1

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

8

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

9

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?

10

Map

Resulting in a tentative

11

Map with linking phrases

For more information, see the Web page:

Why Concept Maps?

12

Concept Map for CHE 133 Activities and Grading

13

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;

15

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

16

Linear/

Rule

Wikipedia: a principle with broad application not intended to be strictly accurate or reliable for

every situation.

11.66

17

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

21

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

25

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

26

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.

27

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?

28

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:

29

(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

30

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!

32

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.

33

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.

35

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

37

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.

38

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

39

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)

40

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

43

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

44

Q2 Answer

45

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

46

• 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

48

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

49

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

||| || |

55

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%

56

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

57

Avg/A.D./Pct Dev Fig