Measurement

Report
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SUSB-003
AVERAGE = M1 + M2 + …. + Mn
n
Introduction to
Laboratory Measurement
SUSB-003
3
? QUESTIONS ?
What are the uses and limitations of
devices we use in the laboratory?
What is involved in making and
reporting a measurement?
What contributes to the accuracy and
precision of measurements?
How do we measure and report accuracy
and precision?
What contributes to uncertainties in
quantities computed from measurements?
Questions
4
Concepts:
Measurement
Mass/Weight
Deliver/Contain
Accuracy
Average
Percent Error
Uncertainty
Volume
Meniscus
Linear
Density
Homogeneity
Precision
Average Deviation
Error Propagation
Significant Figures (see web page)
Techniques:
Weighing
Buret Use
Pipet & Syringe
Error Analysis
Preparing Solutions of given concentration
Concepts/Techniques
5
Apparatus:
Ruler
Analytical Balance
Buret
Transfer Pipet/Syringe
Top loading balance
Volumetric Flask
Apparatus
6
But first, a brief digression.
Concept Maps – A handy study aid
A 4-step process for enhancing and verifying
understanding
7
Concept Maps
1. Formulate a Focus Question
2. List Concepts and write them on “Post-its” [ Road Map]
3. Arrange the “Post-its” on a Map
4. Connect them with Linking Phrases to form Propositions
Use a “flow-chart” type of program to arrange
and connect the concepts
8
How are Isotopes related to the Structure of Matter?
Atoms
Focus
Question
Atomic Number
Atomic Mass
Electrons
Element
Isotope
Roadmap
Matter
Molecules
Nucleus
Number of Neutrons
Number of Protons
9
Resulting in a tentative
Map
10
Map with linking phrases
For more information, see the Web page:
Why Concept Maps?
11
Concept Map for CHE 133 Activities and Grading
12
Back to the Exercise
For latecomers:
Make sure your
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Set clickers to Channel 41
13
Background - Measurement
Measuring devices have intrinsic uncertainties
i.e., limitations due to their design/construction
bathroom scale
 1 lb ( 454 g)
measuring cup
 1 fl oz ( 28 mL)
balance
 0.0002 g
buret
 0.02 mL
Measurement process itself may
introduce additional uncertainty
e.g., try to measure temperature
of five drops of a warm solution
with a cold laboratory thermometer
Uncertainty
14
Background (cont’d)
Measurer/quantities
Measurer often plays a role in the
measurement process
reading a scale or liquid level, or dial
determining a quantity from a graph,
describing the color of a solution
In the physical sciences, certain
Mauvefundamental:
quantities
are considered
Amethyst
Orchid
length Cerise
(area, volume), mass
Periwinkle
Fuchsia
time (intervals),
Plum
Lilac
ElectricHeliotrope
Currrent; Purple
Temperature
Thistle
Lavender
Many more
can be described in terms of m, l, t.
Violet
2vacuum
2
1e.g.
m1 is
the
length ofas
path
traveled
light
in
sec
is defined
asby
9,129,631,770
kgVelocity
is Lilac
defined
mass
of a prototype
made
of
Energy

m
l
/
t
=1the
lthe
/t;
during
the
time interval
of kept
1/299
792
458
a second
oscillations
ofatthe
Cs of
atom.
Wisteria
platinum-iridium
and
the133
International
Magenta
2 s-215
Bureau of Weights and Measures. (Paris)
1
joule
=
1
kg
m
Some cannot, and require other fundamental quantities
Most measuring devices are LINEAR
e.g. RULER: markings at same interval everywhere
ANALOG CLOCK: 1 minute = 6o
around entire dial
RULE OF THUMB:
On a LINEAR SCALE, human eye
is capable
of estimating
Wikipedia:
a principle
with
location of a mark lying between broad
two smallest
divisions
application
not
to the nearest 1/5 th of
a division
intended
to be strictly
accurate or reliable for
every situation.
Linea
r/Rul
16
e
Rule - Demo
11.66
virtual
The eye “squeezes” additional digit out of the ruler!
17
How should the value at the arrow be
recorded?
A.
B.
C.
D.
E.
2.3
2.30
2.36
2.360
2.4
0%
0%
0%
0%
0%
18
A.
B.
C.
D.
E.
2.36
2.30
2.40
2.35 or 2.37 are
also acceptable.
C
2.36
2.3 or 2.4
are NOT!
