chapter 3 scientific measurement - mr. b's science...
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Chapter 3Scientific
Measurement
Measurements 2 types: Qualitative measurements (words) Heavy, hot, or long Quantitative measurements (#’s) & depend on:
1) Reliability of measuring instrument2) Care w/ which it’s read – determined by YOU!
Scientific Notation Coefficient raised to power 10 (ex. 1.3 x 107)
Review: Textbook pages R56 & R57
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Accuracy, Precision, and Error Necessary for reliable lab measurements Accuracy –
Precision –
Reproducible For #’s w/ decimal pt……… decimal place
right-most digit is in
134.900.0157
how close measurement is to true valuehow close measurements to each other
Accuracy, Precision, and Error
For #’s w/o decimal pt…...right-most non-zero #34200
120390
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Precision and Accuracy
Accuracy, Precision, and Error
Accepted value – based on reliable references (Density Table page 90)
Experimental value - measured in lab
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Accuracy, Precision, and Error
Error = accepted value – experimental value
can be + or - Percent error = absolute value of error
divided by accepted value, & multiplied by 100%
| error |
accepted valuex 100%% error =
NFL Flyovers 4:53
Significant Figures in Measurements
Significant figures all known digits + one estimated digitMeasurements must be recorded to
correct # sig figs
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Figure 3.5 Significant Figures - Page 67
Which measurement is the best?
What is the measured value?
What is the measured value?
What is the measured value?
Rules for Counting Sig Figs
Non-zeros always count as sig figs:
3456 has4 sig figs
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Rules for Counting Sig Figs
ZerosLeading zeroes do not count as sig figs:
0.0486 has3 sig figs
Rules for Counting Sig Figs
ZerosCaptive zeroes always count as sig figs:
16.07 has4 sig figs
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Rules for Counting Sig Figs
Zeros
Trailing zeros significant only w/ written decimal point:
9.300 has4 sig figs
Rules for Counting Sig Figs
Two special situations have unlimited # sig figs:
1. Counted itemsa) 23 people, or 425 thumbtacks
2. Exactly defined quantitiesb) 60 minutes = 1 hour
Big Sig Fig Gig (2:27) – Mark Rosengarten
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Sig Fig Practice #1How many significant figures in the following?
1.0070 m 5 sig figs
17.10 kg 4 sig figs
100,890 L 5 sig figs
3.29 x 103 s 3 sig figs
0.0054 cm 2 sig figs
3,200,000 mL 2 sig figs5 dogs unlimited
These all comefrom some
measurements
This is a counted value
Sig Figs in Calculations answer cannot be more precise than
least precise measurement. Sometimes, calculated values need
rounded off
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Rounding Calculated Answers
RoundingDecide how many sig figs needed Round to that many digits, counting from the left Is next digit less than 5? Drop it. Is next digit 5+? Add 1
- Page 69
Be sure to answer the question completely!
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Rounding Calculated Answers
Addition and Subtractionanswer rounded to same # decimal places as least # decimal places in problem
- Page 70
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Rounding Calculated Answers
Multiplication and Divisionanswer rounded to same # of sig figs as least # of sig figs in problem
- Page 71
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Rules for Sig Figs in Mathematical Operations
• Multiplication and Division: # sig figs in result = # in least precisemeasurement used in calculation.
• 6.38 x 2.0 =• 12.76 13 (2 sig figs)
Sig Fig Practice #2
3.24 m x 7.0 mCalculation Calculator says: Answer
22.68 m2 23 m2
100.0 g ÷ 23.7 cm3 4.219409283 g/cm3 4.22 g/cm3
0.02 cm x 2.371 cm 0.04742 cm2 0.05 cm2
710 m ÷ 3.0 s 236.6666667 m/s 240 m/s
1818.2 lb x 3.23 ft 5872.786 lb·ft 5870 lb·ft
1.030 g x 2.87 mL 2.9561 g/mL 2.96 g/mL
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Rules for Sig Figs in Mathematical Operations
• Addition and Subtraction: # decimal places in result = # decimal places in least precise measurement.
• 6.8 + 11.934 =• 18.734 18.7 (3 sig figs)
Sig Fig Practice #3
3.24 m + 7.0 mCalculation Calculator says: Answer
10.24 m 10.2 m
100.0 g - 23.73 g 76.27 g 76.3 g
0.02 cm + 2.371 cm 2.391 cm 2.39 cm
713.1 L - 3.872 L 709.228 L 709.2 L
1818.2 lb + 3.37 lb 1821.57 lb 1821.6 lb
2.030 mL - 1.870 mL 0.16 mL 0.160 mL
*Note the zero that has been added.
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International System of Units p. 73
Measurements depend on unitsThe standards of measurement of science is Metric System
Why science uses the metrics 2:30
International System of Units
Metric system now revised & named International System of Units (SI), (1960)multiples of 105 common base units in chemistry meter, kilogram, kelvin, second & mole
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Nature of Measurements
•
Part 1 – number Part 2 - unit
Examples: 22 grams
3.55 x 103 moles
Measurement - quantitative observation -2 parts:
International System of Units
Sometimes, non-SI units usedLiter, Celsius, calorieDerived unitsjoining unitsSpeed = kilometers/hour (distance/time)Density = grams/mL (mass/volume)
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Length
SI basic unit - meter (m)distance btwn 2 objects use prefixes for larger/smaller units
SI Prefixes – Page 74 - Common to Chemistry
Prefix Abbreviation Meaning Exponent
Mega- M Million 106
Kilo- k thousand 103
Deci- d tenth 10-1
Centi- c hundredth 10-2
Milli- m thousandth 10-3
Micro- millionth 10-6
Nano- n billionth 10-9
Pico- P trillionth 10-12
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Volume Space occupied by matterCalculated for solid…length x width x
heightderived from units of length
SI unit = cubic meter (m3) Everyday unit = Liter (L), non-SI (Note: 1mL = 1cm3)
Devices for Measuring Liquid Volume
Graduated cylindersPipetsBuretsVolumetric FlasksSyringes
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Volume Changes!Volumes of a solid, liquid, or gas generally increases w/ tempMore prominent for GASESTherefore, measuring instruments calibrated for specific temp usually 20 oC, which is about room temp
Ex. Volumetric flask
Units of Mass
Mass - quantity of matter presentMass constant, regardless of location
Weight - force of “g”- changes w/ location
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Working with Mass
SI unit - kilogram (kg)everyday unit is gram (g)measuring instrument: triple beam balance
Units of Temperature
Temp - measures how hot/cold object is.
