University of San Francisco
Chemistry 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 1
The diagram shows a
portion of a burette.
What is the meniscus
reading in milliliters?
A. 24.25
B. 24.00
C. 25.00
D. 25.50
reference: http://www.sfu.ca/chemistry/chem110111/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
 9.250 x 104
 9.2500 x 104

3 sig. figs.
4 sig. figs
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.
18.998 403 2 (F)
18.998 403 2 (F)
 83.80
(Kr)
121.796806
4 (KrF2)
not
significant
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.
3.26 x 10 -5
 1.78
5.80 x 10 -5
34.60
 2.462 87
14.05
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
Random Error
Gross Error
Consistent
tendency of
device to read
higher or lower
than true value
“noise”
Due to mistake
e.g. uncalibrated
buret
Unpredicted
Higher and lower
than true value
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
absolute uncertaint y
Relative uncertaint y 
magnitude of measuremen t
0.02ml
e.g.
 0.002
12.35ml
Percentage uncertaint y  100  relative uncertaint y
e.g. 100  0.002  0.2%
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
1.76 (0.03)  e1
 1.89 (0.02)  e2
- 0.59 (0.02)  e3
3.06 ( e4)
e1, e2, and e3 is the uncertainty of
the measurements, respectively.
e4 is the total uncertainty after
addition/subtraction manipulation
where as, e4  e1 2  e2 2  e3 2
that is, e4  (0.03) 2  (0.02) 2  0.02) 2  0.041  0.041
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
For multiplica tion and division, first convert all uncertaint ies to percent relative
uncertaint ies. Then calculate the error or the product or quotient as follows :
%e 4  (%e1) 2  (%e2) 2  (%e3) 2
for example,
1.76(1.7%) 1.89(1.1%)
1.76 (0.03)  1.89(0.02)
 5.64  e 4
 5.64  e 4 , or
0.59(3.4%)
0.59 (0.02)
%e 4  (1.7%) 2  (1.1%) 2  (3.4%) 2  4.0%
answer is 5.64 (4.0%)
4.0%  5.64  0.040 x 5.64  0.23
So we have,
5.6 (0.2) (absolute uncertaint y); 5.6 (4%) relative uncertaint y 
Its Now Your TURNS
unknown material
mass  4.635  0.002g
volume  1.13  0.05ml
(i) Find % relative uncertaini ty in mass and volume
(ii) Find the density wi th  uncertaint y with correct no. of digits
mass
Hey, do you remember, density 
volume
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
Mean (x) : average of the numerical data
x
i
mean, x 
i
n
1
 ( x1  xx 2  x3  ...  xn )
n
Standard deviation (s) : a measure of the
width of the distributi on
standard deviation, s 
2
(
x
i  x)

i
n 1
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
ts
Confidence Interval :   x 
n
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…..
gap
Q - test for discarding data : Q 
range
“Q-Test” for Bad Data
gap
1.4
Qcalcu lated 

 0.37
range 3.8
If Q(cal.)  Q(tabulate d),
the questionab le value should be
discarded. In this case,
Q (cal.)  Q(tabulate d),
thus the data point should be retained.
Q
(90% confidence)
Number of
observations
0.76
0.64
0.56
0.51
0.47
0.44
0.41
0.39
0.38
0.34
0.30
4
5
6
7
8
9
10
11
12
15
20
“Q-Test” for Bad Data
Q
(90% confidence)
Number of
observations
0.76
0.64
0.56
0.51
0.47
0.44
0.41
0.39
0.38
0.34
0.30
4
5
6
7
8
9
10
11
12
15
20
Least-Square Analysis (Linear
Regression)
Least-Square Analysis (Linear
Regression)

Finding “the best straight line” through a
set of data points
Equation of a straight line: y = mx + b
m = slope; b = y-intercept
vertical deviation di  yi - y  yi - (mx i  b)
di 2  (yi - y) 2  (yi - (mx i  b)) 2
Least-Square Analysis (Linear
Regression)
Least - squares slope :
m 
n ( xiyi )   xi  yi
D
2
(
x
i )
  yi   ( xiyi) xi
Least - squares intercept :
b 
Denominato r, D
D  n ( xi 2 )  ( xi ) 2
D
Least-Square Analysis (Linear
Regression)
standard deviation, sy (deviation of each yi from the centre
of the Gaussian curve)
sy 
standard deviation of slope :
standard deviation of intercept :
s m  sy
sb  sy
2
(
d
i )

n2
n
D
2
(
x
i )

D
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
From the calibratio n curve, we will obatined
the seeked - value, x
The uncertaint y in x from calibratio n curve is
2
2
sy
x n  ( xi ) 2 x  xi
uncertaint y in x 
1


m
D
D
D