Download Analytical Chemistry is Scientific Practice that Tells Us

Chemistry 310; Course Mechanics
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Analytical Chemistry is Scientific
Practice that Tells Us
- What compounds are in a sample, chemical composition?
Qualitative Analysis
- What is the concentration of a compound in a sample?
Quantitative Analysis (the majority of this class)
-The chemical and physical properties of the compounds of interest
are important
- Methods can be “wet chemical” or “instrumental” based
- Determining what is in a sample is harder than determining if a
particular compound is in a sample
- Trace analysis is more difficult than bulk analysis
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Chemistry 310; Section I – Basic Concepts and Error Analysis
-Chapters 0-2 will be glossed over (it should be mostly review, but you to read)
and no recommended problems
- Chapters 3-5 involve error analysis, statistics, etc. (see recommended problems)
Analytical Chemistry As It Relates Broadly to Other Areas
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Steps in An Analytical Method
ÅOften from the literature
Homogeneous & heterogeneous samples Æ
e.g., selectively
derivatize to Æ
ÅSometimes involves a
“chemical separation”
ÅOur resulting # is never
absolutely certain
An example of an analysis problem from another text
(a deer kill) will be covered
Skimming Over Chapter 1
Chapter 2 is largely lab related (read on your own)
Quantities
Most Important to Us - measures of amount and concentration
- amount – moles; grams; etc.
- concentration – molar, normal, part per something (ppm, ppb, etc.); pFunctions
- prefixes: ten to the 3(kilo), 6(mega), -3(milli), -6(micro), -9(nano), -12(pico), ...-24(yocto)
Some Problems
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Chapters 3-5 – Data Treatment
Some quotes on this topic –
“… because data of unknown reliability are worthless.”
“Indeed, the effort involved in establishing the quality of experimental results
is frequently comparable to the effort expended in obtaining them.”
“… a scientist can’t afford to waste time in the pursuit of greater
reliability than is needed.”
Or from the Harris text
“
”
Precision –
A measure of the reproducibility of a measurement.
Accuracy –
A measure of how close a measured value is
to the “true” value.
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Significant Figures
Significant Figures are important because they
communicate how precisely a value is known
experimentally – How good is the number (value)?
Someone’s weight:
Rounding Errors
(Don’t drop insignificant
figures until you report a value).
Uncertainty
200 lbs
Implied in last
201.6 lbs digit
2.016 x 102 lbs
2.0 x 102 lbs
0.1 tons
0.1008 tons
Systematic (Determinate) Error
This type of error is reproducible and results from a
problem with equipment, experiment design, or even
personal. In principle it’s source can be discovered and
eliminated.
ACCURACY
To Detect Systematic Error
• Analyze samples of known composition – Standard Reference Materials
(Does the measured quantity match what is expected?).
• Analyze a “blank” sample (Is the response 0?).
• Measure the the quantity using two different methods (Do both techniques
give the same value?).
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Example of a “Method Type” Systematic Error
The Kjeldahl method (see p. 132) for determining the nitrogen in a sample is
a wet chemical analysis involving reactions and a titration. Its success depends
on the chemical form of the nitrogen in the sample (note – it can’t deal
well with the type in nicotinic acid as results are systemically low)
ÅAnother example of
both accuracy and
precision factors
ÅThe N in Nicotinic acid –
Pyridine with a carboxylic
acid group – is not completely
Reduced to NH4+
Random (Indeterminate) Error
This type of error arises from uncontrolled variables in
the measurement and has an equal chance of being
positive or negative. It can be reduced but never
eliminated.
PRECISION
Uncertainty
Uncertainty in measured quantities is commonly
expressed as ± a numerical value: 5.23 ± 0.03 mM
• Uncertainty can be estimated.
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Absolute Uncertainty
8.102 ± 0.003 g
⇒
0.003 g
Relative Uncertainty
8.102 ± 0.003 g
⇒
0.003 g
= 0.0004
8.102 g
Percent Relative Uncertainty
8.102 ± 0.003 g
⇒
0.003 g
× 100% = 0.04%
8.102 g
Propagation of Uncertainty
What is the resulting error when measured quantities with errors
are used in calculations – How does error propagate?
et =
e 12 + e 22 + e 32 .....
+ and -
%et = %e12 + %e 22 + %e32 .....
X and
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Statistics
Experimental scientists use statistics to
define, quantify, understand and reduce
experimental error.
