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Welcome to CHM 3120: Introduction
To Analytical Chemistry
The required textbook for this
course is
Quantitative Chemical
Analysis
Seventh Edition
by Dan Harris
Instructor: José Almirall, Ph.D.
Office: CP 316
Labs: CP194, CP153, OE109
E-mail: [email protected] Office Hours: Tues/Thurs: 2-3 pm
Tel.: (305) 348-3917
or by appointment
The Almirall Research Group - 2007
LIBS Plasma Evolution
Lecture # 2 Overview
Basic Tools
•Good Laboratory Practice (GLP)
•Labware/Equipment
•Methods
Experimental Error
•Types of Error
•Significant Figures
•Propogation of Error in Analysis
Intensity
10ns
500ns
1μs 10μs
100μs
time
•
Early stages dominated by
broadband continuum 0-1.0μs
•
Rapid expansion and cooling
•
•
Neutral and ionic dominated
emission
Experimental Setup
•
Nd:YAG
– Fundamental 1064nm/
220mJ max energy
– 0.67Hz Rep Rate
– 266 and 532nm lasers
•
New Wave Tempest
– 4th harmonic 266nm
– 27mJ max energy per
pulse
– 0.67Hz Rep Rate
•
Andor iCCD Camera (Mechelle
200-900nm)
1
GLP: Laboratory Safety
Good Laboratory Practice (GLP)
1. Hazard Labeling
Fire Hazard
“embodies a set of principles that provides a
framework within which laboratory studies are
planned, performed, monitored, recorded, reported
and archived…GLP helps assure regulatory
authorities that the data submitted are true
reflection of the results obtained during the study
and can therefore by relied upon when
making…assessments.”
0 = Not combustible
1 = Combustible if heated
2 = CAUTION: Combustible liquid (flashpoint of
100-200°F)
3 = WARNING: Flammable liquid (flashpoint <
100°F)
4 = Flammable gas or extremely flammable liquid
Health Hazard
0 = No unusual hazard
1 = CAUTION: May cause irritation
2 = WARNING: May be harmful if
inhaled or swallowed
3 = WARNING: Corrosive or toxic:
Avoid skin contact/inhalation
4 = DANGER: May be fatal on short
exposure. Specialize protective
equipment required
Specific Hazard
W = Avoid use of water
= Radiation
Instability
Hazard
0
1
2
ACID
0 = Stable
1 = CAUTION: May react if
heated or mixed with water
2 = WARNING: Unstable or may
react if mixed with water
3 = DANGER: Maybe explosive if
shocked, heated, confined or
mixed with water
4 = DANGER: Explosive material
at room temperature
ACID = Acid
ALK = Alkali
COR. = Corrosive
OXY = Oxidizer
GLP: Laboratory Safety
1. Hazard Labeling
GLP: Laboratory Safety
1. Hazard Labeling
2. Material Safety Data Sheet (MSDS)
Physical Data, Toxicity, Health Effects, First Aid, Reactivity,
Storage, Disposal, Protective Equipment, Spill Handling
GLP: Laboratory Safety
1. Hazard Labeling
2. Material Safety Data Sheet (MSDS)
3. Protective Wear
* Proper Clothing (no sandals, shorts, etc.)
* Safety Glasses/Goggles
* Lab Coats (flame- and spill-resistant)
* Gloves
GLP: Laboratory Safety
1.
2.
3.
4.
Hazard Labeling
Material Safety Data Sheet (MSDS)
Protective Wear
Fume Hoods
2
GLP: Laboratory Safety
1.
2.
3.
4.
5.
6.
Hazard Labeling
Material Safety Data Sheet (MSDS)
Protective Wear
Fume Hoods
Waste Disposal
Spills and Accidents
1.
2.
3.
4.
5.
6.
7.
8.
Hazard Labeling
Material Safety Data Sheet (MSDS)
Protective Wear
Fume Hoods
Waste Disposal
Spills and Accidents
Label ALL Containers!!
Other
GLP: Laboratory Safety
1.
2.
3.
4.
5.
6.
7.
GLP: Laboratory Safety
Hazard Labeling
Material Safety Data Sheet (MSDS)
Protective Wear
Fume Hoods
Waste Disposal
Spills and Accidents
Label ALL Containers!!
GLP: Laboratory Notebooks
•A laboratory notebook should state what you did
and what you observed, and should be
understandable to a stranger. The measure of
scientific truth is the ability to reproduce an
experiment.
• Never erase information; cross-out with a single
line to make corrections.
