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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