Chap02 Scientific Measurement

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    CHEMISTRYWorld of

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    Chapter 2

    MeasurementMeasurement

    s ands and

    CalculationsCalculations

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    Scientific Notation

    Scientific notation works by expressing very small

    or very large numbers as the product of two

    numbers that are individually much easier to deal

    with.

    The first numberis called the base.

    The second numberis a power of ten.

    The base is usually written with only one digit in

    front of the decimal point. ex. 2,500 would be written 2.5 103

    The small numeral 3 in 103 is called the

    exponent.

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    Accuracy and Precision

    accuracy is the quality ofbeing exact and free from error.

    how close a measurement is to the true value.

    precision

    is the degree ofmutual agreement among aseries ofindividual measurements, values, or

    results.

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    Wh

    y Is th

    ere Uncertainty? Measurements are performed with

    instruments, and no instrument can read to an

    infinite number of decimal places

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    Significant Figures

    Which measurement is the best?

    What is the

    measured

    value?

    What is the

    measured

    value?

    What is the

    measured

    value?

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    Significant Figures in

    Measurements

    Significant figures in a

    measurement include all ofthe digits that are known,

    plus one more digit that is

    estimated. Measurements must be

    reported to the correct

    n m r f i nifi n

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    Rules for Counting Significant

    Figures

    NonNonzeroszeros always count asalways count as

    significant figures:significant figures:

    34563456 hashas44 significant figuressignificant figures

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    Rules for Counting Significant

    Figures

    Zeros

    Leading zeroes do notcount as significant

    figures:

    0.0486 has

    3 significant figures

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    Rules for Counting Significant

    FiguresZeros

    Captive zeroes always

    count as significant

    figures:

    16.07 has

    4 significant figures

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    Rules for Counting Significant

    FiguresZeros

    Trailing zeros are

    significant only if the

    number contains a

    written decimal point:

    9.300 has

    4 si nificant fi ures

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    Rules for Counting Significant

    Figures

    Two special situations have an

    unlimited number ofsignificant figures:

    1. Counted items

    a) 23 people, or 425 thumbtacks2. Exactly defined quantities

    b) 60 minutes = 1 hour

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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 figs3,200,000 mL 2 sig figs

    5 dogs unlimited

    These all come

    from some

    measurements

    This is a

    counted value

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    Significant Figures inCalculations

    In general a calculated answer

    cannot be more precise than

    the least precise measurement

    from which it was calculated.

    Sometimes, calculated values

    need to be rounded off.

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    Rounding Calculated

    Answers Rounding Decide how many significant

    figures are needed (more on thisvery soon)

    Round to that many digits,

    counting from the left

    Is the next digit less than 5?

    Drop it.

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    Rounding Calculated

    Answers Addition and Subtraction

    The answer should berounded to the same

    number of decimal places

    as the least number ofdecimal places in the

    problem.

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    Rounding Calculated

    Answers

    Multiplication and Division

    Round the answer to thesame number of

    significant figures as theleast number of

    significant figures in the

    roblem.

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    Rules for Significant Figures inRules for Significant Figures in

    Mathematical OperationsMathematical Operations

    Multiplication andMultiplication and

    DivisionDivision: # sig figs in the: # sig figs in the

    result equals the number inresult equals the number in

    thethe least preciseleast precise

    measurement used in themeasurement used in thecalculation.calculation.

    6.38 x 2.0 =6.38 x 2.0 =

    12.7612.76 1313 2 si fi s2 si fi s

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    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 lbft 5870 lbft

    1.030 g x 2.87 mL 2.9561 g/mL 2.96 g/mL

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    Rules for Significant Figures inRules for Significant Figures in

    Mathematical OperationsMathematical Operations

    Addition and SubtractionAddition and Subtraction::

    The number of decimalThe number of decimal

    places in the result equalsplaces in the result equalsthe number of decimalthe number of decimal

    places in theplaces in the least preciseleast precise

    measurement.measurement.

    6.8 + 11.934 = 18.7346.8 + 11.934 = 18.734 18.718.7(3 sig figs)(3 sig figs)

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    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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    Two Systems of Units

    Science problem solving requires both:

    Metric system

    English system

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    International System of

    Units

    Measurements depend upon

    units that serve asreference standards

    The standards ofmeasurement used in

    science are those of the

    Metric S stem

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    International System of

    UnitsMetric system is now revised andnamed as the International

    System of Units (SI), as of 1960

    It has simplicity, and is based on10 or multiples of 10

    7 base units, but only fivecommonly used in chemistry: meter,kilogram, kelvin, second, and mole.

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    Measurements

    Part 1Part 1

    numbernumber Part 2Part 2 scale (unit)scale (unit)

    Examples:Examples:20 grams20 grams

    6.636.63 x 10x 103434 JouleJoule

    Measurement quantitativeobservationconsisting of 2 parts:

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    International System ofUnitsSometimes, non-SI units are used

    Liter, Celsius, calorieSome are derived units

    They are made by joining other

    units Speed = miles/hour

    (distance/time)

    Densit = rams/mL

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    Distance and Length

    Key Question:

    How do we accurately communicate length and

    distance?

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    Distance and Length

    measurement -

    a quantity and a unit

    distance - is a length

    the amount of space

    between two points

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    LengthIn SI, the basic unit of length is

    the meter(m) Length is the distance

    between two objects

    measured with rulerWe make use of prefixes for

    units larger or smaller

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    Units of Length

    The common units ofmeasurement in the

    English system are inches, feet, yards, and

    miles.These four length units are related to the meter.

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    Convert length

    Afootball field is 100 yards long.

