Section 2.1 Units and Measurements Pages 32-39. International System of Units (SI System) In 1960, the metric system was standardized in the form of the

Section 2.1Section 2.1Units and MeasurementsUnits and Measurements

Pages 32-39

International System of UnitsInternational System of Units (SI System) (SI System)

In 1960, the metric system was standardized in the form of the International System of Units (SI). These SI units were accepted by the international scientific community as the system for measuring all quantities.

SI Base UnitsSI Base Units are defined by an object or event in the physical are defined by an object or event in the physical

world.world.

QuantityQuantity Base UnitBase UnitTimeTime second (s)second (s)

LengthLength meter (m)meter (m)MassMass kilogram (kg)kilogram (kg)

TemperatureTemperature Kelvin (K)Kelvin (K)Amount of a Amount of a

SubstanceSubstancemole (mol)mole (mol)

Electric CurrentElectric Current ampere (A)ampere (A)Luminous IntensityLuminous Intensity candela (cd)candela (cd)

The foundation of the SI is seven independent quantities and their SI base units. You must learn the first 5 quantities listed!

SI PrefixesSI Prefixes

Prefix Symbol Numerical Value

Power of 10

Mega M 1,000,000

106

Kilo k 1000 103

---- ---- 1 100

Deci d 0.1 10-1

Centi c 0.01 10-2

Milli m 0.001 10-3

Micro u 0.000001 10-6

Nano n 0.000000001 10-9

Pico P 0.000000000001

10-12

SI base units are not always convenient to use so prefixes are attached to the base unit, creating a more convenient easier-to-use unit. You must memorize these!

TemperatureTemperature

Temperature is a measure of the average kinetic energy of the particles in a sample of matter.

273Kelvin Co

The Fahrenheit scale is not used in chemistry.

SI Derived UnitsSI Derived Units• In addition to the seven base units, other In addition to the seven base units, other

SI units can be made from combinations SI units can be made from combinations of the base units. of the base units.

• Area, volume, and density are examples Area, volume, and density are examples of derived units.of derived units.

Volume (mVolume (m33 or dm or dm3 3 or cmor cm33 ) ) length length length length length length

1 cm3 = 1 mL1 dm3 = 1 L

DensityDensity

Density (kg/m3 or g/cm3 or g/mL) is a physical property of matter.

D = mV

m = massV = volume

DensityDensityAn object has a volume of 825 cm3 and a

density of 13.6 g/cm3. Find its mass.

GIVEN:

V = 825 cm3

D = 13.6 g/cm3

m = ?

WORK:

m = DV

m = (13.6 g/cm3)(825cm3)

m = 11,220 g

m = 11,200 g (correct sig figs)

V

mD

DensityDensityA liquid has a density of 0.87 g/mL. What

volume is occupied by 25 g of the liquid?

GIVEN:

D = 0.87 g/mL

V = ?

m = 25 g

WORK:

V = m D

V = 25 g

0.87 g/mL

V = 29 mL (correct sig figs) V

mD

= 28.736 mL

Non SI UnitsNon SI UnitsThe volume unit, liter (L), and temperature unit, Celsius (C), are examples of non-SI units frequently used in chemistry.

SI & English RelationshipsSI & English Relationships

• One meter is approximately 3.3 feet.• One kilogram weighs approximately 2.2 pounds at the surface of the earth.

Remember: Mass (amount of material in the object) is constant,but weight (force of gravity on the object) may change.• One liter or one dm3 is slightly more than a quart, 1.06 quart to be exact.

Section 2.2Section 2.2Scientific NotationScientific Notation

Pages 40-43

Scientific Scientific NotationNotation

In science, we deal with some In science, we deal with some very very LARGELARGE numbers: numbers:

1 mole = 6020000000000000000000001 mole = 602000000000000000000000

In science, we deal with some In science, we deal with some very very SMALLSMALL numbers: numbers:

Mass of an electron =Mass of an electron =0.000000000000000000000000000000091 kg0.000000000000000000000000000000091 kg

Scientific NotationScientific Notation

Imagine the difficulty of Imagine the difficulty of calculating the mass of 1 mole calculating the mass of 1 mole of electrons!of electrons!

