PROBLEMS IN ANALYTICAL CHEMISTRY
CHEM 824, Spring 2015
MWF 9:30-10:20, Rm 130, Hamilton Hall
COURSE OUTLINE
Instructor: Dr. Robert Powers
Office
Labs
Address: 722 HaH
721 HaH
Phone: 472-3039
472-5316
e-mail:rpowers3@unl.edu
web 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:
Exam 2:
Exam 3:
Final:
Problem Sets:
Total:
100 pts.
100 pts.
100 pts.
100 pts.
150 pts.
550 pts.
(Tues., Sept. 22)
(Fri., Oct. 16)
(Wed., Nov. 18)
(10-12, Tues., Dec. 15)
(various due dates)
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.
Course Outlined (cont.)
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.)
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
I. Introduction to Analytical Chemistry
Aug 24
Powers
Aug 26
“
Aug 28
“
II. Elemental Analysis
a. Classical Methods
Aug 31
Powers
Sep 2
“
b. Electrochemical methods
Sep 4
Powers
Sep 9
“
Sep 10 (9:30 am)
“
Sep 14
“
c. Spectroscopic Methods
Sep 16
Morin
Sep 18
“
Sep 22 (6:00 pm)
Sep 23
Morin
Sep 25
“
III. Structure & Molecular Weight Determination
a. Mass Spectrometry
Sep 28
Dodds
Sep 30
Dodds
Oct 2
“
Oct 5
Cerny
Oct 7
Cerny
Oct 9
Cerny
b. Infrared/Raman Spectroscopy
Oct 12
Powers
Oct 14
Powers
Oct 16 (6:00 pm)
Topic
Basic Principles of Chemical Analysis
Data Handling & Statistical Methods
Combustion/Classic Screening Methods
Titrations/Gravimetry/Colorimetry
Overview of Electrochemical Methods
Potentiometry/Polarography
Voltammetry/Coulometry
Atomic Spectroscopy
EXAM 1 (Tues)
X-Ray Analytical Methods
Overview of Mass Spectrometry
Ionization & Analyzers
Molecular Weight Measurements
Structure Determination
Tour of mass spec facility
Overview of Infrared Spectroscopy
Overview of Raman Spectroscopy
EXAM 2 (Fri)
Lecture Topics
Date
Lecturer
c. Nuclear Magnetic Resonance
Oct 21
Morton
Oct 32
Powers
Oct 26
“
Oct 28
“
Oct 30
“
Nov 2
Morton
IV. Compound Isolation & Separation
a. Chromatography
Nov 4
Hage
Nov 6
“
Nov 9
“
Nov 11
“
Nov 13
“
Nov 16
Morton
Nov 18 (6:00 pm)
Nov 20
Snow
V. Analysis of Mixtures & Special Topics
Nov 23
Hage
Nov 30
Cerny
Dec 2
Powers
Dec 4
Lai
Dec 7 (6:00 pm)
Sinitski
Dec 9
Cheung
Dec 11
Powers
Dec 15 (10: 00 am)
Topic
Overview of NMR
Tour of NMR facility
Overview of Chromatography
Gas Chromatography
Liquid Chromatography
Tour of Research Instrument Facility
EXAM 3 (Wed.)
LC/MS & Environmental Analysis
Hyphenated Techniques
Immunoassays
Biosensors
Scanning Electron Microscopy
Scanning Electron Microscopy
Course Evaluation & Review
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, distillation
b.) 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 Properties
a.) Electromagnetic properties
b.) Solubility, Viscosity, etc.
c.) Reaction Rates
d.) Equilibrium Constants
2.) Determination of Compound Structure
a.) Elemental Composition
b.) Functional Group Analysis
c.) Structure Determination
3.) Separation of Compounds
a.) Solute Purification
b.) Mixture Analysis
4.) Analysis and Quantitation of Samples
a.) Quantitative Analysis
b.) 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 – m)
Relative Error (%) = 100(X – m)/m
where:
X = The experimental result
m = 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.
Illustrating the difference between “accuracy” and “precision”
Low accuracy, low precision
High accuracy, low precision
Low accuracy, high precision
High accuracy, high 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):
SD 
n
2
(
X
i

X
)
/( n  1)

i 1
Relative Standard Deviation (RSD) or
Coefficient of Variation (CV):
RSD (%)  ( SD / X )100
where: n = total number of measurements
Xi = measurement made for the ith trial
X = mean result for the data sample
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 curve
y = 14427x - 12024
R2 = 0.999
1400000
1200000
peak area
1000000
800000
600000
400000
200000
0
0
10
20
30
40
50
60
concentration (ppm )
by area
Linear (by area)
70
80
90
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 (g): 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
g = m/SD
where:
g = 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
g = 1.12/0.025 = 45 at 1.00 ppm
g = 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?
70
60
50
Method A
40
30
Method B
20
10
0
0
2
4
6
8
Concentration (mM)
10
12
CHARACTERISTICS OF ANALYTICAL METHODS
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
70
No method is totally free from
interference from other species.
60
50
Selectivity coefficient (k):
40
Species A
kB,A = mB/mA
30
20
Relative slopes of calibration
curves indicate selectivity:
Species B
10
S = mA(cA + kB,Acb) + Sbl
0
0
2
4
6
8
10
12
Concentration (mM)
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
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
S/N = 3
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
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
cm = (minimum analyte signal (Sm) - mean blank signal(Sbl))/slope(m)
2.) Estimation from best-fit lines to calibration curves
Signal (S)
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)
Concentration (c)
Sm = Sbl + 3sbl
CHARACTERISTICS OF ANALYTICAL METHODS
Ways to Characterize a Calibration Curve:
Assay range:
method
The range of analyte levels or properties over which the
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
for the
Found by determining the upper and lower limits of the detection
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.
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
A serum sample gave an absorbance of 0.350. Find the glucose concentration and its
standard deviation, calibration sensitivity, detection limit and dynamic range.
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
Error
Precision
Response
Sensitivity Limits of Detection
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 Standard Deviation
Lower Limit of Detection
Analytical Sensitivity
Dynamic Range
Relative Error
Range
Upper Limit of Detection
Signal-to-Noise Ratio
Standard Deviation
Coefficient of Variation
Calibration Sensitivity
Linear Range
5. The student should know how to use the above procedures and parameters in the
characterization of results from analytical methods