10 g of NaCl

10 g of NaCl

10 g of NaCl
• Basic Elements: Purpose, Materials, Method,
Results, Conclusions
Measuring Mass: Gravimetric Analysis
Analytical Balance
Shielding doors
prevent drafts
Typically sensitive
to 0.01 to 0.1 mg
Use weighing
vessel (e.g. pan,
weighing paper)
NOTE: Brush clean
after use!!
Tare = “zero”
the balance
3
Measuring Mass: Gravimetric Analysis
Measuring Mass: Gravimetric Analysis
Filtration and Gravimetric Analysis I
Filtration and Gravimetric Analysis II
Gooch Crucible
Adapter
Glass
Funnel
Mother Liquor
*Ashless Filter Paper
Rubber
Stopper
Vacuum
Filtrate
Trap
“Weighing By Difference”
Weightanalyte =
Weightfinal - Weightinitial
Where “Weightinitial” is the weight of the vessel (e.g.
crucible), filter paper, etc., and “Weightfinal” is the
weight of the vessel (e.g. crucible), filter paper, etc.
containing the analyte.
Moisture and Gravimetric
Analysis
Hygroscopic = “rapidly absorb moisture (water)”
Methods/Tools for Hygroscopic Substances
1. Drying Ovens
2. (Vacuum) Dessicators
3. Dessicants
4. Repeated “Weighing by Difference”
4
Measuring Volume: Volumetric Analysis
Preventing Weighing Errors
1.
2.
3.
4.
5.
6.
7.
Water Absorption
Contact with Vessel/Sample
Effects of Temperature/Drafts
Vibrations
Level
Spills
Calibration
Burets
Meniscus
Volume = Final - Initial
Example:
24.16 mL - 9.63 mL = 14.53 mL
Measuring Volume: Volumetric Analysis
Digital Burets
5
Measuring Volume:
Volumetric Flask
Measuring Volume: Pipets
and Syringes
Preparing Solutions
= Transfer Pipet
meniscus
Preparing Dilutions
TD = To Deliver
TC = To Contain
Fill and
Dispense
Measuring Volume: Pipets
and Syringes
Measuring Volume: Pipets
and Syringes
Eject Tip
Decimal
Microliter Syringe
* Rinse repeatedly to remove air bubbles
* Steel needle sensitive to strong acids
Experimental Error
Good Laboratory Practice (GLP)
“embodies a set of principles that provides a
framework within which laboratory studies are
planned, performed, monitored, recorded, reported
and archived…GLP helps assure regulatory
authorities that the data submitted are true reflection
of the results obtained during the study and can
therefore by relied upon when
making…assessments.”
“Every measurement has some uncertainty which
is called experimental error”
…a measurement is an ESTIMATE.
Types of Error
Systematic (Determinate) = “flaw in equipment or design of
an experiment”
Random (Indeterminate) = “uncontrolled (or maybe
uncontrollable) variables in the measurement”
6
Experimental Error
Experimental Error
Precision = “reproducibility of a result [= measurement]”
Accuracy = “how close a measured value is to the ‘true’ value”
Significant Figures
= “minimum number of digits needed to write a given
value in scientific notation without loss of accuracy”
= expressed in powers of 10
Examples:
4
1.234 x 10-5
Four (4) significant figures
4
0.00001234
Accurate
NOT Precise
Precise
NOT Accurate
Accurate
and Precise
123 400
?
Experimental Error
4
5
6
1.234 x 105, 1.2340 x 105, 1.23400 x 105
Experimental Error
Significant Figures
“The Rules for Zeros”
•Zeros are significant when they occur in the
middle of a number
“The last significant digit in a measured quantity
always has associated uncertainty”
KNOWN
Example:
1.2034 x 105
•Zeros are significant when they occur at the end
of a number on the right-hand side of a decimal
point
e.g. 9.63 mL
* Interpolation = Estimation of readings
to the nearest tenth of distance
between scale readings
5
Example:
1.2340 x 105
NOTE: Assumes that zero is accurate estimate.
