10:20, Rm 130, Hamilton Hall

COURSE OUTLINE

Instructor: Dr. Robert Powers Office Labs

Address: 722 HaH 721 HaHPhone: 472-3039 472-5316e-mail:rpowers3@unl.eduweb page: http://bionmr.unl.edu/Office Hours: 10:30-11:30 am MWF or by Special Appointment.

Required Items:(i) CHEM 821 is a prerequisite(ii)Text: No official text, but some recommendations are:

“Principles of Instrumental Analysis" by D. A. Skoog, J. F. Holler and T. A. Nieman"Instrumental Analysis" by G. D. Christian and J. E. O'Reilly“Analytical Chemistry and Quantitative Analysis” by D. S. Hage and J. D. Carr

(iii) Calculator for exams (TI-89 style or a simpler model)

Course Outlined (cont.) Course Work:

Exam 1: 100 pts. (Tues., Sept. 22)Exam 2: 100 pts. (Fri., Oct. 16)Exam 3: 100 pts. (Wed., Nov. 18)Final: 100 pts. (10-12, Tues., Dec. 15)Problem Sets: 150 pts. (various due dates)

Total: 550 pts.

The due dates for problem sets will be announced when the problem sets are handed out. ALL PowerPoint presentations, and answer keys for the problem sets and exams will be posted on BlackBoard.

Grading scale: A+=95%; A=90%; A-=85%; B+=80%; B=75%; B-=70%; C+=65%; C=60%; C-=55%; D=50%; D-=45%; F=40%

As an 800 level course, a final grade of “C” or greater is needed for this class to count towards a graduate degree.

Class Participation•Reading assignments should be completed prior to each lecture.

•You are expected to participate in ALL classroom discussions

Exams

•All exams (except the final) will take place at 6 pm in Rm 130, Hamilton Hall on the scheduled date.

•The length of each exam will be open-ended. You will have as much time as needed to complete the exam.

•Bring TI-89 style calculator or a simpler model, approved translator and text book (you will be able to use certain charts, tables and appendix)

•A review session will take place during the normal class time.

•ALWAYS SHOW ALL WORK!!!!

Course Outlined (cont.)

Course Outlined (cont.) Problem Sets

•~11 Problem sets are worth between 5 to 20 points each for a total of ~150 points

•You may work together in groups, but everyone must submit their own set of answers to the problem set.

•Please feel free to visit me during office hours for assistance in answering the problem sets.

•You must show all work to receive full credit.

•Due dates will be announced when problem sets are distributed.

•Problem sets are due at the beginning of class on the due dates.

Late Problem sets will not be accepted.

Lecture Topics

Date Lecturer Topic

I. Introduction to Analytical ChemistryAug 24 Powers Basic Principles of Chemical AnalysisAug 26 “ Data Handling & Statistical MethodsAug 28 “

II. Elemental Analysisa. Classical MethodsAug 31 Powers Combustion/Classic Screening MethodsSep 2 “ Titrations/Gravimetry/Colorimetryb. Electrochemical methodsSep 4 Powers Overview of Electrochemical MethodsSep 9 “

Sep 10 (9:30 am) “ Potentiometry/PolarographySep 14 “ Voltammetry/Coulometryc. Spectroscopic MethodsSep 16 Morin Atomic SpectroscopySep 18 “

Sep 22 (6:00 pm) EXAM 1 (Tues)Sep 23 Morin X-Ray Analytical MethodsSep 25 “

III. Structure & Molecular Weight Determinationa. Mass SpectrometrySep 28 Dodds Overview of Mass SpectrometrySep 30 Dodds Ionization & AnalyzersOct 2 “Oct 5 Cerny Molecular Weight MeasurementsOct 7 Cerny Structure Determination Oct 9 Cerny Tour of mass spec facilityb. Infrared/Raman Spectroscopy Oct 12 Powers Overview of Infrared SpectroscopyOct 14 Powers Overview of Raman Spectroscopy