19
Q1 Answer
Estimating measurements between values is called
INTERPOLATION
Apparatus designers expend major effort
to make a user interface linear, through
mechanical (cams, gears) or electronic means.
When scales are not linear,
visual interpolation becomes
difficult
e.g., some auto fuel gauges
conical measuring cups
Rule of thumb does not apply!
Interpol
/nonlinear
We occasionally encounter
non-linear scales!
20
e.g., logarithmic scale
10 units
log scale
100 units
RULE OF THUMB DOES NOT APPLY TO
NON-LINEAR SCALES
21
Units & Dimensions
What distinguishes scientific computation from
arithmetic primarily is that most scientific
numbers include units.
joule

Bad news:
calculators don’t keep track of units.

Good news:
Proper attention to units by users
often shows whether or not a
calculation makes sense
22
units
Units & Dimensions
E.g., you will measure a weight of water, W, and
use its tabulated density, d, to calculate volume, V
V, w, d example
W = 34.78 g, d = 0.9953 g/mL
From Table
VMeasured
=?
V = 34.78
W gX
X 0.9953
d g / mL = 34.62 g2/mL
V = 34.78 g
0.9953 g / mL = 34.94 mL
Suppose we have forgotten
the definition of density
Common sense suggests that the
answer should be ~ 35 mL
23
SUSB-003 Procedures
1. Measure Diameter of Plastic Sphere
2. Weigh Plastic Sphere on two types of balance
3. Compute Density using Diameter & Weight
4. Explore uncertainty in calculation
5. Make Direct Measurement of Liquid Volumes
using Pipet & Buret
6. Prepare a solution of known concentration
using a volumetric flask
X
Note that while this is the order in
which the manual describes procedures,
you may do them in any order you wish.
24
Procedure
1. Measure DIAMETER, d
Cube
From that, compute AREA and VOLUME of a sphere from
their mathematical relationships to its diameter.
A =  d2
V =  d3 / 6
Purpose: To explore error propagation in
quantities derived from diameter
I.e., suppose we make a small error in measuring d.
How large an error will that produce in A and V?
(Note that “” , “2”, “3” and “6” in the geometricL = 10
formulas have no associated uncertainty.
The uncertainty in A and V will be solely due to
The uncertainty in d!)
As an illustration, let’s look at a cube of side
L = 10
25
L = 9.00 L = 10.0 L = 11.0
VOLUME = L3
Diff from L=10 (cm)
729
271
1000*
0
 1 cm uncertainty in the edge ( 1 /10 = 10% )
produces an uncertainty of
~ 300 cm3 in the volume ( 300 / 1000 = 30% )
1331*
331
10.0 1.0
1000  300
Cube Table 2
We often use the symbol ~ to
(10 ±“approximately”.
e)3 ˜ 103 ∓ 300 e ……
indicate
* Significant Figures
26
In the exercise, you perform analogous calculation for
computed area and volume of a plastic sphere.
The cm scale of your ruler has its smallest markings
at 1 mm intervals.
1 mm
By our rule of thumb, you should be able to
read ruler to nearest 0.2
1/5mm
mm( = 0.02 cm)
Assuming you have measured diameter as
accurately as you are able:
e.g., 3.5
7 cm
You are asked to calculate the effect of an uncertainty
of + & - 0.02 cm in the diameter, area and volume.
i.e.
3.55 cm and 3.59 cm
27
The volume of an icosahedron with a side
of length a is given exactly by:
V =
5 (3 + √5) a3
12
If the percent error in the length of a side is 10%,
approximately what percent error will that cause in the
volume?
A.
B.
C.
D.
10%
20%
30%
It depends on the error
in the coefficient of a3
0%
A.
0%
0%
B.
C.
0%
D. 28
The volume of an icosahedron with a side
of length a is given exactly by:
V =
5 (3 + √5) a3
12
If the percent error in the length of a side is 10%,
approximately what percent error will that cause in the
volume?
Analysis is identical to that done for
cube. Coefficient of a3 is known
with as much precision as desired.
C
30%
29
2. Weight of a Plastic Sphere
Labs are equipped with 2 types of balances:
Balance
s
1.Single pan electronic Analytical Balance
used in exercises that require highly
quantitative (  0.0002 g ) results.
Capacity < 220g
2. Top loading balance
appropriate for weighing in exercises
requiring less quantitative (  0.01 g )
results
30
You weigh the sphere whose diameter you
measure with both balances.
