1. is your clicker set to channel 41? 2 a.yes b.no
TRANSCRIPT
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Is your clicker set to Channel 41?
2A. B.
0%0%
A. YesB. No
Introduction to Laboratory
MeasurementSUSB-003
3
SUSB-003
M1 + M2 + …. + Mn
nAVERAGE =
What is involved in making and
reporting a measurement? What contributes to the accuracy and precision of measurements?
What contributes to uncertainties in quantities computed from measurements?
What are the uses and limitations of devices we use in the laboratory?
? QUESTIONS ?
4Questions
How do we measure and report accuracy and precision?
Avg,
2 ,
Concepts:Measurement Uncertainty Linear Mass/Weight Volume Density Deliver/Contain Meniscus Homogeneity Accuracy PrecisionAverage Average DeviationPercent Error Error Propagation
Techniques:
5Concepts/Techniques
Significant Figures (see web page)
Weighing Pipet & Syringe
Buret Use Error Analysis
Preparing Solutions of given concentration
Apparatus:
6Apparatus
RulerAnalytical Balance
Top loading balanceTransfer Pipet/Syringe
Buret Volumetric Flask
7
Concept Maps – A handy study aid
But first, a brief digression.
A 4-step process for enhancing and verifying understanding
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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
PropositionsUse a “flow-chart” type of program to
arrange and connect the concepts
Concept Maps
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Matter
Molecules
Electrons
Nucleus
Atoms
Number of Protons
Number of Neutrons
IsotopeElement
Atomic Mass
Atomic Number
Roadmap
Focus Questio
n
How are Isotopes related to the Structure of Matter?
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Map
Resulting in a tentative
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Map with linking phrases
For more information, see the Web page:
Why Concept Maps?
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Concept Map for CHE 133 Activities and Grading
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For latecomers:
Make sure your clickers are set to
Channel 41
Set clickers to Channel 41
Back to the Exercise
Measuring devices have intrinsic uncertainties i.e., limitations due to their design/construction
Background - Measurement
14Uncertainty
Measurement process itself may introduce additional uncertainty
bathroom scale 1 lb ( 454 g)
balance 0.0002 g
measuring cup 1 fl oz ( 28
mL)
buret 0.02 mL
e.g., try to measure temperature of five drops of a warm solution with a cold laboratory thermometer
p x ~ h/2
Measurer often plays a role in the measurement process
reading a scale or liquid level, or dialdetermining a quantity from a graph, describing the color of a solution
Background (cont’d)
In the physical sciences, certain quantities are considered fundamental:length mass time (intervals),
(area, volume),
Many more can be described in terms of m, l, t. e.g.
Temperature
Energy m l2 / t2Velocity = l /t;
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Measurer/quantities
puc
e
Electric Currrent;
Some cannot, and require other fundamental quantities
1 m is the length of the path traveled by light in vacuum during the time interval of 1/299 792 458 of a second
1 sec is defined as 9,129,631,770 oscillations of the 133Cs atom.
1 kg is defined as the mass of a prototype made of platinum-iridium and kept at the International
Bureau of Weights and Measures. (Paris)
AmethystCeriseFuchsiaLilacHeliotropeLavenderLilacMagenta
MauveOrchidPeriwinklePlumPurpleThistleVioletWisteria
1 joule = 1 kg m2 s-
2
Most measuring devices are LINEAR
e.g. RULER: markings at same interval everywhere
RULE OF THUMB:
On a LINEAR SCALE, human eye is capable of estimating location of a mark lying between two smallest
divisionsto the nearest 1/5 th of a division
ANALOG CLOCK: 1 minute = 6o around entire dial
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Linear/
Rule
Wikipedia: a principle with broad application not intended to be strictly accurate or reliable for
every situation.
11.66
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Rule - Demo
The eye “squeezes” additional digit out of the ruler!
virtual
How should the value at the arrow be recorded?
18A. B. C. D. E.
0% 0% 0%0%0%
A. 2.3B. 2.30C. 2.36D. 2.360E. 2.4
19Q1 Answer
2.30 2.40
2.36
C 2.36
2.35 or 2.37 are also acceptable.
2.3 or 2.4 are NOT!
Estimating measurements between values is called INTERPOLATION
Apparatus designers expend major effortto make a user interface linear, through mechanical (cams, gears) or electronic means.
