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)

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: Composition of a metal alloy GC: Gas phase quantitation

titrations

Chapter 1:Chemical Measurements

Chemical Concentrations

liter

moles(M)Molarity

L

mg

grams 1000

mg

grams10

grams10

grams10

gram 1 ppm

3

-3

6

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

precision = reproducibility of the measurement

Significant Figures

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

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

6077063.56542

ans = 63.5

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

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, round UP if result is EVEN

158.5 = 158157.5 = 157

Wait until the END of a calculation in order to Wait until the END of a calculation in order to avoid a “rounding error”avoid a “rounding error”

(1.23(1.2355 - 1.0 - 1.022) x 15.23) x 15.2399 = 2.923438 = = 2.923438 = 1.11.122

1.231.2355-1.0-1.022

0.20.21515 = 0.2 = 0.222

? sig figs? sig figs 5 sig figs5 sig figs

3 sig figs3 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%

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 0.15129.31 et

......eeee

......eeee

2

3

2

2

2

1t

2

3

2

2

2

1

2

t

Multplication & Division

......ee%ee

......eeee

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*0.03e

222

t

222 )4.3()1.1(

Combined Example

0.35)( 2.57

0.020)( 0.25 0.10)( 1.10

Chapter 4:Statistics

Gaussian Distribution:

Fig 4.2

22 2/)(exp2

1);;(

ii xxP

N

xN

ii

1

2)(

1

)(1

2_

N

xx

s

N

ii

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

iixN

1

1lim

Infinite population

N

iixN

x1

_ 1

Finite population

N

Standard Deviation and Probability

Confidence Intervals

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

_

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

Rejection of Data - the "Q" Test

A way to reject data which is outside the parent population.

value smallest-value largest

neighbor nearestvalue lequestionabQexp

Compare to Qcrit from a table at a given confidence interval.

Reject if Qexp > Qcrit

Example: Analysis of a calcite sample yielded CaO percentages of 55.95, 56.00, 56.04, 56.08, and 56.23. Can the last value be rejected at a confidence interval of 90%?

Linear Least Squares- finding the best fit to a straight line