Chemistry Chapter Chemistry Chapter 22

Measurements Measurements and and

CalculationsCalculations

Steps in the Scientific MethodSteps in the Scientific Method

1.1. ObservationsObservations

-- quantitativequantitative

- - qualitativequalitative

2.2. Formulating hypothesesFormulating hypotheses

- - possible explanation for the possible explanation for the observationobservation

3.3. Performing experimentsPerforming experiments

- - gathering new information to gathering new information to decidedecide

whether the hypothesis is validwhether the hypothesis is valid

Outcomes Over the Long-Outcomes Over the Long-TermTerm

Theory (Model)Theory (Model)

- - A set of tested hypotheses that give anA set of tested hypotheses that give an overall explanation of some natural overall explanation of some natural

phenomenonphenomenon..

Natural LawNatural Law

-- The same observation applies to many The same observation applies to many different systemsdifferent systems

-- Example - Law of Conservation of Example - Law of Conservation of MassMass

Law vs. TheoryLaw vs. Theory

A A lawlaw summarizes what summarizes what happenshappens

A A theorytheory (model) is an attempt (model) is an attempt to explain to explain whywhy it happens. it happens.

Nature of MeasurementNature of Measurement

Part 1 - Part 1 - numbernumberPart 2 - Part 2 - scale (unit)scale (unit)

Examples:Examples:2020 gramsgrams

6.63 x 106.63 x 10-34-34 Joule secondsJoule seconds

Measurement - quantitative Measurement - quantitative observation observation consisting of 2 partsconsisting of 2 parts

The Fundamental SI UnitsThe Fundamental SI Units (le Système International, SI)(le Système International, SI)

Physical Quantity Name Abbreviation

Mass kilogram kg

Length meter m

Time second s

Temperature Kelvin K

Electric Current Ampere A

Amount of Substance mole mol

Luminous Intensity candela cd

SI UnitsSI Units

SI PrefixesSI PrefixesCommon to ChemistryCommon to Chemistry

Prefix Unit Abbr. ExponentKilo k 103

Deci d 10-1

Centi c 10-2

Milli m 10-3

Micro 10-6

Uncertainty in MeasurementUncertainty in Measurement

A A digit that must be digit that must be estimatedestimated is is called called uncertainuncertain. A . A measurementmeasurement always has some degree of always has some degree of uncertainty.uncertainty.

Why Is there Uncertainty?Why Is there Uncertainty? Measurements are performed with instruments No instrument can read to an infinite number of decimal placesWhich of these balances has the greatest

uncertainty in measurement?

Precision and AccuracyPrecision and AccuracyAccuracyAccuracy refers to the agreement of a refers to the agreement of a particular value with the particular value with the truetrue value.value.

PrecisionPrecision refers to the degree of agreement refers to the degree of agreement among several measurements made in the among several measurements made in the same manner.same manner.

Neither accurate nor

precise

Precise but not accurate

Precise AND accurate

Types of ErrorTypes of Error

Random ErrorRandom Error (Indeterminate Error) - (Indeterminate Error) - measurement has an equal probability of measurement has an equal probability of being high or low.being high or low.

Systematic ErrorSystematic Error (Determinate Error) - (Determinate Error) - Occurs in the Occurs in the same directionsame direction each time each time (high or low), often resulting from poor (high or low), often resulting from poor technique or incorrect calibration.technique or incorrect calibration.

Rules for Counting Rules for Counting Significant Figures - DetailsSignificant Figures - Details

Nonzero integersNonzero integers always count always count as significant figures.as significant figures.

34563456 hashas

44 sig figs.sig figs.

Rules for Counting Rules for Counting Significant Figures - DetailsSignificant Figures - Details

ZerosZeros-- Leading zerosLeading zeros do not count do not count as as

significant figuressignificant figures..

0.04860.0486 has has

33 sig figs. sig figs.

Rules for Counting Rules for Counting Significant Figures - DetailsSignificant Figures - Details

ZerosZeros-- Captive zeros Captive zeros always always

count ascount assignificant figures.significant figures.

16.07 16.07 hashas

44 sig figs. sig figs.

Rules for Counting Rules for Counting Significant Figures - DetailsSignificant Figures - Details

ZerosZerosTrailing zerosTrailing zeros are significant are significant only if the number contains a only if the number contains a decimal point.decimal point.

9.3009.300 has has

44 sig figs. sig figs.

Rules for Counting Rules for Counting Significant Figures - DetailsSignificant Figures - Details

Exact numbersExact numbers have an infinite have an infinite number of significant figures.number of significant figures.

11 inch = inch = 2.542.54 cm, exactlycm, exactly

Sig Fig Practice #1Sig Fig Practice #1How many significant figures in each of 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 2 sig figs

Rules for Rounding OffRules for Rounding Off

1.If the digit to be removed a. is less than 5, the preceding digit stays the same for example, 1.33 rounds to 1.3.b. is equal to or greater than 5, the preceding digit is increases by 1. For example, 1.36 rounds to 1.4 and 3.15 rounds to 3.2.

Rules for rounding offRules for rounding off

2. In a series of calculations, carry the extra digits through t the final results and then round off. This means that you should carry all of the digits that show on your calculator until you arrive at the final number ( the answer) and then you round off, using the procedure in rule 1.

Rules for Significant Figures in Rules for Significant Figures in Mathematical OperationsMathematical Operations

Multiplication and DivisionMultiplication and Division:: # sig # sig figs in the result equals the number figs in the result equals the number in the least precise measurement in the least precise measurement used in the calculation.used in the calculation.

6.38 x 2.0 =6.38 x 2.0 =

12.76 12.76 13 (2 sig figs)13 (2 sig figs)

Sig Fig Practice #2Sig Fig Practice #2

3.24 m x 7.0 m

Calculation 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 ÷ 2.87 mL 2.9561 g/mL 2.96 g/mL

Rules for Significant Figures Rules for Significant Figures in Mathematical Operationsin Mathematical Operations

Addition and SubtractionAddition and Subtraction: The : The number of decimal places in the number of decimal places in the result equals the number of decimal result equals the number of decimal places in the least precise places in the least precise measurement.measurement.

6.8 + 11.934 =6.8 + 11.934 =

18.734 18.734 18.7 ( 18.7 (3 sig figs3 sig figs))

Sig Fig Practice #3Sig Fig Practice #3

3.24 m + 7.0 m

Calculation 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

Direct ProportionsDirect Proportions The quotient of two variables is a constant As the value of one variable increases, the other must also increase As the value of one variable decreases, the other must also decrease The graph of a direct proportion is a straight line

Inverse ProportionsInverse Proportions The product of two variables is a constant As the value of one variable increases, the other must decrease As the value of one variable decreases, the other must increase The graph of an inverse proportion is a hyperbola

Converting from one Unit to Converting from one Unit to AnotherAnother

Step one To convert from one unit to another , use the

conversion that relates to that statement.1m=100cm

Step twpChoose the appropriate conversion factor by

looking at the direction of the required change. Make sure the unwanted units are on the bottom, cancel out.

12in x 2.54cm/1in

Converting from One Unit to Converting from One Unit to AnotherAnother

Step 3Multiply the quantity to be converted by the conversion factor to give the quantity with the desired units.

12in x 2.54cm/1in=30.48 cm

Step 4 Check that you have the correct number if

significant figures.30 cm

Converting from One Unit to Converting from One Unit to AnotherAnother

Step 5Ask whether your answer makes since.