Heat moves from hi - low temp2 temp scales:◦Celsius – named after Anders Celsius◦Kelvin – named after Lord Kelvin
(Measured with a thermometer.)
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Units of TemperatureCelsius scale◦Water Freezing point = 0 oC◦Water Boiling point = 100 oC
Kelvin scale does not use degree sign, just K• absolute zero = 0 K (no negative values)
• formula to convert: K = oC + 273
- Page 78
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Units of Energy
Energy - ability to do work, or produce heat
energy can be measured 2 common units:
1) Joule (J) = SI unit of energy, named after James Prescott Joule
2) calorie (cal) = heat needed to raise 1g of water 1 oC
Units of Energy
Conversions btwn joules & calories carried out by using following relationship:
1 cal = 4.184 J
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Sec 3.3 Conversion factorsA “ratio” of equivalent measurements Start with two things that are the same:
one meter is one hundred centimeters write it as an equation
1 m = 100 cmDivide on each side of equation to come
up with 2 ways of writing the number “1”
Conversion factors
100 cm1 m =100 cm 100 cm
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Conversion factors
11 m =100 cm
Conversion factors
11 m =100 cm
100 cm=1 m1 m 1 m
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Conversion factors
11 m =100 cm
100 cm=1 m
1
Conversion factorsunique way of writing the # 1 In same system they are defined
quantities so unlimited number of sig figs
big # small unit = small # big unit100 cm = 1 m
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Practice writing two possible conversion factors for the following:
Between kilograms and gramsbetween feet and inchesusing 1.096 qt. = 1.00 L
What are they good for?
We can multiply by # “one” creatively to change units
Question: 13 inches is how many yards? We know that 36 inches = 1 yard 1 yard = 1
36 inches 13 inches x 1 yard =
36 inches
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What are they good for?
We can multiply by a conversion factor to change the units .
Problem: 13 inches is how many yards?
Known: 36 inches = 1 yard.
1 yard = 136 inches
13 inches x 1 yard = 0.36 yards36 inches
Dimensional AnalysisMethod of analyzing & solving problems,
by using units (dimensions) of measurement
Dimension = unit (g, L, cm)Analyze = solve◦ Using units to solve problems
If units of answer correct, you probably did math correctly!
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Dimensional Analysis provides alternative approach to problem
solving, instead of with equation or algebra. ruler is 12.0 inches long. How long is it in
cm? ( 1 inch = 2.54 cm)How long is this in meters?A race is 10.0 km long. How far is this in
miles, if:◦ 1 mile = 1760 yards◦ 1 meter = 1.094 yards
p. 82 practice problem #28 How many minutes are there in exactly one week?
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p. 83 practice problem # 30
An experiment requires that each student use an 8.5-cm length of magnesium ribbon. How many students can do the experiment if there is a 570-cm length of magnesium ribbon available?
Converting Between Unitsmeasurements with one unit converted to
equivalent measurement with another unit easily solved using dimensional analysis
Sample: Express 750 dg in grams.Many complex problems are best solved
by breaking the problem into manageable parts.
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p. 84 practice problem #32Using tables from this chapter, convert these:
a. 0.044 km to meters
b. 4.6 mg to grams
c. 0.107 g to centigrams
Converting Between Units Let’s say you need to clean your car:
1) Start by vacuuming the interior2) Next, wash the exterior3) Dry the exterior4) Finally, put on a coat of wax
• What problem-solving methods can help you solve complex word problems? Break the solution down into steps, and use
more than one conversion factor if necessary
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p. 85 practice problem # 34(p. 30 in workbook)
The radius of a potassium atom is 0.227 nm. Express this radius in the unit centimeters.
Converting Complex Units? Complex units are those that are
expressed as a ratio of two units:◦ Speed might be meters/hour
Sample: Change 15 meters/hour to units of centimeters/second
How do we work with units that are squared or cubed? (cm3 to m3, etc.)
BONUS: Crash of Flight 143 – see my webpage
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- Page 86
Section 3.4 DensityWhich is heavier- a pound of steel or a pound of styrofoam?Most people answer “steel”, but the weight is exactly the sameThey are normally thinking about equal volumes of the two
The relationship here between mass and volume is called Density
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Density The formula for density is:
massvolume
• Common units are: g/mL, or g/cm3, (or g/L for gas)
• Density is a physical property, and does not depend upon sample size• A gold nugget has the same density as a
gold bar
Density =
- Page 90Note temperature and density units
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Density and Temperature
What happens to the density as the temperature of an object increases?Mass remains the sameMost substances increase in volume as temperature increases
Thus, density generally decreases as the temperature increases
Density and WaterWater is an important exception to
the previous statement.Over certain temperatures, the volume
of water increases as the temperature decreases (You don’t want your water pipes to freeze in the winter, right?)Why does ice float in liquid water?
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- Page 91
- Page 92
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