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University of San FranciscoChemistry 260: Analytical
Chemistry
Dr. Victor Lau
Room 413, Harney Hall, USF
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
)(%e )(%e )(%e %e
:follows asquotient or product or theerror thecalculateThen ies.uncertaint
relativepercent toiesuncertaint allconvert first division, andtion multiplicaFor
34040
04
04174
4
4
17
,4
321
222
2224
e
ee
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
n
i
xxxxnn
xx i
1
)( deviation, standard
2
ondistributi theofwidth theof measure a :(s)deviation Standard
n
xxs i
i
xx
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
4.1
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
)()( :intercept squares-Least
)( :slope squares-Least
2
2
ii
iiii
iiii
xxnD
D
xyxyix b
D
yxyxn m
Least-Square Analysis (Linear Regression)
D
xss
D
nss
n
ds
i
yb
ym
i
y
)(:intercept ofdeviation standard
:slope ofdeviation standard
2
)(
curve)Gaussian theof
centre thefrom yeach of (deviation s deviation, standard
2
2
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
D
x
D
nx
m
s iiy 2)(
1 in x y uncertaint
is curven calibratio fromin x y uncertaint The xvalue,-seeked the
obatined will wecurve,n calibratio theFrom
22