    What is this distance expressed in meters?

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    Knot (unit)knot is a unit ofspeed equal to one nautical

    mile (which is defined as 1.852 km) per hour,

    approximately 1.151 mph

    kn is preferred by the International Hydrographic

    Organization (IHO), which includes every major sea-

    faring nation; however, the abbreviations kt (singular)

    and kts (plural) are also widely used

    is a non-SI unit accepted for use with

    the International System ofUnits

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    1 international Knot =1 international Knot =

    1 nautical mile per hour

    1.852 kilometres per

    hour (exactly),

    0.514 metres per second,1.151 miles per hour

    (approximately).

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    KNOTS

    The U.S. adopted theinternational definition in

    1954, having previously used

    the U.S. nautical mile(1,853.248 m).

    The U.K. adopted the

    international nautical miledefinition in 1970, having

    previously used the U.K.

    Admiralt nautical mile

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    Conversions between common units of speed

    m/s km/h mph knot ft/s

    1 m/s = 1 3.6 2.236936 1.943844 3.280840

    1 km/h = 0.277778 1 0.621371 0.539957 0.911344

    1 mph = 0.44704 1.609344 1 0.868976 1.466667

    1 knot = 0.514444 1.852 1.150779 1 1.687810

    1 ft/s = 0.3048 1.09728 0.681818 0.592484 1

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    Volume

    The space occupied by any sampleof matter.

    Calculated for a solid by

    multiplying the length x width xheight; thus derived from units of

    length.

    SI unit = cubic meter (m3)Everyday unit = Liter (L), which is

    nonSI. (Note: 1mL = 1cm3)

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    Time

    Key Question:

    How do we measure and describe time?

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    Time

    T i ime:W ime i i

    . . e Time il

    , ,H m ime e

    : mi : e .

    i ime i e

    lle ime i e l.

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    Time Units

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    Measuring Mass

    kilogram -

    is the mass of1 liter

    ofwater or 1,000

    cubiccentimeters of

    water.

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    Units of Mass

    Mass is a measure of thequantity of matter present

    eight is a force thatmeasures the pull by

    gravity it changes with

    location

    Mass is constant, regardless of

    location

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    Working with MassThe SI unit of mass is the

    kilogram (kg), even though amore convenient everyday

    unit is the gram

    Measuring instrument is the

    balance scale

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    Units of Temperature

    Temperature is a measure of how

    hot or cold an object is.

    eat moves from the object at thehigher temperature to the object

    at the lower temperature.

    We use two units of temperature:Celsius named after Anders Celsius

    Kelvin named after Lord Kelvin

    (Measured with

    a

    thermometer.)

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    Units of Temperature

    Celsius scale defined by tworeadily determinedtemperatures:

    Freezing point of water = 0 oCBoiling point of water = 100 oC

    Kelvin scale does not use thedegree sign, but is justrepresented by K

    absolute zero = 0 K(thus no

    ne a ive value

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    Units of Energy

    Energy is the capacity to dowork, or to produce heat.

    Energy can also be measured,and two common units are:

    1) Joule (J) = the SI unit of

    energy, named after JamesPrescott Joule

    2) calorie (cal) = the heat needed

    to raise 1 gram of water by 1 oC

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    Units of EnergyConversions between

    joules and calories can becarried out by using the

    following relationship:

    1 cal = 4.18 J(sometimes you will see 1 cal = 4.184 J)

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    Conversion factors

    A unique way of writing thenumber 1

    In the same system they are

    defined quantities so they have an

    unlimited number of significant

    figures

    Equivalence statements always

    have this relationship:

    big # small unit = small # big unit

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    Conversion factorsC

    onversion factors

    100 cm1 m =100 cm 100 cm

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    Conversion factorsConversion factors

    11 m =

    100 cm

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    Conversion factorsConversion factors

    11 m =100 cm

    100 cm=1 m

    1 m 1 m

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    Conversion factorsConversion factors

    11 m =100 cm

    100 cm=

    1 m1

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    Conversion factorsCalle conversion factors

    eca se t e allo s toconvert nits.

    reall j st lti l inone, in a creative

    a .

    Di i l

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    Dimensional

    AnalysisA way to analyze and solveproblems, by using units (or

    dimensions) of the

    measurement

    Dimension = a unit (such as g,

    L, mL)Analyze = to solveUsing the units to solve the

    problems.

    Di i l A l i

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    Dimensional AnalysisDimensional Analysis provides analternative approach to problemsolving, instead of with anequation or algebra.

    A ruler is 12.0 inches long. owlong is it in cm? ( 1 inch = 2.54 cm)

    ow long is this in meters?

    A race is 10.0 km long. ow far isthis in miles, if:

    1 mile = 1760 yards

    1 meter = 1.094 yards

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    Density

    Which is heavier a pound of leador a pound of feathers?

    Most people will answer lead, butthe weight is exactly the same

    They are normally thinking about

    equal volumes of the twoThe relationship here betweenmass and volume is called Density

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    DensityThe formula for density is:

    mass

    volumeCommon units are: g/mL, or

    possibly g/cm3

    , (or g/L forgas)

    Density is a physical property,

    and does not de end u on

    Density

    =

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    - 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 same

    Most substances increase in

    volume as temperatureincreases

    Thus, density generally

    decreases as the

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    Density and Water

    Water is an importantexception to the previousstatement.

    Over certain temperatures,the volume of water increasesas the temperature decreases(Do you want your water pipesto freeze in the winter?)

    Does ice float in liquid water?

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    Ice floats in liquid water

    because hydrogen bonds

    more ordered, making

    ice less dense

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    Ice vs. Liquid Water

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