Experimental Error
Significant Figures
“Some numbers are exact - with an infinite
number of unwritten significant digits”
Experimental Error
Arithmetic and Significant Figures
1. Addition/Subtraction
Express numbers with the same exponent
Significant figures are limited to the leastcertain number
Example:
5 people
= 5.0 people
= 5.00 people
= 5.000 people
1.234 x 10-5
+ 6.78 x 10-9
1.234
x 10-5
+ 0.000678 x 10-5
1.234678 x 10-5
Significant
Answer: 1.235 x 10-5
7
Significant Figures…………
Number of all certain digits plus the first uncertain digit
30.5 mL
30.67 mL
30.6 mL
30.68 mL
30.69 mL
30.7 mL
31
3 sig figs
31
Rules for determining the number of sig figs
1) Disregard all initial zeros
30
30
Significant Figures…………
4 sig figs
0.03068 L
2) Disregard all final (terminal) zeros unless they
follow a decimal point
3) All remaining digits including zeros between nonzero digits are significant
Tip: Express data in scientific notation to avoid confusion
in determining whether terminal zeros are significant
2.0 L or 2000 mL best expressed as 2.0 X 103 mL
2 sig figs ? sig figs
2 sig figs
Significant Figures…………
Numerical Computation Conventions
When adding and subtracting, express the numbers to
the same power of ten.
3.4
2.432 X 106 = 2.432 X 106
0.020
6.512 X 104 = 0.06512 X 106
7.31
-1.227 X 105 = -0.1227 X 106
10.73
= 2.37442 X 106
Answer: 10.7
Answer: 2.374 X106
For Multiplication or Division, round the answer to contain the same
# of sig figs as the original number with the smallest # of sig figs.
Arithmetic and Significant Figures
1. Addition/Subtraction
The number of significant figures in the answer may
exceed or be less than that in the original data.
If the numbers being added do not have
the same number of significant figures, we
are limited by the least-certain one.
5.345 (4 sig figs)
+ 6.728 (4 sig figs)
12.073 (5 sig figs)
7.26 X 1014
- 6.69 X 1014
0.57 X 1014
Experimental Error
“Rules for Rounding”
If a number is less than “halfway” (< 5), then
round DOWN.
e.g. 1.234 rounds to 1.23 (with 3 significant digits)
If a number is more than “halfway” (> 5), then
round UP.
e.g. 1.23456 rounds to 1.2346 (with 5 significant digits)
If a number is exactly “halfway” (5), then round to
the nearest EVEN number.
e.g. 1.2345 rounds to 1.234 (with 4 significant digits)
1.2355 rounds to 1.236 (with 4 significant digits)
Arithmetic and Significant Figures
1. Addition/Subtraction
Express numbers with the same exponent
Significant figures are limited to the leastcertain number
1.234 x 10-5
+ 6.78 x 10-9
1.234
x 10-5
+ 0.000678 x 10-5
1.234678 x 10-5
= 1.23 x 10-5
8
Experimental Error
Experimental Error
Significant Figures and “Rounding-Off”
“Rounding should only be done on final answers (not
intermediate results), to avoid accumulating round-off
errors”
24.16 mL - 9.63 mL = 14.53 mL
= 14.5 mL
24.2 mL - 9.6 mL = 14.6 mL
Arithmetic and Significant Figures
1. Addition/Subtraction
2. Multiplication/Division
Significant figures are limited to the leastcertain number
Multiply
Example:
1.234 x 10-5
x 6.78 x 10-9
8.36652 x 10-14
Add exponents
= 8.37
Experimental Error
Arithmetic and Significant Figures
Experimental Error
Arithmetic and Significant Figures
1. Addition/Subtraction
1. Addition/Subtraction
2. Multiplication/Division
2. Multiplication/Division
Significant figures are limited to the leastcertain number
Example: Measure blood glucose level for three
people, and calculate average level.
4.5 mM + 6.78 mM + 9.10 mM
= 6.7933333
Exact number has
3
= 6.8
infinite significant
3. Logarithms and Antilogarithms
log n = a
“logarithm of n is a”
* a is comprised of characteristic and mantissa
e.g. a = 1.234
characteristic
mantissa
n = 10a
“n is the antilogarithm of a”
figures
Experimental Error
Arithmetic and Significant Figures
Experimental Error
Arithmetic and Significant Figures
1. Addition/Subtraction
1. Addition/Subtraction
2. Multiplication/Division
2. Multiplication/Division
3. Logarithms and Antilogarithms
3. Logarithms and Antilogarithms
* Number of digits in the mantissa of the log of a
number should equal the number of significant figures
in that number
* Number of significant figures in the antilog should
equal the number of digits in the mantissa
4 digits
Example:
log 1.234 x 10-5
=
- 4.9086848
=
- 4.9087
4 significant
9
Experimental Error
Experimental Error
Arithmetic and Significant Figures
Propogation of Uncertainty from Random Error
“We can usually estimate or measure the random error
associated with a measurement”
1. Addition/Subtraction
2. Multiplication/Division
(more next week!)