In this course we will primarily use
statistics to define and quantify random
(indeterminate) error associated with
experiments – Precision!
Gaussian Distributions
•All experiments have some random error.
•If a measurement is made multiple times, the data distribute
themselves to form a Gaussian distribution (e.g. Figures 4-1, 4-2).
•The overall shape of the curves don’t change, but the width of the
curve does change. Wide distributions (broad curves) mean poor
precision. Narrow distributions (sharp curves) mean good precision.
Some Statistical Terms
• The mean defines the
center of the Gaussian
distribution.
x=
∑x
i
n
i
• The Standard Deviation
defines the width of the
Gaussian distribution.
s=
∑ (x
i
− x) 2
i
n −1
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A Physical Picture of the
Gaussian Error Curve
Hypothetical case of calibrating a pipet – steps:
1. Fill with water; 2. Dispense into weighing vessel;
3. Weigh; 4. Measure temperature
Some More Statistical Terms
u
x
σ
If we use
in place of
and we use
in place
of
, this means the measurement has been repeated
an “a very large” number of times (see Table 4.2).
s
Degrees of Freedom = n-1
Variance = s2
Relative Standard Deviation (RSD) and Coefficient of
Variation (CV) are both: 100% ⋅ s / x
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LECTURE 1-20-04 Review Questions
What are the differences between systematic and random errors?
Associate propagation of uncertainties of math operations with absolute
or relative uncertainties?
What is CV?
What is the equation for a Gaussian error curve?
&
How does one report Confidence Limits?
Area Under A Gaussian Error Curve
~ 95 % of the entire
Error curve is between
+2s
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Reporting the Mean of a Measurement with Confidence Limits
When s is a good estimate of σ
CL for µ = x + z σ / N1/2
z values found in table
You will not
Be tested on
Å this
When s is a not a good estimate of σ
CL for µ = x + t s / N1/2
t values found in table
Comparison of Means Cases
Case 1: Is the measured value different than a “known” value?
tcalculated
x − known value
=
n
s
If tcalculated is greater than ttable (Tab 4.2),
then the answer is Yes – there is greater
than a XX% (which t used) probability that
they are different.
Case 2: Are the “true values” of two sets of replicate
measurements different?
tcalculated
x −x
= 1 2
s pooled
s pooled =
n1n2
n1 + n2
s12 (n1 − 1) + s22 (n2 − 1)
n1 + n2 − 2
If tcalculated is greater than ttable , then the
answer is Yes – there is greater than a XX%
(which t used) probability that they are
different.
Be able to deal with “pooled data”
Case 3: From Text - Skip altogether
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F-test to Determine if Separate Sets of Data are
Significantly Different
Fcalc = s12 / s22
If Fcalc is greater than Ftab then the standard
deviations are significantly different
Work Problem 4-13
Q Test to Reject (or not) Suspect Data
• If you know you made a significant experimental error while making a
measurement, make a note in you lab notebook and do not use the
measurement.
• If you see a value that seems anomalous, but you don’t know what
happened, you can use the Q test to decide if it might make sense to
discard this value (or repeat the experiment more times to be more
certain of your result).
Qcalculated =
gap
range
If Qcalculated is greater than Qtable it may be reasonable to discard the data point.
Work Q test question from “placekicker ?”
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Calibration Plots Take Different Forms
External Standard
Known analyte concentrations for several
Solutions spanning expected range of unknowns
Standard Addition
Internal Standard with each above
Also contains a compound that
“resembles” the analyte and is at a
known concentration
Most calibration plots come from
inherently linear relationships (e.g.,
Abs = Constant x Concentration)
or are made so (as with the log
plot shown at left)
However the plots do exhibit a “LDR”
Method of Least Squares
How do we determine the “best” fit of a linear calibration curve:
y = mx + b ?
• Know how to do this with a calculator or spreadsheet.
• Understand what the computer programs are doing.
What is our handy program doing?
• Basically……The program assumes the values on the x-axis are correct/true –
all error is in the y values.
• The program then minimizes the squares of the vertical deviations – it finds
values of m and b that result in this minimum (for all the data points).
•R and R2 (correlation coefficients, regression coefficients) are measures of
how “good” the fit is. The closer to 1, the better the fit.
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Least Squares Determinations (Text Figure)
We will ignore the math
(simply use calculator or spread sheet)
Work Problem 5-10
Standard Addition Techniques
•This approach is effective when there are significant matrix effects – the
instrument response can be increase or decrease “affected” due to the presence
of sample components other than the analyte.