When scales are not linear, visual interpolation becomes difficult
We occasionally encounter
non-linear scales! 20
Interpol/non-linear
Rule of thumb does not apply!
e.g., some auto fuel gaugesconical measuring cups
e.g., logarithmic scale
RULE OF THUMB DOES NOT APPLY TO NON-LINEAR SCALES
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log scale
10 units 100 units
Units & Dimensions
What distinguishes scientific computation from
arithmetic primarily is that most scientific numbers include units.
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 sense22units
gm
L oCmol/L
joule
cmsec
E.g., you will measure a weight of water, W, and
W = 34.78 g, d = 0.9953 g/mLV = ?Measure
dFrom TableV = 34.78 g X 0.9953 g / mL =
34.62g2/mL
V = 34.78 g 0.9953 g / mL = 34.94
mL
Common sense suggests that the
answer should be ~ 35 mL 23
V, w, d example
use its tabulated density, d, to calculate volume, V
W X d
Suppose we have forgotten the definition
of density
Units & Dimensions
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
Note that while this is the order in which the manual describes
procedures, you may do them in any order you wish.
SUSB-003 Procedures
24Procedure
The Lab
Manual is not
a Cookbook
X
1. Measure DIAMETER, d
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 geometric formulas have no associated uncertainty. The uncertainty in A and V will be solely due toThe uncertainty in d!)
As an illustration, let’s look at a cube of side
L = 10
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Cube
L = 10
L = 9.00
L = 10.0
L = 11.0
VOLUME = L3 729 1000* 1331*Diff from L=10 (cm)
271 0 331
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Cube Table 2
We often use the symbol ~ to indicate “approximately”.
* Significant Figures
(10 ± e)3 ˜ 103 300 e ……
1 cm uncertainty in the edge ( 1 /10 = 10% ) produces an uncertainty of ~ 300 cm3 in the volume ( 300 / 1000 = 30% )
10.0 1.0
1000 300
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.
By our rule of thumb, you should be able to read ruler to nearest 0.2 mm ( = 0.02 cm)
Assuming you have measured diameter as accurately as you are able:
You are asked to calculate the effect of an uncertainty of + & - 0.02 cm in the diameter, area and volume.
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1/5 mm
1 mm
e.g., 3.57 cm
i.e. 3.55 cm and 3.59 cm
If the percent error in the length of a side is 10%, approximately what percent error will that cause in
the volume?
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A. 10%B. 20%C. 30%D. It depends on the
error in the coefficient of a3
The volume of an icosahedron with a side
of length a is given exactly by:
(3 + √5) a3 512
V =
A. B. C. D.
0% 0%0%0%
The volume of an icosahedron with a side of length a is given exactly by:
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(3 + √5) a3 512
V =
If the percent error in the length of a side is 10%, approximately what percent error will that cause in the volume?
C 30%
Analysis is identical to that done for cube. Coefficient of a3 is known with as much precision as desired.
2. Weight of a Plastic Sphere
Labs are equipped with 2 types of balances:
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
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Balances
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
SIGNIFICANT FIGURES
For devices with digital output, our rule of thumb does not apply
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). 31
Sig Figs Transition
3.3660 3.37
PRECISION
SIGNIFICANT FIGURES Bad news:
calculators don’t keep track of significant figures
Good news:
You simply must learn to handle significant figures.
There is no good news!
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Sig Figs News
2.3 / 7.1 =
0.323943662
CHE 133 Web PageIntroduction to Significant Figures
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.
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3. DENSITY OF A PLASTIC SPHERE
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
34Density - errors
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 error-prone.
Chemistry uses a wide variety of objects designed to measure volumes.
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4. Measurement of Liquid volumes
These devices can be classified in a number of ways• Precision • Accuracy • Fixed or variable volume• Whether they
36Contain/Deliver/
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.
a specified volume of liquid
when filled to ONE or MOREAPPROPRIATE MARKS
Contain or Deliver
Some devices have only a single mark:
Transfer Pipets are used to DELIVER a specified volume of solution from one container to another
most transfer pipets have only asingle mark (e.g., 5 mL, 10mL, 25mL, etc.)