Oct 16 (6:00 pm) EXAM 2 (Fri)

Lecture Topics

Date Lecturer Topic c. Nuclear Magnetic ResonanceOct 21 Morton Overview of NMROct 32 Powers

Oct 26 “ Oct 28 “ Oct 30 “

Nov 2 Morton Tour of NMR facilityIV. Compound Isolation & Separation

a. ChromatographyNov 4 Hage Overview of ChromatographyNov 6 “ Gas Chromatography Nov 9 “Nov 11 “ Liquid ChromatographyNov 13 “Nov 16 Morton Tour of Research Instrument Facility

Nov 18 (6:00 pm) EXAM 3 (Wed.)Nov 20 Snow LC/MS & Environmental Analysis

V. Analysis of Mixtures & Special Topics Nov 23 Hage Hyphenated TechniquesNov 30 CernyDec 2 Powers ImmunoassaysDec 4 Lai Biosensors

Dec 7 (6:00 pm) Sinitski Scanning Electron MicroscopyDec 9 Cheung Scanning Electron MicroscopyDec 11 Powers Course Evaluation & Review

Dec 15 (10: 00 am) Final Exam (Tues.)

Introduction to Analytical Chemistry Background

A.) ANALYTICAL CHEMISTRY: The Science of Chemical Measurements.

B.) ANALYTE: The compound or chemical species to be measured, separated or studied

C.) TYPES of ANALYTICAL METHODS:

1.) Classical Methods (Earliest Techniques)a.) Separations: precipitation, extraction, distillationb.) Qualitative: boiling points, melting points, refractive index,

color, odor, solubilities

c.) Quantitative: titrations, gravimetric analysis

2.) Instrumental Methods (~post-1930’s)a.) separations: chromatography, electrophoresis, etc.b.) Qualitative or Quantitative: spectroscopy, electrochemical

methods, mass spectrometry, NMR, radiochemical methods, etc.

Introduction to Analytical Chemistry Application Examples

1.) Determination of Physiochemical Propertiesa.) Electromagnetic propertiesb.) Solubility, Viscosity, etc. c.) Reaction Ratesd.) Equilibrium Constants

2.) Determination of Compound Structurea.) Elemental Compositionb.) Functional Group Analysisc.) Structure Determination

3.) Separation of Compoundsa.) Solute Purificationb.) Mixture Analysis

4.) Analysis and Quantitation of Samplesa.) Quantitative Analysisb.) Qualitative Analysis

Choosing an Analytical Method

Defining the Experimental Problem (what factors to consider):

1.) Questions regarding the type of information desired:a.) Compound structure (elemental composition, 3D structure, etc.)b.) Physiochemical properties (mass, solubility, etc.)c.) Purity, amount, stability, reactivity, etc.d.) What compounds are present?

2.) Questons regarding the nature of the sample:a.) How much or how little sample is required?b.) How much or how little analyte can be detected?c.) What types of samples can the method be used with?d.) Will other components of the sample cause interference?

3.) Questions regarding the analytical method to be used:a.) What type of information does the method provide?b.) What are the advantages or disadvantages of the technique versus other methods?

c.) How reproducible and accurate is the technique?d.) Other factors: speed, convenience, cost, availability, skill required.

How Do We Answer or Address These Questions?

CHARACTERISTICS OF ANALYTICAL METHODS Accuracy: The degree to which an experimental result

approaches the true or accepted answer.

Ways to Describe Accuracy:

Error: An experimental measure of accuracy. The difference between the result obtained by a method and the true or accepted value.

Absolute Error = (X – )

Relative Error (%) = 100(X – )/

where: X = The experimental result = The true result

CHARACTERISTICS OF ANALYTICAL METHODS Accuracy: The degree to which an experimental result

approaches the true or accepted answer.

