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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

5

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 UP158.7 = 159

digit to be dropped < 5, round DOWN158.4 = 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*100x1

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 0.1242.98 0.2243.06 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

23

22

21t

23

22

21

2t

%%

%%%

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

xN

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

x1

_ 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 critG

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