0.00000000000000000000000000000000.000000000000000000000000000000091 kg91 kg x 602000000000000000000000x 602000000000000000000000

???????????????????????????????????

Scientific Scientific Notation:Notation:A method of representing very large A method of representing very large

or very small numbers in the or very small numbers in the form:form:

M x 10M x 10nn

• MM is a number betweenis a number between 11 andand 1010• nn is an integeris an integer

2 500 000 000

Step #1: Insert an understood decimal pointStep #1: Insert an understood decimal point

Step #2: Decide where the decimal Step #2: Decide where the decimal must end must end up so that one number is to its up so that one number is to its leftleftStep #3: Count how many places you Step #3: Count how many places you bounce bounce the decimal pointthe decimal point

123456789

Step #4: Re-write in the form Step #4: Re-write in the form M x 10M x 10nn

..

2.5 x 102.5 x 1099

The exponent is the number of places we moved the decimal.

0.00005790.0000579

Step #2: Decide where the decimal Step #2: Decide where the decimal must end must end up so that one number is to its up so that one number is to its leftleftStep #3: Count how many places you Step #3: Count how many places you bounce bounce the decimal pointthe decimal pointStep #4: Re-write in the form M x 10Step #4: Re-write in the form M x 10nn

1 2 3 4 5

5.79 x 105.79 x 10-5-5

The exponent is negative because the number we started with was less than 1.

PERFORMING PERFORMING CALCULATIONS CALCULATIONS IN SCIENTIFIC IN SCIENTIFIC

NOTATIONNOTATION

ADDITION AND ADDITION AND SUBTRACTIONSUBTRACTION

ReviewReview::Scientific notation Scientific notation expresses a number in the expresses a number in the form:form: M x 10M x 10nn

1 1 M M 1010

n is an n is an integerinteger

4 x 104 x 1066

+ 3 x 10+ 3 x 1066

IFIF the exponents the exponents are the same, we are the same, we simply add or simply add or subtract the subtract the numbers in front numbers in front and bring the and bring the exponent down exponent down unchanged.unchanged.

77 x 10x 1066

4 x 104 x 1066

- 3 x 10- 3 x 1066

The same holds The same holds true for true for subtraction in subtraction in scientific scientific notation.notation.

11 x 10x 1066

4 x 104 x 1066

+ 3 x 10+ 3 x 1055

If the exponents If the exponents are NOT the are NOT the same, we must same, we must move a decimal to move a decimal to makemake them the them the same.same.

4.00 x 104.00 x 1066

+ + 3.00 x 103.00 x 1055 + + .30 x 10.30 x 1066

4.304.30 x 10x 1066

Move the Move the decimal decimal on the on the smallersmaller number!number!

4.00 x 104.00 x 1066

A Problem for A Problem for you…you…

2.37 x 102.37 x 10-6-6

+ 3.48 x 10+ 3.48 x 10-4-4

2.37 x 102.37 x 10-6-6

+ 3.48 x 10+ 3.48 x 10-4-4

Solution…Solution…002.37 x 10002.37 x 10--

66

+ 3.48 x 10+ 3.48 x 10-4-4

Solution…Solution…0.0237 x 100.0237 x 10-4-4

3.5037 x 103.5037 x 10-4-4

PERFORMING PERFORMING CALCULATIONS CALCULATIONS IN SCIENTIFIC IN SCIENTIFIC

NOTATIONNOTATION

Multiplication and DivisionMultiplication and Division

4.0 x 104.0 x 1066

XX 3.0 x 103.0 x 1055

Exponents do NOT Exponents do NOT have to be the same. have to be the same. MULTIPLY the MULTIPLY the coefficients and then coefficients and then ADD the exponents.ADD the exponents.

MultiplicationMultiplication

12 x 12 x 10101111

1.2 x 101.2 x 101212 Rewrite in properRewrite in proper

scientific notation.scientific notation.