•Known quantities of analyte are added to the unknown. The increase in
signal is used to determine the unknown analyte concentration.
•This approach assumes (requires) the response to be linear for modest changes
in concentration near the unknown concentration of analyte in the sample.
[X ]i
[S ] f + [X ] f
=
IX
I S+X
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Internal Standards
Internal standards are useful if your instrument or
technique response is not stable (drifts) or if you have
concerns about sample loss during the experiment.
- Add a known concentration of a standard as early as is feasible during the
experiment.
- The signal from the unknown analyte is compared to the signal for the internal
standard to determine the concentration of the unknown analyte in the sample.
- The relative response of the internal standard to the analyte must be known
through calibration and must be constant over a range of concentrations! It must
be possible to detect the internal standard selectively in the presence of the
analyte (often separations are needed)!
- However it is desirable that the internal standard process (e.g., is extracted if
extractions involved) similarly to the analyte.
- More on Standard Addition and Internal Standards later
PROBLEM: A driver of a car is arrested after a fatal accident. The
legal blood alcohol level in TN is 0.08%. The driver’s
blood alcohol level was measured 4 times: 0.078%, 0.081%,
0.082%, 0.080%. Calculate the mean blood alcohol level and the
standard deviation. Calculate the confidence interval at 90% and
99.9%. Based on these measurements, would you want to send the
driver to prison for the deaths of the victims?
0.078%, 0.081%, 0.082%, 0.080%.
u=x±
u90%
x = 0.080 25
s = 0.00171
ts
df = 3 t90% = 2.353 t99.9% = 12.924
n
2.353 × 0.00171
= 0.08025 ±
= 0.0803 ± 0.0020
4
u99.9% = 0.08025 ±
12.924 × 0.00171
= 0.080 ± 0.011
4
2
To get 0.0803±0.0002
What if s was a σ?
2
⎛ ts ⎞ ⎛ 3.3 × 0.00171 ⎞
n=⎜
⎟ =⎜
⎟ = 796.1
⎝ 0.0002 ⎠ ⎝ 0.0002 ⎠
Then one needs a table for z not t.
Work more problems
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0.1 L
Standard Addition Problem
A spectrophotometric method for the quantitative determination of the
concentration of Pb2+ in blood yields a signal of 0.712 for a 5.00-mL sample of
blood. After spiking the blood with 5.00 µL of a 1560-ppb Pb2+ standard (5.00
µL spike added to 5.00 mL sample), a signal of 1.546 is measured. Determine
the concentration of Pb2+ in the original sample of blood.
[X ]i
[S ] f + [X ] f
[X ]f = [X ]i V0 = [X ]i
V
[S ]f
= 1560 ppb
=
IX
I S+X
5.00 mL
= 0.999[ X ]i
5.005 mL
5 × 10−3 mL
= 1.56 ppb
5.00 mL
[X ]i
1.56 ppb + 0.999[X ]i
=
0.712
1.546
[X ]i = 1.33 ppb
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Mean = Σxi/N = -6 + -5 + 2(-4) ….. / 31
= -1.32
The middle value falls in the 8 at –2 m group
Mean – x correct = -1.32 m
Q concept covered later
σ = [Σ(xi – µ)2 / N ]1/2
= 2.31 m (use calculator)
If he corrects his systematic error his mean value will change from –1.32 m to 0 m (dead center)
With σ or s = 1.25 the uprights are + and - two standard deviations from the mean. From
Table 4.1 ~95% of the error curve falls in this range
+ = ts/N½
=
4.3 (1.25 m) / 3 ½ = + 3.1 m
Systematic
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Example Problems
Example Problems
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Section I Learning Topics
Chapter 3
-Carrying through correct significant figures in simple (add, subtract, multiply, divide) math
operations
-Know difference between the following:
systematic and random errors
accuracy and precision
absolute and relative uncertainty
-Be able to compute uncertainty in simple math operations
Chapter 4
- Understand the significance of the Gaussian-shape error curve and area under curve
- Be able to compute means and standard deviations
- Be able to calculate confidence intervals (using t-tables)
- Be able to compute standard deviation from pooled data
- Q testing for questionable data
Chapter 5
- Be able to generate equations of linear calibration plots using your calculator; determine slope,
intercept, and given a y-value (signal) calculate and x-value (unknown concentration)
- Understand difference between external calibration and standard addition calibration methods
- Be able to perform calculations for the standard addition method
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