Ways of Measuring Accuracy:

All Methods, except counting, contain errors – don’t know “true” value

Two types of error: random or systematic

With multiple measurements (replicates), we can then apply simple statistics to estimate how close the measured values would be to the true value if there was no systematic error in the system. 

CHARACTERISTICS OF ANALYTICAL METHODS Random Error: results in a scatter of results centered on the true

value for repeated measurements on a single sample.

Systematic Error: results in all measurements exhibiting a definite difference from the true value

Random Error Systematic Error

plot of the number of occurrences or population of each measurement (Gaussian curve)

CHARACTERISTICS OF ANALYTICAL METHODS Precision: The reproducibility of results. The degree to which an

experimental result varies from one determination to the next.

Precision is related to random error and Accuracy is related to systematic error.

Low accuracy, low precision Low accuracy, high precision

High accuracy, low precision High accuracy, high precision

Illustrating the difference between “accuracy” and “precision”

CHARACTERISTICS OF ANALYTICAL METHODS Ways to Describe Precision:

Range: a list of the high to low values measured in a series of experiments.

Standard Deviation: describes the distribution of the measured results about the mean or average value.

Absolute Standard Deviation (SD):

Relative Standard Deviation (RSD) or Coefficient of Variation (CV):

where: n = total number of measurements Xi = measurement made for the ith trial = mean result for the data sample

n

i

i nXXSD1

2 )1/()(

100)/((%) XSDRSD

X

CHARACTERISTICS OF ANALYTICAL METHODS Response: The way in which the result or signal of a method

varies with the amount of compound or property being measured.

Ways to Describe Response:

Calibration Curve: A plot of the result or signal vs. the known amount of a known compound or property (standard) being measured.

sulfate calibration curvey = 14427x - 12024R2 = 0.999

0

200000

400000

600000

800000

1000000

1200000

1400000

0 10 20 30 40 50 60 70 80 90

concentration (ppm )

pea

k ar

ea

by area Linear (by area)

CHARACTERISTICS OF ANALYTICAL METHODS

Sensitivity: The change in the response of the calibration curve at a given property or amount of compound; a measure of the smallest change in the amount or property that can be detected

Ways to Measure Sensitivity:

Calibration Sensitivity: The slope of the calibration curve at a given value of the independent variable (x)

Example – for a linear curve:

y = mx + b or S = mc + Sbl

where: m = slope or calibration sensitivity b – Intercept or Sbl – instrument signal for blank

x – Independent variable or c – analyte concentration y – Dependent variable or S – measured signal

CHARACTERISTICS OF ANALYTICAL METHODS

Ways to Measure Sensitivity:

Analytical Sensitivity (): The calibration sensitivity (slope) at a given value for the independent variable (x) divided by the standard deviation of the signal obtained at the same x value

= m/SD

where: = Analytical sensitivity m = Slope at given analyte level or property SD = Standard deviation of the response at the given

property or level for the analyte

CHARACTERISTICS OF ANALYTICAL METHODS

Example: calibration curve for determination of lead S = 1.12cpb + 0.312. Ten replicate measurements for a 1.00 and 10.0 ppm Pb samples yielded 1.12 ± 0.025 and 11.62 ± 0.15, respectively.

calibration sensitivity = m = 1.12

analytical sensitivity = m/SD

= 1.12/0.025 = 45 at 1.00 ppm

= 1.12/0.15 = 7.5 at 10.0 ppm

Analytical sensitivity is typically concentration dependent – reason why not commonly reported

But, analytical sensitivity independent of amplification factors or measurement units

CHARACTERISTICS OF ANALYTICAL METHODS

Which Method has a higher sensitivity?

0

10

20

30

40

50

60

70

0 2 4 6 8 10 12

Concentration (mM)

Method A

Method B

Selectivity: The ability of a method to measure the analyte of interest vs. its ability to measure other compounds. The degree to which the method is free from interference by other species in the sample

0

10

20

30

40

50

60

70

0 2 4 6 8 10 12

Concentration (mM)

Species A

Species B

No method is totally free frominterference from other species.

