analytical chemistry - western oregon universitypostonp/ch312/pdf/ch312...analytical chemistry...
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1
Analytical Chemistry
Definition: the science of extraction, identification, and
quantitation of an unknown sample.
Example Applications:
•Human Genome Project
•Lab-on-a-Chip (microfluidics) and Nanotechnology
•Environmental Analysis
•Forensic Science
Course Philosophy
develop good lab habits and technique
background in classical “wet chemical”
methods (titrations, gravimetric analysis,
electrochemical techniques)
Quantitation using instrumentation (UV-Vis,
AAS, GC)
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Analyses you will perform
Basic statistical exercises
%purity of an acidic sample
%purity of iron ore
%Cl in seawater
Water hardness determination
UV-Vis: Amount of caffeine and sodium benzoate in a
soft drink
AAS: %Cu in pre- and post-1982 pennies
GC: Gas phase quantitation using an internal standard
titrations
Chapter 1:Chemical Measurements
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4
Example, p. 15: convert 0.27 pC to electrons
Chemical Concentrations
liter
moles(M)Molarity
L
mg
grams 1000
mg
grams10
grams10
grams10
gram 1 ppm
3
-3
6
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Example, p. 19: Molarity of Salts in the Sea
(a) Calculate molarity of 2.7 g NaCl/dL
(b) [MgCl2] = 0.054 M. How many grams in 25 mL?
Dilution Equation
Concentrated HCl is 12.1 M. How many
milliliters should be diluted to 500 mL to
make 0.100 M HCl?
M1V1 = M2V2
(12.1 M)(x mL) = (0.100 M)(500 mL)
x = 4.13 M
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Chapter 3:Math Toolkit
accuracy = closeness to the true or accepted value
(given by the AVERAGE)
precision = reproducibility of the measurement
(given by the STANDARD DEVIATION)
Significant Figures
Digits in a measurement which are known with
certainty, plus a last digit which is estimated
beaker graduated cylinder buret
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Rules for Determining How Many Significant Figures There are in a Number
All nonzero digits are significant (4.006, 12.012,
10.070)
Interior zeros are significant (4.006, 12.012, 10.070)
Trailing zeros FOLLOWING a decimal point are
significant (10.070)
Trailing zeros PRECEEDING an assumed decimal
point may or may not be significant
Leading zeros are not significant. They simply locate
the decimal point (0.00002)
Reporting the Correct # of Sig Fig’s
Multiplication/Division 12.154
5.23
Rule: Round off to the
fewest number of sig figs
originally present
36462
24308
60770
63.56542
ans = 63.5
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Reporting the Correct # of Sig Fig’s
Addition/Subtraction 15.02
9,986.0
3.518
Rule: Round off to the least certain decimal place
10004.538
Express all of the numbers with the same exponent first:
1.632 x 105
+ 4.107 x 103
+ 0.984 x 106
Reporting the Correct # of Sig Fig’s
Addition/Subtraction in Scientific Notation
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Reporting the Correct # of Sig Fig’s
Logs and anti-logs
Rounding Off Rules
digit to be dropped > 5, round UP
158.7 = 159
digit to be dropped < 5, round DOWN
158.4 = 158
digit to be dropped = 5, make answer EVEN
158.5 = 158.0 157.5 = 158.0
BUT 158.501 = 159.000
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Wait until the END of a calculation in order to avoid a “rounding error”
(1.235 - 1.02) x 15.239 = 2.923438 =1.12
1.235
-1.02
0.215 = 0.22
? sig figs 5 sig figs
3 sig figs
Propagation of Errors
A way to keep track of the error in a calculation
based on the errors of the variables used in the
calculation
error in variable x1 = e1 = "standard deviation" (see Ch 4)
e.g. 43.27 0.12 mL
percent relative error = %e1 = e1*100
x1
e.g. 0.12*100/43.27 = 0.28%
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Addition & Subtraction
Suppose you're adding three volumes together and
you want to know what the total error (et) is:
43.27 0.12
42.98 0.22
43.06 0.15
129.31 et
......eeee
......eeee
2
3
2
2
2
1t
2
3
2
2
2
1
2
t
Multplication & Division
......ee%e%e
......eee%e
2
3
2
2
2
1t
2
3
2
2
2
1
2
t
%%
%%%
0.02)( 0.59
0.02)( 1.89 x 0.03)( 1.76
4.0%
1.7
0.59
100*0.02
1.89
100*0.02
1.76
100*0.03%e
222
t
222)4.3()1.1(
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Combined Example
0.35)( 2.57
0.020)( 0.25 0.10)( 1.10
Chapter 4:Statistics
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Gaussian Distribution:
Fig 4.2
22 2/)(exp2
1);;(
ii xxP
N
x
N
i
i
1
2)(
1
)(
1
2_
N
xx
s
N
i
i
Standard Deviation – measure of the spread of the data
(reproducibility)
Infinite population Finite population
Mean – measure of the central tendency or average of the data
(accuracy)
N
i
ixN
1
1lim
Infinite population
N
i
ixN
x
1
_ 1
Finite population
N
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Standard Deviation and Probability
Confidence Intervals
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Confidence Interval of the Mean
The range that the true mean lies within at a given confidence interval
x
True mean “” lies within this range
N
ts
N
ts
N
ts xμ
_
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Example - Calculating Confidence Intervals
In replicate analyses, the carbohydrate content of a
glycoprotein is found to be 12.6, 11.9, 13.0, 12.7, and
12.5 g of carbohydrate per 100 g of protein. Find the
95% confidence interval of the mean.
ave = 12.55, std dev = 0.465
N = 5, t = 2.776 (N-1)
= 12.55 ± (0.465)(2.776)/sqrt(5)
= 12.55 ± 0.58
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Rejection of Data - the Grubbs Test
A way to statistically reject an “outlier”
s
Xoutlier expG
Compare to Gcrit from a table at a given confidence
interval.
Reject if Gexp > Gcrit
Sidney: 10.2, 10.8, 11.6
Cheryl: 9.9, 9.4, 7.8
Tien: 10.0, 9.2, 11.3
Dick: 9.5, 10.6, 11.3
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Linear Least Squares (Excel’s “Trendline”)- finding the best fit to a straight line