Measurement
-
Upload
elijah-wolfe -
Category
Documents
-
view
35 -
download
0
description
Transcript of Measurement
Measurement
• 100 mL Graduated Cylinder• Units of Measuring Volume• Reading a Meniscus• Units for Measuring Mass• Quantities of Mass• SI-English Conversion Factors• Accuracy vs. Precision• Accuracy Precision Resolution• SI units for Measuring Length• Comparison of English and SI Units• Reporting Measurements• Measuring a Pin• Practice Measuring
Measurement• 100 mL Graduated Cylinder• Units of Measuring Volume• Reading a Meniscus• Units for Measuring Mass• Quantities of Mass• SI-English Conversion Factors• Accuracy vs. Precision• Accuracy Precision Resolution• SI units for Measuring Length• Comparison of English and SI Units• Reporting Measurements• Measuring a Pin• Practice Measuring
100 mL Graduated Cylinder
Zumdahl, Zumdahl, DeCoste, World of Chemistry 2002, page 119
Instruments for Measuring Volume
Graduatedcylinder
Syringe Volumetric flaskBuret Pipet
Units of Measuring Volume
1 L = 1000 mL
1 qt = 946 mL
Timberlake, Chemistry 7th Edition, page 3
Reading a Meniscus
10
8
6
line of sight too high
reading too low
reading too high
line of sight too low
proper line of sightreading correct
graduatedcylinder
10 mL
Christopherson Scales
Made in Normal, Illinois USA
Units for Measuring Mass
1 kg = 2.20 lb
1 kg(1000 g) 1 lb 1 lb
0.20 lb
Quantities of Mass
Kelter, Carr, Scott, Chemistry A Wolrd of Choices 1999, page 25
Earth’s atmosphere to 2500 km
Ocean liner
Indian elephant
Average human
1.0 liter of water
Grain of table salt
Typical protein
Uranium atomWater molecule
1024 g
1021 g
1018 g
1015 g
1012 g
109 g
106 g
103 g
100 g
10-3 g
10-6 g
10-9 g
10-12 g
10-15 g
10-18 g
10-21 g
10-24 g
Giga- Mega-
Kilo-Kilo-
base
milli-milli-
micro-
nano-
pico-
femto-
atomo-
Factor Name Symbol Factor Name Symbol
10-1 decimeter dm 101 decameter dam
10-2 centimeter cm 102 hectometer hm
10-3 millimeter mm 103 kilometer km
10-6 micrometer m 106 megameter Mm
10-9 nanometer nm 109 gigameter Gm
10-12 picometer pm 1012 terameter Tm
10-15 femtometer fm 1015 petameter Pm
10-18 attometer am 1018 exameter Em
10-21 zeptometer zm 1021 zettameter Zm
10-24 yoctometer ym 1024 yottameter Ym
Scientific Notation: Powers of Ten
Rules for writing numbers in scientific notation:
Write all significant figures but only the significant figures.
Place the decimal point after the first digit, making the number have a value between 1 and 10. Use the correct power of ten to place the decimal point properly, as indicated below. a) Positive exponents push the decimal point to the right. The number becomes larger. It is multiplied by the power of 10. b) Negative exponents push the decimal point to the left. The number becomes smaller. It is divided by the power of 10. c) 10o = 1
Examples: 3400 = 3.20 x 103 0.0120 = 1.20 x 10-2
Nice visual display of Powers of Ten (a view from outer space to the inside of an atom) viewed by powers of 10!
Multiples of bytesas defined by IEC 60027-2
SI prefix Binary prefixes
Name Symbol Multiple NameSymbol
Multiple
kilobyte kB 103 (or 210) kibibyte KiB 210
megabyte MB 106 (or 220) mebibyte MiB 220
gigabyte GB 109 (or 230) gibibyte GiB 230
terabyte TB 1012 (or 240) tebibyte TiB 240
petabyte PB 1015 (or 250) pebibyte PiB 250
exabyte EB 1018 (or 260) exbibyte EiB 260
zettabyte ZB 1021 (or 270)
yottabyte YB 1024 (or 280)
A yottabyte (derived from the SI prefix )
SI-US Conversion FactorsRelationship Conversion Factors
Length
Volume
Mass
2.54 cm = 1 in.