Selectivity coefficient (k):

kB,A = mB/mA

Relative slopes of calibration curves indicate selectivity:

S = mA(cA + kB,Acb) + Sbl

Interested in detecting species A, but signal will be a combination of signal from the presence of species A and species

B.

CHARACTERISTICS OF ANALYTICAL METHODS

CHARACTERISTICS OF ANALYTICAL METHODS

Limits of Detection (cm ): The lowest (or highest) value of x that can be reliably determined by an analytical method.

Lower Limit of Detection: The minimum value of the independent variable (x) that can be reliably determined.

Upper Limit of Detection: The maximum value of the independent variable (x) that can be reliably determined.

Which are the real peaks?

?

CHARACTERISTICS OF ANALYTICAL METHODS Ways to Measure Limit of Detection:

Signal-to-noise Ratio (S/N):

Noise: random variation in signal or background that is associated with the response of a method

Signal: net response recorded by a method for a sample

Signal-to-Noise Ratio: The ratio of the response produced by a sample divided by the noise level

Note: a value of S/N = 2 or 3 is considered to be the minimum ratio needed for the reliable detection of a true signal from a sample

Signal

Noise

S/N = 3

CHARACTERISTICS OF ANALYTICAL METHODS Ways to Estimating Signal-to-Noise Ratios:

1.) Multiple determination of blank samples and samples containing analyte levels or properties approaching the detection limit

2.) Estimation from best-fit lines to calibration curves

Sign

al (

S)

Concentration (c)

Use best-fit line to determine the amount of analyte (c) that will give a minimum signal (Sm) that is equal to the signal at the intercept plus three or two times the standard deviation (sbl) of the intercept’s value (i.e., S/N = 2 or 3)

Sm = + 3sblblS

cm = (minimum analyte signal (Sm) - mean blank signal( ))/slope(m)blS

CHARACTERISTICS OF ANALYTICAL METHODS Ways to Characterize a Calibration Curve:

Assay range: The range of analyte levels or properties over which the method gives a reliable response

Linear range: The range of x values that produces a linear change in the response

Found by determining what range gives a response that falls within ± 5% (or some other fixed value) of that predicted by a best-fit line through the data

Linear range

CHARACTERISTICS OF ANALYTICAL METHODS Ways to Characterize a Calibration Curve:

Dynamic range: The range of x values that produces any change in the response

Found by determining the upper and lower limits of the detection for the assay. The dynamic range always includes the linear range

Additional analyte does not result in an increase in response

Example: The data in the table below were obtained during a colorimetric determination of glucose in blood serum.

A serum sample gave an absorbance of 0.350. Find the glucose concentration and its standard deviation, calibration sensitivity, detection limit and dynamic range.

Glucose Concentration, mM

Absorbance, A

0.0 0.002

2.0 0.150

4.0 0.294

6.0 0.434

8.0 0.570

10.0 0.704

CHARACTERISTICS OF ANALYTICAL METHODS Learning Objectives:

1.The student should be familiar with the general definition of “Analytical Chemistry” and some examples of the application of this field.

2.The student should be able to discuss various questions and items that need to be considered in the design, selection, and comparison of analytical methods

3.The student should be able to define and describe various terms used in the characterization of analytical methods, including:

Accuracy Precision Sensitivity Limits of Detection Error Response Selectivity Calibration Curves

4.The student should be familiar with common formulas and parameters used in

quantitating the above properties of analytical methods, including:

Absolute Error Relative Error Standard DeviationRelative Standard Deviation Range Coefficient of VariationLower Limit of Detection Upper Limit of Detection Calibration SensitivityAnalytical Sensitivity Signal-to-Noise Ratio Linear RangeDynamic Range

5.The student should know how to use the above procedures and parameters in the characterization of results from analytical methods