University of San Francisco Chemistry 260: Analytical Chemistry Dr. Victor Lau Room 413, Harney Hall, USF lauv@ace.usfca.edu.

University of San FranciscoChemistry 260: Analytical

Chemistry

Dr. Victor Lau

Room 413, Harney Hall, USF

lauv@ace.usfca.edu

What is Analytical Chemistry Using chemistry principle on analyzing

something “unknown”…. Qualitative Analysis: the process of

identifying what is in a sample Quantitative Analysis: the process of

measuring how much of the substance is in a sample.

Here is the SAMPLE … DO NOTHING ON THE RECEIVED

SAMPLE !!!!!!!!!! LOOK AT THE SAMPLE Report all your observations on the log

book before doing any non-destructive or destructive analysis

Reading a Burette 1The diagram shows a portion of a burette. What is the meniscus reading in milliliters?

A. 24.25

B. 24.00

C. 25.00

D. 25.50reference: http://www.sfu.ca/chemistry/chem110-111/Lab/titration.html

Reading a Burette 2

How about this is?

A. 41.00

B. 41.10

C. 41.16

D. 41.20

Reading a Burette A 50 mL burette can be read to ± 0.01 ml, and the last digit is

estimate by visual inspection. However, in order to be able to interpolate to the last digit, the perpendicular line of sight must be followed with meticulous care. Note in these two photographs, one in which the line of sight is slightly upward and the other in which it is downward, that an interpolation is difficult because the calibration lines don't appear to be parallel.

upward downward perpendicular

Section I: Math Toolkit I: Significant Figures

Significant Figures is the minimum number of digits needed to write a given value in scientific notation without the loss of accuracy.

To be simple, sig. figs = meaningful digits 9.25 x 104 3 sig. figs. 9.250 x 104 4 sig. figs

9.2500 x 104 5 sig. figs

Significant Figures in Arithmetic Addition and Subtraction

If the numbers to be added or subtracted have equal numbers of digits, the answer goes to the same decimal place as in any of the individual numbers.

e.g.

)(KrF4 806 6121.79

(Kr)83.80

(F)2 403 18.998

(F)2 403 18.998

2

tsignificannot

Significant Figures in Arithmetic Multiplication and Division

In multiplication and division, we are normally limited to the number of digits contained in the number with the fewest significant figures.

e.g.

14.05

87 2.462

34.60

5-

-5

10 x 5.80

1.78

10 x 3.26

Significant Figures in Arithmetic Logarithms and Antilogarithms

log y = x, means y = 10x

A logarithm is composed of a characteristic and a mantissa

log 339 = 2 .530 characteristic mantissa

# of digits in the mantissa = # of sig. fig in the original number

log 1,237 = 3.0924

Types of Error Every measurement has some uncertainty,

which is called Experimental Error Experimental Error can be classified as

Systematic, Random; and Gross Error

Experimental Error

Systematic Error

Consistent tendency of device to read higher or lower than true value

e.g. uncalibrated buret

Random Error

“noise”

Unpredicted

Higher and lower than true value

Gross Error

Due to mistake

Precision and Accuracy Precision is a measure of the reproducibility or

a result Accuracy refers to how close a measured

value is to the “true “ value

Absolute and Relative Uncertainty

0.2% 0.002 100 e.g.

yuncertaint relative 100 y uncertaint Percentage

0.00212.35ml

0.02ml e.g.

tmeasuremen of magnitude

yuncertaint absolute y uncertaint Relative

Propagation of Uncertainty When we used measured values in a

calculation, we have to consider the rules for translating the uncertainty in the initial value into an uncertainty in the calculated value. A simple example of this is the subtraction for two buret readings to obtain a volume delivered

Addition and Subtraction

14

23

22

214

4

3

2

1

04.0104.0)02.0)02.0()03.0(e is,that

e e e e as, where

)e ( 3.06

e0.02)( 0.59 -

e 0.02)( 1.89

e 0.03)( 1.76

222

e1, e2, and e3 is the uncertainty of the measurements, respectively.

e4 is the total uncertainty after addition/subtraction manipulation

Although there is only one significant figure in the uncertainty, we wrote it initially as 0.041, with the first insignificant figure subscripted.

Therefore, percentage of uncertainty = 0.041/3.06 x 100% = 1.3% = 1.3%

3.06 (+/- 0.04) (absolute uncertainty), or 3.06 (+/- 1%)

Multiplication and Division

yuncertaint relative 4%)( 5.6 y);uncertaint (absolute 0.2)( 5.6

have, weSo

0.2 5.6 x 0.04 5.6 %4.

%)4.( 5.6 isanswer

%.4%).3(%).1(%).1(%

64.5%).3(59.0

%).1(89.1%).1(76.1or 64.5

0.02)( 0.59

0.02)1.89( 0.03)( 1.76

example,for

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Its Now Your TURNS

volume

mass density remember,you do Hey,

digits of no.correct y with uncertaint th density wi theFind (ii) volumeand massin ty uncertaini relative % Find (i)

0.05ml 1.13 volume0.002g 4.635 mass

materialunknown

Statistics Gaussian Distribution

The most probable values occur in the center of the graph, and as you go to either side, the probability falls off

Gaussian Distribution

)...(1

mean, 321

data numerical theof average :)x(Mean

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Gaussian Distribution For Gaussian curve representing an

“infinity” number of data set, we have (mu) = true mean (sigma) = true standard deviation For an ideal Gaussian distribution, about 2/3

of the measurements (68.3%) lie within one standard deviation on either side of the mean.

Student’s t - Confidence Intervals From a limited number of measurements, it is

impossible to find the true mean, , or the true standard deviation, .

What we can determine are x and s, the sample mean and the sample standard deviation.

The confidence intervals is a range of values within which there is a specified probability of find the true mean

Student’s t - Confidence Intervals

n

tsxIntervalConfidence :

t can be obtained from “Values of Student's t table” see textbook, pp.78

“ Q-Test” for Bad Data What to do with outlying data points? Accept? Or Reject? How to determine…..

range

gap Q :data discardingfor test -Q

“ Q-Test” for Bad Data

retained. be shouldpoint data thethus d),Q(tabulate (cal.) Q case, In this discarded.

be should valuelequestionab the d),Q(tabulate Q(cal.) If

37.08.3

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range

gapQcalculated

Q

(90% confidence)Number of

observations

0.76 40.64 50.56 60.51 70.47 80.44 90.41 100.39 110.38 120.34 150.30 20

“ Q-Test” for Bad DataQ

(90% confidence)Number of

observations

0.76 40.64 50.56 60.51 70.47 80.44 90.41 100.39 110.38 120.34 150.30 20

Least-Square Analysis (Linear Regression)

Least-Square Analysis (Linear Regression) Finding “the best straight line” through a

set of data pointsEquation of a straight line: y = mx + b

m = slope; b = y-intercept

22 b)) (mx - (y y) - (y d

b) (mx - y y - y ddeviation vertical

iii 2

i

iiii

Least-Square Analysis (Linear Regression)

2)()(D r,Denominato

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Least-Square Analysis (Linear Regression)

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centre thefrom yeach of (deviation s deviation, standard

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iy

Calibration Curve Calibration Curve is a graph showing

how the experimentally measured property (e.g. absorbance) depends on the known concentrations of the standards

A solution containing a known quantity of analyte is called a standard solution

Calibration Curve

Calibration Curve

D

xx

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x

D

nx

m

s iiy 2)(

1 in x y uncertaint

is curven calibratio fromin x y uncertaint The xvalue,-seeked the

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22