1 m = 39.4 in.
946 mL = 1 qt
1 L = 1.06 qt
454 g = 1 lb
1 kg = 2.20 lb
1 in2.54 cm
39.4 in 1 m
1 m 39.4 in.
946 mL 1 qt
1 qt 946 mL
1.06 qt 1 L
1 L 1.06 qt
454 g 1 lb
1 lb 454 g
2.20 lb 1 kg
1 kg 2.20 lb
2.54 cm 1 in and
and
and
and
and
and
Accuracy vs. Precision
Random errors: reduce precision
Good accuracyGood precision
Poor accuracyGood precision
Poor accuracyPoor precision
Systematic errors: reduce accuracy
(person)(instrument)
Precision Accuracy
reproducibility
check by repeating measurements
poor precision results from poor technique
correctness
check by using a different method
poor accuracy results from procedural or equipment flaws.
Types of errors
Systematic
• Instrument not ‘zeroed’ properly
• Reagents made at wrong concentration
Random
• Temperature in room varies ‘wildly’
• Person running test is not properly trained
Errors
SystematicErrors in a single direction (high or low)
Can be corrected by proper calibration or running controls and blanks.
RandomErrors in any direction.
Can’t be corrected. Can only be accounted
for by using statistics.
Accuracy Precision Resolution
subsequent samples
time
off
set
[arb
itrar
y un
its]
not accurate, not precise accurate, not precise not accurate, precise
accurate and precise accurate, low resolution
-2
-3
-1
0
1
2
3
SI Prefixes
kilo- 1000
deci- 1/10
centi- 1/100
milli- 1/1000
Also know…
1 mL = 1 cm3 and 1 L = 1 dm3
SI System for Measuring Length
Unit Symbol Meter Equivalent _______________________________________________________________________
kilometer km 1,000 m or 103 m
meter m 1 m or 100 m
decimeter dm 0.1 m or 10-1 m
centimeter cm 0.01 m or 10-2 m
millimeter mm 0.001 m or 10-3 m
micrometer m 0.000001 m or 10-6 m
nanometer nm 0.000000001 m or 10-9 m
The SI Units for Measuring Length
Zumdahl, Zumdahl, DeCoste, World of Chemistry 2002, page 118
Comparison of English and SI Units
1 inch
2.54 cm
1 inch = 2.54 cmZumdahl, Zumdahl, DeCoste, World of Chemistry 2002, page 119
Reporting Measurements
• Using significant figures
• Report what is known with certainty
• Add ONE digit of uncertainty (estimation)
Davis, Metcalfe, Williams, Castka, Modern Chemistry, 1999, page 46
Measuring a Pin
Zumdahl, Zumdahl, DeCoste, World of Chemistry 2002, page 122
Practice Measuring
4.5 cm
4.54 cm
3.0 cm
Timberlake, Chemistry 7th Edition, page 7
cm0 1 2 3 4 5
cm0 1 2 3 4 5
cm0 1 2 3 4 5
Implied Range of Uncertainty
5 643
Implied range of uncertainty in a measurement reported as 5 cm.
5 643
Implied range of uncertainty in a measurement reported as 5.0 cm.
Dorin, Demmin, Gabel, Chemistry The Study of Matter 3rd Edition, page 32
5 643
Implied range of uncertainty in a measurement reported as 5.00 cm.
20
10
?
15 mL ?15.0 mL1.50 x 101 mL
Reading a Vernier
A Vernier allows a precise reading of some value. In the figure to the left, the Vernier moves up and down to measure a position on the scale.
This could be part of a barometer which reads atmospheric pressure.
The "pointer" is the line on the vernier labeled "0". Thus the measured position is almost exactly 756 in whatever units the scale is calibrated in.