The weights you measure should be consistent, but will
differ in one critical aspect
PRECISION
SIGNIFICANT
FIGURES
3.3660
For devices with digital output, our
rule of thumb does not apply
3.37
All we can do is to record all digits that the device
provides and rely on the manufacturer’s specifications
of the intrinsic precision of the device.
For the analytical balance, this always includes 4
decimals. Include all zeros (0).
Sig Figs Transition
31
SIGNIFICANT FIGURES
 Bad news:
calculators don’t keep track of
significant figures
Sig Figs
News
 Good news:
There is
no good news!
You simply must learn to handle
significant figures.
CHE 133 Web Page
Introduction to Significant Figures
32
3. DENSITY OF A PLASTIC SPHERE
Density is a reproducible physical characteristic of pure
materials.
For a homogeneous substance
(uniform composition throughout),
density is:
d
=
m / V
In this part of the exercise, we use the measured mass &
computed volume of the sphere to calculate its apparent
density. (Is the sphere homogeneous? How could you tell?)
In other parts of this exercise, you use the measured mass
of a sample of water and the tabulated density of water to
calculate the volume of the water.
33
How do uncertainties in the
• measured DIAMETER ( 0.02 cm) and
• measured MASS ( ?)
affect the uncertainty in the density of the sphere.
From the measured data, we calculate 2 values, Dmax, Dmin.
The uncertainty in the result, Davg, is measured by:
• the range of the values of the density (Dmax – Dmin)
and
• the percent deviation of the density
Dmax – Dmin
100 X −−−−−−−−− %
Davg
Density - errors
34
4. MEASUREMENT OF LIQUID VOLUMES
Liquids adopt the shapes of their containers.
These are often irregular objects where using
rulers and geometry would be complex and errorprone.
Chemistry uses a wide variety of
objects designed to measure volumes.
4. Measurement of
Liquid volumes
35
These devices can be classified in a number of ways
• Precision
• Accuracy
• Fixed or variable volume
• Whether they
Contain or Deliver
a specified volume of liquid
when filled to ONE or MORE
APPROPRIATE MARKS
Appropriate mark is determined by
comparing position of a liquid’s surface,
i.e, the tangent to its meniscus,
with marks on a vertical scale.
Contain/Deliver/Ma
rks
36
Some devices have only a single mark:
e.g., Volumetric Flasks are made
to CONTAIN a specified volume
of liquid when filled to the mark
Transfer Pipets are used to DELIVER
a specified volume of solution from one
container to another
most transfer pipets have only a
single mark (e.g., 5 mL, 10mL,
25mL, etc.)
Vol flask/pipet
Pipets are to be filled ONLY
by using a syringe
Mark indicates volume DELIVERED when pipet is
emptied under ONLY THE FORCE OF GRAVITY
37
The volume markings on beakers, cylinders
or flasks are sufficiently inaccurate that
Used
only when approximate, arbitrary
the designations “contain” and “deliver” do
volumes of liquids
must be delivered.
not matter.
BEAKERS, FLASKS
Used only for approximate volume
measurements.
Cylinder/Beaker
Cylinder is a somewhat more precise
Should read & record
volume consistent with
the rule of thumb –
e.g.,0.2 mL 38
Buret Pix
THE BURET
Buret Pix
B14
Assigned
number
14
39
BURET
Device to measure arbitrary DELIVERED
volume of liquid with high accuracy & precision
Buret Init
Final Reading
Initial Reading
27.68
-4.34
Delivered Volume
23.34
Proper Use:
Initial reading
must not be 0.00
Final reading: often depends on some other
observation (e.g., a color change in solution to
which liquid is being added)
READ / RECORD BOTH TO NEAREST 0.02 mL
(1/5th OF SMALLEST DIVISION)
40
BURET
Device to measure arbitrary DELIVERED
volume of liquid with high accuracy & precision
Buret Init
Final Reading
Initial Reading
27.68
-4.34
Delivered Volume
23.34
41
Read Buret
Using our
rule of
thumb
18.7
18.78
18.8
42
This buret reads
A. 16.2 mL
B. 16.18 mL
C. 15.98 mL
D. 15.82 mL
E. 16. mL
0%
0%
0%
A.
B.
C.
0%
D.
0%
43
E.
Q2 Answer
15.80 mL
D
15.82 mL
15.90 mL
44
Weighing by Difference
Most errors in weighing are due to loss of material in
the transfer from one container to another!