4.0 x 104.0 x 1066

÷÷ 3.0 x 103.0 x 1055

Exponents do NOT Exponents do NOT have to be the same. have to be the same. DIVIDE the DIVIDE the coefficients and then coefficients and then SUBTRACT the SUBTRACT the exponents.exponents.

DivisionDivision

1.3 x 101.3 x 1011

Section 2.2Section 2.2Dimensional AnalysisDimensional Analysis

Pages 44-46

Dimensional AnalysisDimensional Analysis


A tool often used in science for A tool often used in science for converting units within a converting units within a measurement system measurement system

Conversion FactorConversion Factor

A numerical factor by which a A numerical factor by which a quantity expressed in one system quantity expressed in one system of units may be converted to of units may be converted to another system another system

3

3

cm

gcm


The “Factor-Label” Method Units, or “labels” are canceled,

or “factored” out

g

Dimensional AnalysisDimensional AnalysisSteps to solving problems:

1. Identify starting & ending units.

2. Line up conversion factors so units cancel.

3. Multiply all top numbers & divide by each bottom number.

4. Check units & answer.

Fractions in which the numerator Fractions in which the numerator and denominator are EQUAL and denominator are EQUAL quantities expressed in different quantities expressed in different unitsunits

Example: Example: 1 in. = 2.54 cm1 in. = 2.54 cm

Factors:Factors: 1 in. 1 in. and and 2.54 cm 2.54 cm

2.54 cm2.54 cm 1 in. 1 in.

Conversion FactorsConversion Factors

conversion factor

cancel

By using dimensional analysis / factor-label method, the UNITS ensure that

you have the conversion right side up, and the UNITS are calculated as well as

the numbers!

How many minutes are in 2.5 How many minutes are in 2.5 hours?hours?

2.5 hr2.5 hr

1 1

xx 60 min

1 hr

= 150 min

ConvertConvert 400 mL to Liters400 mL to Liters

400 mL400 mL== LL

mLmL

LL

10001000

11 .400.400

== 0.4 L0.4 L

== 4x104x10-1-1 L L

ConvertConvert 0.02 kilometers to m0.02 kilometers to m

0.02 km0.02 km== mm

kmkm

mm

11

1 0001 0002020

= 2x10= 2x1011 m m

Squared and Cubed Squared and Cubed ConversionsConversions

Convert 455.5 cm3 to dm3.1dm=10cm

33

0.4555dm10cm1dm

X10cm1dm

X10cm1dm

X1

455.5cm

Multiple Unit ConversionsMultiple Unit Conversions

Convert 568 mg/dL to g/L.1 g = 1000 mg1L = 10 dL

Lg5.68

1L10dL

X1000mg

1gX

dL568mg

Section 2.3Section 2.3 Uncertainty in Data Uncertainty in Data

Pages 47-49

Types of Observations and Types of Observations and MeasurementsMeasurements

We make QUALITATIVE observations of reactions — changes in color and physical state.

We also make QUANTITATIVE MEASUREMENTS, which involve numbers.

Nature of MeasurementNature of Measurement

Measurement – quantitative observation consisting of two parts:

NumberScale (unit)

Examples:20 grams6.63 6.63 × 10× 10-34-34 joule·seconds

Accuracy vs. PrecisionAccuracy vs. Precision

Accuracy - how close a measurement is to the accepted value

Precision - how close a series of measurements are to each other

ACCURATE = CORRECT

PRECISE = CONSISTENT

Accuracy vs. PrecisionAccuracy vs. Precision

Precision and Accuracy in Precision and Accuracy in MeasurementsMeasurements

In the real world, we never know whether the measurement we make is accurate

We make repeated measurements, and strive for precision

We hope (not always correctly) that good precision implies good accuracy

Percent ErrorPercent ErrorIndicates accuracy of a measurement

100accepted

acceptedalexperimenterror %

your value

given value

Percent ErrorPercent ErrorA 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 %

3%1001.360.04

(correct sig figs)

Section 2.3Section 2.3 Significant Figures or Digits Significant Figures or Digits

Pages 50-54

Uncertainty in Uncertainty in MeasurementMeasurement

A digit that must be A digit that must be estimatedestimated is called is 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 places

Significant FiguresSignificant FiguresIndicate precision of a measurement.