If you look closely you will see that the distance between the divisions on the vernier are not the same as the divisions on the scale. The 0 line on the vernier lines up at 756 on the scale, but the 10 line on the vernier lines up at 765 on the scale. Thus the distance between the divisions on the vernier are 90% of the distance between the divisions on the scale.
756
750
760
770
Sca
le 5
0
10V
ern
ier
http://www.upscale.utoronto.ca/PVB/Harrison/Vernier/Vernier.html
If we do another reading with the vernier at a different position, the pointer, the line marked 0, may not line up exactly with one of the lines on the scale. Here the "pointer" lines up at approximately 746.5 on the scale.
If you look you will see that only one line on the vernier lines up exactly with one of the lines on the scale, the 5 line. This means that our first guess was correct: the reading is 746.5.
5
0
10
750
740
760
What is the reading now? 741.9
http://www.upscale.utoronto.ca/PVB/Harrison/Vernier/Vernier.html
750
740
760
If we do another reading with the vernier at a different position, the pointer, the line marked 0, may not line up exactly with one of the lines on the scale. Here the "pointer" lines up at approximately 746.5 on the scale.
If you look you will see that only one line on the vernier lines up exactly with one of the lines on the scale, the 5 line. This means that our first guess was correct: the reading is 746.5.
5
0
10
What is the reading now? 756.0
http://www.upscale.utoronto.ca/PVB/Harrison/Vernier/Vernier.html
750
740
760 Here is a final example, with the vernier at yet another position. The pointer points to a value that is obviously greater than 751.5 and also less than 752.0. Looking for divisions on the vernier that match a division on the scale, the 8 line matches fairly closely. So the reading is about 751.8.
In fact, the 8 line on the vernier appears to be a little bit above the corresponding line on the scale. The 8 line on the vernier is clearly somewhat below the corresponding line of the scale. So with sharp eyes one might report this reading as 751.82 ± 0.02.This "reading error" of ± 0.02 is probably the correct error of precision to specify for all measurements done with this apparatus.
5
0
10
http://www.upscale.utoronto.ca/PVB/Harrison/Vernier/Vernier.html
How to Read a Thermometer(Celcius)
10
5
0
4.0 oC
10
5
0
8.3 oC
100
50
0
64 oC
5
0
3.5 oC
0oC
10oC
20oC
30oC
40oC
50oC
60oC
0oC
1oC
2oC
3oC
4oC
5oC
6oC
0oC
5oC
10oC
15oC
20oC
25oC
0oC
20oC
40oC
60oC
80oC
100oC
0oC
20oC
40oC
60oC
80oC
100oC
Record the Temperature(Celcius)
AA BB CC DD EE30.0oC 3.00oC 19.0oC 48oC 60.oC
MeasurementsMeasurements
Metric (SI) unitsMetric (SI) units PrefixesPrefixes UncertaintyUncertainty
Significant figures
Significant figures
Conversionfactors
Conversionfactors
LengthLength
DensityDensity
MassMass VolumeVolume
Problem solving withconversion factors
Problem solving withconversion factors
Timberlake, Chemistry 7th Edition, page 40
I
II
III
Using Measurements
MEASUREMENT
Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem
Accuracy vs. Precision
AccuracyAccuracy - how close a measurement is to the accepted value
PrecisionPrecision - how close a series of measurements are to each other
ACCURATE = Correct
PRECISE = ConsistentCourtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem
Percent Error
Indicates accuracy of a measurement
100literature
literaturealexperimenterror %
your value
accepted valueCourtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem
Percent Error
A student determines the density of a substance to be 1.40 g/mL. Find the % error if the accepted value of the density is 1.36 g/mL.
100g/mL 1.36
g/mL 1.36g/mL 1.40error %
% error = 2.9 %
Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem
Significant Figures
Indicate precision of a measurement.