3. Logarithms and Antilogarithms
Example:
antilog 1.234
3 significant
=
17.1395731
=
17.1
3 digits
Experimental Error
Absolute Uncertainty
Experimental Error
Absolute Uncertainty
Relative Uncertainty
= “compares the size of the absolute uncertainty
with the size of its associated measurement”
± 0.0001 g
9.63 ± 0.01 mL
Relative Uncertainty =
absolute uncertainty
magnitude of the measurement
*Note: No Units
% Relative Uncertainty =
absolute uncertainty
x 100%
magnitude of the measurement
Experimental Error
Experimental Error
Propogation of Uncertainty from Random Error
Propogation of Uncertainty from Random Error
1. Addition/Subtraction
efinal =
1. Addition/Subtraction
efinal = e4
√Σ(en)2
Where efinal is the final
calculated error, and “Σ (en)2”
is sum (Σ) of the squared
errors (en2).
1.23 (±0.01)
4.56 (±0.02)
+ 7.89 (±0.03)
13.68 (+ efinal)
= 13.68 (± 0.03)
?
e1
e2
e3
e4
= √Σ (en)2
= √(e1)2 + (e2)2 + (e3)2
= √(0.01)2 + (0.02)2 + (0.03)2
= √0.0001 + 0.0004 + 0.0009
= √0.0014
= 0.037
10
Experimental Error
Experimental Error
Propogation of Uncertainty from Random Error
Propogation of Uncertainty from Random Error
1. Addition/Subtraction
1. Addition/Subtraction
2. Multiplication/Division
Percent Relative Uncertainty?
Relative Uncertainty=
Percent Relative
Uncertainty
=
0.037 =
13.68
%efinal =
0.0027
0.0027 x 100%
√Σ (%en)2
Where %efinal is the final
calculated percent error, and
“Σ (en)2” is sum (Σ) of the
squared percent error (en2).
= 0.27%
= 0.3%
Experimental Error
Experimental Error
Propogation of Uncertainty from Random Error
Propogation of Uncertainty from Random Error
1. Addition/Subtraction
2. Multiplication/Division
%efinal = %e3 = √Σ (%en)2
= √(%e1)2 + (%e2)2
1.23 (±0.01)
x 4.56 (±0.02)
5.61 (± efinal)
= 5.61 (±0.9%)
= 5.61 (±0.05)
e1
e2
e3
%e1 = 0.01/1.23x100 = 0.81%
%e2 = 0.02/4.56x100 = 0.44%
= √(0.81)2 + (0.44)2
= √0.65 + 0.19
= √0.85
= 0.92%
Experimental Error
Example 1: Uncertainty in Molecular Mass
Systematic Error
Atomic Mass of Oxygen = 15.9994 ± 0.0003
*Note: Difference due to number of neutrons in atoms = isotope variation
We simply ADD systematic error…
O2 = O + O = (0.0003) + (0.0003) = 0.0006
NOT
(0.0003)2
+
(0.0003)2
y = xa
%ey = a(%ex)
y = log x
ey =
1
ln 10
ex
x
y = 10x
ey =
y
(ln 10)
ex
y = ln x
ey = ex
x
ey = ex
y
y = ex
Experimental Error
Propogation of Uncertainty from Systematic Error
Uncertainty in molecular mass of O2 ?
1. Addition/Subtraction
2. Multiplication/Division
3. Exponents and Logarithms
Propogation of Uncertainty from Systematic Error
Example 1: Uncertainty in Molecular Mass
Uncertainty in molecular mass of C2H4 ?
Systematic Error
C2 = C + C = 2 x (0.0008) = 0.0016
H4 = H+H+H+H = 4 x (0.00007) = 0.00028
C2 + H4 = (0.0016)2 + (0.00028)2
= 0.0016
Random Error
(error in C and H independent)
11
Experimental Error
Propogation of Uncertainty from Systematic Error
Example 2: Multiple Deliveries from One Pipet.
Uncalibrated 25-mL Class A Volumetric Pipet:
25.00 ± 0.03 mL
Systematic Error
Four (4) deliveries…
(0.03) + (0.03) + (0.03) + (0.03) = ± 0.12
Experimental Error
Propogation of Uncertainty from Systematic Error
Example 2: Multiple Deliveries from One Pipet.
Calibrate* a 25-mL Class A Volumetric Pipet
*Weigh the water it delivers; calibrate based on mass, density and temperature
25.991 ± 0.006 mL
Four (4) deliveries…
Random Error
(0.006)2 + (0.006)2 + (0.006)2 + (0.006)2
= ± 0.012
12