Recording Sig Figs

Sig figs in a measurement include the known digits plus a final estimated digit

2.31 cm

Significant FiguresSignificant Figures

What is the length of the cylinder?

Significant figuresSignificant figuresThe cylinder is 6.3 cm…plus a little moreThe next digit is uncertain; 6.36? 6.37?We use three significant figures to express

the length of the cylinder.

When you are given a When you are given a measurement to work with in measurement to work with in a chemistry problem you may a chemistry problem you may

not know the type of not know the type of instrument that was used to instrument that was used to make the measurement so make the measurement so

you must apply a set of rules you must apply a set of rules in order to determine the in order to determine the

number of significant digits number of significant digits that are in the measurement.that are in the measurement.

Rules for Counting Rules for Counting Significant FiguresSignificant Figures

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

34563456 hashas

44 significant figuressignificant figures


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

significant figuressignificant figures..

0.04860.0486 hashas



ZerosZeros-- Captive zeros Captive zeros always always

count ascount assignificant figures.significant figures.

16.07 16.07 hashas



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

9.3009.300 hashas


9,3009,300 has has

22 significant figures significant figures


Exact Numbers do not limit the # of sig figs in the answer. They have an infinite number of sig figs.

Counting numbers: 12 students

Exact conversions: 1 m = 100 cm

“1” in any conversion: 1 in = 2.54 cm

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

Significant Numbers in Significant Numbers in CalculationsCalculations

• A calculated answer cannot be more A calculated answer cannot be more precise than the measuring tool. precise than the measuring tool.

• A calculated answer must match the A calculated answer must match the least precise measurement.least precise measurement.

• Significant figures are needed for final Significant figures are needed for final answers fromanswers from

1) multiplying or dividing1) multiplying or dividing

2) adding or subtracting2) adding or subtracting

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

Multiplication and DivisionMultiplication and Division Use the same number of significant figures in the Use the same number of significant figures in the

result as the data with the result as the data with the fewest significant fewest significant figuresfigures..

1.827 m x 0.762 m1.827 m x 0.762 m = 1.392174 m= 1.392174 m22 (calculator)(calculator)

= 1.39 m= 1.39 m22 (three sig. fig.) (three sig. fig.)

453.6 g / 21 people453.6 g / 21 people = 21.6 g/person = 21.6 g/person (calculator)(calculator)

= 21.60 g/person (four = 21.60 g/person (four sig. fig.)sig. fig.)

(Question: why didn’t we round to 22 (Question: why didn’t we round to 22 g/person?)g/person?)

Rounding Numbers in Rounding Numbers in ChemistryChemistry

• If the digit to the right of the last sig fig is less than 5, do not change the last sig fig.

2.532 2.53• If the digit to the right of the last sig fig is greater than 5, round up the last sig fig.

2.536 2.54• If the digit to the right of the last sig fig is a 5 followed by a nonzero digit, round up the last sig fig. 2.5351 2.54• If the digit to the right of the last sig fig is a 5 followed by zero or no other number, look at the last sig fig. If it is odd round it up; if it is even do not round up. 2.5350 2.54

2.5250 2.52

Sig Fig Practice #2Sig Fig Practice #2

3.24 m x 7.0 m3.24 m x 7.0 m

Calculation Calculator says: Answer

22.68 m22.68 m22 23 m23 m22

100.0 g ÷ 23.7 cm100.0 g ÷ 23.7 cm33 4.219409283 g/cm4.219409283 g/cm33 4.22 g/cm4.22 g/cm33

0.02 cm x 2.371 cm0.02 cm x 2.371 cm 0.04742 cm0.04742 cm22 0.05 cm0.05 cm22

710 m ÷ 3.0 s710 m ÷ 3.0 s 236.6666667 m/s236.6666667 m/s 240 m/s240 m/s

1818.2 lb x 3.23 ft1818.2 lb x 3.23 ft 5872.786 lb·ft5872.786 lb·ft 5870 lb·ft5870 lb·ft

1.030 g ÷ 2.87 mL1.030 g ÷ 2.87 mL 2.9561 g/mL2.9561 g/mL 2.96 g/mL2.96 g/mL

Rules for Significant Figures Rules for Significant Figures in Mathematical Operationsin Mathematical OperationsAddition and SubtractionAddition and Subtraction: The number of : The number of decimal places in the result equals the decimal places in the result equals the number of decimal places in the least number of decimal places in the least precise measurement.precise measurement. Use the same Use the same number of decimal places in the result as number of decimal places in the result as the data with the the data with the fewest decimal placesfewest decimal places..