Recording Sig Figs
Sig figs in a measurement include the known digits plus a final estimated digit
2.35 cm
Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem
Significant Figures
Counting Sig Figs (Table 2-5, p.47)
Count all numbers EXCEPT:
Leading zeros -- 0.0025
Trailing zeros without a decimal point -- 2,500
Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem
4. 0.080
3. 5,280
2. 402
1. 23.50
Significant Figures
Counting Sig Fig Examples
1. 23.50
2. 402
3. 5,280
4. 0.080
4 sig figs
3 sig figs
3 sig figs
2 sig figs
Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem
Significant Figures
Calculating with Sig Figs
Multiply/Divide - The # with the fewest sig figs determines the # of sig figs in the answer.
(13.91g/cm3)(23.3cm3) = 324.103g
324 g
4 SF 3 SF3 SF
Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem
Significant Figures
Calculating with Sig Figs (con’t)
Add/Subtract - The # with the lowest decimal value determines the place of the last sig fig in the answer.
3.75 mL
+ 4.1 mL
7.85 mL
224 g
+ 130 g
354 g 7.9 mL 350 g
3.75 mL
+ 4.1 mL
7.85 mL
224 g
+ 130 g
354 g Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem
Significant Figures
Calculating with Sig Figs (con’t)
Exact Numbers do not limit the # of sig figs in the answer.Counting numbers: 12 studentsExact conversions: 1 m = 100 cm “1” in any conversion: 1 in = 2.54 cm
Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem
Significant Figures
5. (15.30 g) ÷ (6.4 mL)
Practice Problems
= 2.390625 g/mL
18.1 g
6. 18.9 g
- 0.84 g18.06 g
4 SF 2 SF
2.4 g/mL2 SF
Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem
Scientific Notation
Converting into scientific notation:
Move decimal until there’s 1 digit to its left. Places moved = exponent.
Large # (>1) positive exponentSmall # (<1) negative exponent
Only include sig. figs.
65,000 kg 6.5 × 104 kg
Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem
Scientific Notation
7. 2,400,000 g
8. 0.00256 kg
9. 7 10-5 km
10. 6.2 104 mm
Practice Problems
2.4 106 g
2.56 10-3 kg
0.00007 km
62,000 mmCourtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem
Scientific Notation
Calculating with scientific notation
(5.44 × 107 g) ÷ (8.1 × 104 mol) =
5.44EXPEXP
EEEE÷÷
EXPEXP
EEEE ENTERENTER
EXEEXE7 8.1 4
= 671.6049383 = 670 g/mol = 6.7 × 102 g/mol
Type on your calculator:
Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem
Proportions
Direct Proportion
Inverse Proportion
xy
xy
1
y
x
y
xCourtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem
Reviewing ConceptsMeasurement
• Why do scientists use scientific notation?
• What system of units do scientists use for measurements?
• How does the precision of measurements affect the precision of scientific calculations?
• List the SI units for mass, length, and temperature.
Rules for Counting Significant Figures
1. Nonzero integers always count as significant figures.
2. Zeros: There are three classes of zeroes.
a. Leading zeroes precede all the nonzero digits and DO NOT count assignificant figures. Example: 0.0025 has ____ significant figures.
b. Captive zeroes are zeroes between nonzero numbers. These alwayscount as significant figures. Example: 1.008 has ____ significant figures.
c. Trailing zeroes are zeroes at the right end of the number.
Trailing zeroes are only significant if the number contains a decimal point.Example: 1.00 x 102 has ____ significant figures.
Trailing zeroes are not significant if the number does not contain a decimalpoint. Example: 100 has ____ significant figure.
3. Exact numbers, which can arise from counting or definitions such as 1 in = 2.54 cm, never limit the number of significant figures in a calculation.
2
4
3
1
Ohn-Sabatello, Morlan, Knoespel, Fast Track to a 5 Preparing for the AP Chemistry Examination 2006, page 53
Significant figures: Rules for zeros
Leading zeros are not significant.
Captive zeros are significant.
Trailing zeros are significant.
Leading zeroLeading zero
Captive zeroCaptive zero
Trailing zeroTrailing zero
0.421
4012
114.20
– three significant figures
– four significant figures
– five significant figures
How to pick a lab partner
?