Mark indicates volume DELIVERED when pipet is emptied under ONLY THE FORCE OF GRAVITY
Pipets are to be filled ONLY by using a syringe
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Vol flask/pipet
e.g., Volumetric Flasks are made to CONTAIN a specified volume of liquid when filled to the mark
BEAKERS, FLASKS
Used only when approximate, arbitrary volumes of liquids must be delivered.
Used only for approximate volume measurements.
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Cylinder/Beaker
The volume markings on beakers, cylinders or flasks are sufficiently
inaccurate that the designations “contain” and “deliver” do not matter.
Should read & record volume
consistent with the rule of thumb –
e.g.,0.2 mL
Cylinder is a somewhat more precise
THE BURET
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Buret Pix
Buret Pix
14
B14
Assigned number
BURETDevice to measure arbitrary DELIVERED volume of liquid with high accuracy & precision
Final ReadingInitial Reading
Delivered Volume
-4.3427.68
23.34
Proper Use:
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)
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Buret Init
Initial reading must not be
0.00
BURETDevice to measure arbitrary DELIVERED volume of liquid with high accuracy & precision
Final ReadingInitial Reading
Delivered Volume
-4.3427.68
23.34
41
Buret Init
18.7
18.78
18.8
42
Read Buret
Using our rule of thumb
This buret reads
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A. 16.2 mL
B. 16.18 mL
C. 15.98 mL
D. 15.82 mL
E. 16. mLA. B. C. D. E.
0% 0% 0%0%0%
D 15.82 mL
15.80 mL
15.90 mL
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Q2 Answer
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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
transfersDon’t use intermediate containers or devices
X X
Weighing by Difference
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• 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
Weighing by Difference (cont’d)
47
Preparing solutions of accurately known concentration is central to experimental chemistry. It requires two coordinated measurement techniques:
Accurate volume of solution
Accurate amount of substanceGenerally by weighing (by difference)*
Generally by adding solvent to a mark
5. PREPARING ACCURATE SOLUTIONS
* If specified amount is in mol, also need precise molar mass to convert mass to moles
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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 *
* Any amount within that range is acceptable.
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
6. MEASURES OF ACCURACY AND PRECISION (SUPL-001)
Lab provides opportunity to use some simple concepts in error analysis
OPERATIONAL CONCEPTS:
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
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Accuracy/Precision SigFigs 2
Accuracy and precision are central to laboratory science and, therefore, to the grading of exercises.
AVERAGE (mean): M1 + M2 + …. + Mn
n
AVERAGE DEVIATION:
|M1 – AVG| + |M2 – AVG| + … + |Mn – AVG| n
PERCENT DEVIATION:
100 X AVG DEV AVG
50Avg/A.D./Pct Dev Def
The average deviation is what % of the mean?
The average of the deviations from the mean.
SPECTROSCOPY OF FOOD DYES
Read SUSB – 037
Do Pre-Lab for SUSB – 037
Also, READSUPL-004 – Graphing
(Pre-lab questions NOT assigned)&
SUPL-005 – Spectroscopy51
NEXT LECTURE
ANY
?
52
QUESTIONS
53
54
The rest of the slides are bonus. If time permits.
AVERAGE, AVERAGE DEVIATION AND PERCENT ERROR
So, instead, we define
AVG 75.75 gwhere:
AVG = ( 75.63 + 76.05 + 75.58 ) / 3
SUM = 0.00
Result should be reported as WEIGHT = 75.75 0.20 g
AVG DEV = ( 0.12 + 0.30 0.18) / 3 = 0.20
||| || |
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Avg/Avg Dev 2Suppose a measurement is reproduced three
times WEIGHT OF STEEL BALL
SAMPLE 1 75.63 g
SAMPLE 2 76.05 g
SAMPLE 3 75.57 g
DEVIATIONFROM AVG
- 0.12+0.30- 0.18
SUM = 0.60
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
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:
or, in the first casePERCENT ERROR = 100 X 0.20 / 75.75 = 0.26%
PERCENT ERROR = 100 X 0.20 / 7.57 = 2.6%
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Percent Error
M1 M2 M3
Mavg
d1
d2d3
Or, visually:
0
Mavg is the average length of the three blue lines
Avg Dev is the average length of the three green lines
Avg Dev
Avg/A.D./Pct Dev
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Avg/A.D./Pct Dev Fig