49.146 m + 72.13 m – 9.1434 m = ?= 112.1326 m (calculator)

= 112.13 m (2 decimal places)

Adding and Subtracting withAdding and Subtracting with Trailing Zeros Trailing Zeros

The answer has the same number of The answer has the same number of trailing zeros as the measurement trailing zeros as the measurement with the with the greatest numbergreatest number of trailing of trailing zeros.zeros.

110 110 one trailing zero

25002500 two trailing zerostwo trailing zeros

+ 230.3+ 230.3

2840.32840.3

answer 28answer 280000 two trailing zerostwo trailing zeros

Sig Fig Practice #3Sig Fig Practice #3

3.24 m + 7.0 m3.24 m + 7.0 m

Calculation Calculator says: Answer

10.24 m10.24 m 10.2 m10.2 m

100.0 g - 23.73 g100.0 g - 23.73 g 76.27 g76.27 g 76.3 g76.3 g

0.02 cm + 2.371 cm0.02 cm + 2.371 cm 2.391 cm2.391 cm 2.39 cm2.39 cm

713.1 L - 3.872 L713.1 L - 3.872 L 709.228 L709.228 L 709.2 L709.2 L

1818.2 g + 3.37 g1818.2 g + 3.37 g 1821.57 g1821.57 g 1821.6 1821.6 gg

2.030 mL - 1.870 mL2.030 mL - 1.870 mL 0.16 mL0.16 mL 0.160 mL0.160 mL

Learning Check Learning Check

A.A. Which answers contain 3 significant Which answers contain 3 significant figures?figures?1) 0.47601) 0.4760 2) 0.00476 2) 0.00476 3) 4760 3) 4760

B. All the zeros are significant in B. All the zeros are significant in

1) 0.00307 2) 25.3001) 0.00307 2) 25.300 3) 2.050 x 3) 2.050 x 101033

C. 534,675 rounded to 3 significant C. 534,675 rounded to 3 significant figures isfigures is

1) 535 1) 535 2) 535,000 2) 535,000 3) 5.35 x 10 3) 5.35 x 1055

Learning CheckLearning Check

In which set(s) do both numbers In which set(s) do both numbers contain the contain the same same number of number of significant figures? significant figures?

1) 22.0 and 22.00 1) 22.0 and 22.00

2) 400.0 and 40 2) 400.0 and 40

3) 0.000015 and 3) 0.000015 and

150,000150,000


In each calculation, round the answer to In each calculation, round the answer to the correct number of significant figures.the correct number of significant figures.

A. 235.05 + 19.6 + 2.1 = A. 235.05 + 19.6 + 2.1 =

1) 256.751) 256.75 2) 256.8 2) 256.8 3) 257 3) 257

B. 58.925 - 18.2B. 58.925 - 18.2 ==

1) 40.7251) 40.725 2) 40.73 2) 40.73 3) 40.7 3) 40.7


A. 2.19 X 4.2 = A. 2.19 X 4.2 = 1) 91) 9 2) 9.2 2) 9.2 3) 3)

9.1989.198

B. 4.311 ÷ 0.07 = B. 4.311 ÷ 0.07 = 1)1) 61.5861.58 2) 62 2) 62 3) 60 3) 60

C. C. 2.54 X 0.00282.54 X 0.0028 = =

0.0105 X 0.060 0.0105 X 0.060

1) 11.31) 11.3 2) 112) 11 3) 0.041 3) 0.041

Documents

Section 2.1 Units and Measurements Pages 32-39. International System of Units (SI System) In 1960, the metric system was standardized in the form of the