How do we minimize this problem?
Minimize the number of transfers
Don’t use intermediate containers or devices
X
X
45
Weighing by Difference (cont’d)
• Process:
• weigh sample container,
• transfer sample directly into final
container by tapping
• reweigh original sample container
•Repeat until
•Difference between initial and final weights of
container is the desired sample weight
You are NOT “weighing by difference” if you:
• bring a spatula to the balance
• place heavy flask or beaker on balance pan
• use a watch glass or piece of paper
• record only weight of sample
46
5. PREPARING ACCURATE SOLUTIONS
Preparing solutions of accurately known concentration is
central to experimental chemistry. It requires two
coordinated measurement techniques:
Accurate amount of substance
Generally by weighing (by difference)*
Accurate volume of solution
Generally by adding solvent to a mark
* If specified amount is in mol, also need
precise molar mass to convert mass to moles
47
Preparing a solution
Suppose you are asked to make a solution of potassium
bromide (KBr) with an accurately known concentration of
5 g/L  20% - using a 500.0 mL volumetric flask.
How much KBr should you weigh?
To make 1 L (= 1000.0 mL), you would need 5  20% = 5  1 g
To make 500.0 mL, you would need
(500.0 / 1000.0) (5  1) = 2.5  0.5 g
i.e., between 2.0 and 3.0 g *
Suppose you actually weigh 2.7845 g. After bringing the
volume to 500.0 mL, the concentration is:
2.7845 g / 0.5000 L = 5.5690 g/L
* Any amount within that range is acceptable.
48
6. MEASURES OF ACCURACY AND
PRECISION (SUPL-001)
Lab provides opportunity to use some simple concepts in
error analysis
OPERATIONAL CONCEPTS:
Accuracy/Precision
SigFigs 2
ACCURACY: measured deviation from "true“ value.
PRECISION: measures reproducibility of results
when compared with one another
Exercises involve small numbers of repetitions.
 We use simple statistical measures:
Accuracy/Precision SigFigs
Accuracy and precision are central to laboratory
science and, therefore, to the grading of exercises.
49
AVERAGE (mean):
M1 + M2 + …. + Mn
n
The average of the
deviations from the
AVERAGE DEVIATION:
mean.
|M1 – AVG| + |M2 – AVG| + … + |Mn – AVG|
n
PERCENT DEVIATION:
The average deviation
is what % of the mean?
100 X AVG DEV
AVG
Avg/A.D./Pct Dev Def
50
NEXT LECTURE
SPECTROSCOPY OF FOOD DYES
Read SUSB – 037
Do Pre-Lab for SUSB – 037
Also, READ
SUPL-004 – Graphing
(Pre-lab questions NOT assigned)
&
SUPL-005 – Spectroscopy
51
ANY
?
QUESTIONS
52
53
The rest of the slides are bonus.
If time permits.
54
AVERAGE, AVERAGE DEVIATION AND PERCENT ERROR
Suppose a measurement is reproduced three times
WEIGHT OF DEVIATION
FROM AVG
STEEL BALL
| - 0.12|
SAMPLE 1
75.63 g
| +0.30|
SAMPLE 2
76.05 g
| - 0.18|
SAMPLE 3
75.57 g
AVG
75.75 g SUM = 0.60
0.00
where:
AVG = ( 75.63 + 76.05 + 75.58 ) / 3
So, instead, we define
Avg/Avg Dev 2
AVG DEV =
( 0.12 + 0.30  0.18) / 3
= 0.20
Result should be reported as
WEIGHT = 75.75  0.20 g
55
WEIGHT = 75.75  0.20 g
Suppose in weighing a plastic ball, we get the
same average deviation (0.20 g) but the weight
is only 7.57 g.
WEIGHT = 7.57  0.20 g
Percent Error
Intuitively, the deviation is much “larger”
in the second case. We can distinguish the
precision by employing the measure:
PERCENT ERROR, which we calculate as follows:
PERCENT ERROR = 100 X 0.20 / 7.57 = 2.6%
or, in the first case
PERCENT ERROR = 100 X 0.20 / 75.75 = 0.26%
56
Or, visually:
Avg/A.D./Pct Dev
Avg/A.D./Pct Dev Fig
d2
d1
0
M1
M2
d3
M3
Avg Dev
Mavg
Mavg
is the average length of the three blue lines
Avg Dev is the average length of the three green lines
57

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