Transcript Analytical Chemistry

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
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develop good lab habits and technique
background in classical “wet chemical”
methods (titrations, gravimetric analysis,
electrochemical techniques)
Quantitation using instrumentation (UV-Vis,
AAS, GC)
Analyses you will perform
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Basic statistical exercises
%purity of an acidic sample
%purity of iron ore
titrations
%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
Chapter 1:
Chemical Measurements
Example, p. 15: convert 0.27 pC to electrons
Chemical Concentrations
moles
Molarity (M) 
liter
1 gram
10 -3 grams
mg
mg
ppm  6
 3


10 grams 10 grams 1000 grams
L
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
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
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Digits in a measurement which are known with
certainty, plus a last digit which is estimated
beaker
graduated cylinder
buret
Rules for Determining How Many Significant
Figures There are in a Number
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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
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Multiplication/Division
Rule: Round off to the
fewest number of sig figs
originally present
12.154
5.23
36462
24308
60770
63.56542
ans = 63.5
Reporting the Correct # of Sig Fig’s
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Addition/Subtraction
15.02
9,986.0
3.518
10004.538
Rule: Round off to the least certain decimal place
Reporting the Correct # of Sig Fig’s
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Addition/Subtraction in Scientific Notation
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
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Logs and anti-logs
Rounding Off Rules
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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
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BUT
157.5 = 158.0
158.501 = 159.000
Wait until the END of a calculation in order to
avoid a “rounding error”
? sig figs
5 sig figs
(1.235 - 1.02) x 15.239 = 2.923438 =
1.12
3 sig figs
1.235
-1.02
0.215 = 0.22
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%
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
e 2t  e12  e 22  e 32  ......
e t  e12  e 22  e 32  ......
Multplication & Division
%e 2t  %e12  %e22  %e32  ......
1.76 ( 0.03) x 1.89 ( 0.02)
0.59 ( 0.02)
%e t  %e12  %e22  %e32  ......
2
2
 0.03 * 100   0.02 * 100   0.02 * 100 
%e t  
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 1.76   1.89   0.59 

1.7 2  (1.1) 2  (3.4) 2
 4.0%
2
Combined Example
1.10 ( 0.10)  0.25 ( 0.020)
2.57 ( 0.35)
Chapter 4:
Statistics
Gaussian Distribution: P( xi ;  ;  ) 
1
 2
exp  ( xi   ) 2 / 2 2
Fig 4.2
Mean – measure of the central tendency or average of the data
(accuracy)
1
  lim
NN
N

xi
_
x 
i 1
Infinite population
N
x
1
N
i
i 1
Finite population
Standard Deviation – measure of the spread of the data
(reproducibility)
N
 (x
i
 
 )
N
2
i 1
N
Infinite population
 (x
i
s 
_
 x) 2
i 1
N 1
Finite population
Standard Deviation and Probability
Confidence Intervals
Confidence Interval of the Mean
The range that the true mean lies within at a given confidence interval
True mean “” lies within this range
_
μ x 
ts
N
ts
ts
N
N
x
Example - Calculating Confidence Intervals
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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)
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= 12.55 ± (0.465)(2.776)/sqrt(5)
= 12.55 ± 0.58
Rejection of Data - the Grubbs Test
A way to statistically reject an “outlier”
G crit 
outlier  X
s
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
Linear Least Squares (Excel’s “Trendline”)
- finding the best fit to a straight line