Chemistry Chapter 2

Chemistry Chapter Chemistry Chapter 22

Analyzing DataAnalyzing Data

SI Base UnitsSI Base Units (le Système International, SI)(le Système International, SI)

Quantity Base Unit

Time second (s)

Length meter (m)

Mass kilogram (kg)

Temperature kelvin (K)

Amount of a Substance mole (m)

Electric Current ampere (A)

Luminous Intensity candela (cd)

SI PrefixesSI PrefixesCommon to ChemistryCommon to Chemistry

Prefix Unit Abbr. Exponent

mega M 106

kilo k 103

deci d 10-1

centi c 10-2

milli m 10-3

micro 10-6

nano n 10-9

SI PrefixesSI PrefixesCommon to ChemistryCommon to Chemistry

Unit Abbr. Relation to meter

Relation to meter

Small in a big (pennies in a $)

M 106 m1 Mm

1 Mm106 m

106 m1 Mm

k 103 m1 km

1 km10 3 m

103 m1 km

d 10-1 m1 dm

1 dm10-1 m

10 dm1 m

c 10-2 m1 cm

1 cm10-2 m

102 cm1 m

mm 10-3 m1 mm

1 mm10-3 m

103 mm1 m

10-6 m1

1 10-6 m

106 1 m

n 10-9 m1 nm

1 nm10-9 m

109 nm 1 m

Temperature ConversionsTemperature Conversions

⁰F = 1.8C + 32

K = ⁰C + 273

Note: Do not change precision of original measurement

SI UnitsSI Units

DerivedDerived SI Units SI Units

Quantity Unit Abbr. Derivation

Area m2 length x width

Volume m3 l x w x h

Density kg/m3 mass/vol

Concentration

mol/L (M)

(molarity)

amount/vol

Energy J (joule) force x length

VolumeVolume

•The amount of space occupied by an object

•Derived unit is m3

•Chemists also use liters• 1L = 1000 mL1L = 1000 mL• 1L = 1dm1L = 1dm33

• 1mL = 1cm3 (Interchangeable)

DensityDensity

Mass (any mass unit)Volume (any volume unit)

• The ratio of mass to volume• Derived unit is kg/m3

• Expresses a physical property• Varies with T (usually

decreases with increasing T)• P. 38 Practice problemP. 38 Practice problem

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 form:or very small numbers in the form:

M x 10M x 10nn

MM is a number between is a number between 11 and and 1010 nn is an integer is 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 M x 10Step #4: Re-write in the form M 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 CALCULATIONCALCULATION

S IN S IN SCIENTIFIC 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

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

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

Student AStudent A40.0 x 1040.0 x 1055

43.0043.00 x 10x 1055 Is this Is this good good

scientific scientific notation?notation?

NO!NO!

== 4.300 x 104.300 x 1066

To avoid To avoid this this problem, problem, move the move the decimal on decimal on the the smallersmaller number!number!

4.00 x 104.00 x 1066

+ + 3.00 x 103.00 x 1055

Student BStudent B

.30 x 10.30 x 1066

4.304.30 x 10x 1066 Is this Is this proper proper

scientific scientific notation?notation?

YESYES!!

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

0.0237 x 100.0237 x 10--

44

3.5037 x 103.5037 x 10-4-4

Conversion FactorConversion Factor

• A A ratioratio derived from the derived from the equality between two different equality between two different units that can be used to units that can be used to convert from one unit to convert from one unit to anotheranother

• Example:Example: 1 inch/2.54 cm 1 inch/2.54 cm• Or:Or: 2.54 cm/1 inch 2.54 cm/1 inch• 1000 mL/1L1000 mL/1L• Or:Or: 1L/1000 mL 1L/1000 mL

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 how close a measured value refers to how close a measured value is to an is to an acceptedaccepted value. value.

PrecisionPrecision refers to how close a series of refers to how close a series of measurements are to one another.measurements are to one another.

Neither accurate nor

precise

Precise but not accurate

Precise AND accurate

Percent ErrorPercent Error

Error = Experimental Value-Accepted Value

Percent Error = Percent Error = |error| |error| (100) (100) accepted valueaccepted value

Practice problem, p. 49Practice problem, p. 49

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 are always are always significant significant

34563456 hashas

44 sig figs.sig figs.


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.


ZerosZeros-- Captive zeros Captive zeros always always

count ascount assignificant figures.significant figures.

16.07 16.07 hashas



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



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

2424 class members (counted) class members (counted)

11 inch = inch = 2.542.54 cm, exactly (conversion cm, exactly (conversion factors)factors)

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 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

The MoleThe Mole

1 dozen =1 gross =

1 ream =

1 mole =

12

144

500

6.02 x 1023

There are exactly 12 grams of carbon-12 in one mole of carbon-12.

End. Ch. 2End. Ch. 2

Avogadro’s NumberAvogadro’s Number6.02 x 1023 is called “Avogadro’s Number” in honor of the Italian chemist Amadeo Avogadro (1776-1855).

Amadeo Avogadro

I didn’t discover it. Its just named after

me!

Calculations with Moles:Calculations with Moles:Converting moles to gramsConverting moles to grams

How many grams of lithium are in 3.50 moles of lithium?

3.50 mol Li= g Li

1 mol Li

6.94 g Li45.1

Calculations with Moles:Calculations with Moles:Converting grams to molesConverting grams to moles

How many moles of lithium are in 18.2 grams of lithium?

18.2 g Li= mol Li

6.94 g Li

1 mol Li2.62

Calculations with Moles:Calculations with Moles:Using Avogadro’s NumberUsing Avogadro’s Number

How many atoms of lithium are in 3.50 moles of lithium?

3.50 mol Li = atoms Li

1 mol Li

6.022 x 1023 atoms Li 2.11 x 1024

Calculations with Moles:Calculations with Moles:Using Avogadro’s NumberUsing Avogadro’s Number

How many atoms of lithium are in 18.2 g of lithium?

18.2 g Li

= atoms Li

1 mol Li 6.022 x 1023 atoms Li

1.58 x 1024

6.94 g Li 1 mol Li

(18.2)(6.022 x 1023)/6.94

Calculating Molar MassCalculating Molar MassCalculate the formula mass of magnesium Calculate the formula mass of magnesium carbonate, MgCOcarbonate, MgCO33..

24.31 g + 12.01 g + 3(16.00 g) 24.31 g + 12.01 g + 3(16.00 g) ==

84.32 g84.32 g

Calculating Percentage Calculating Percentage CompositionComposition

Calculate the percentage composition of Calculate the percentage composition of magnesium carbonate, MgCOmagnesium carbonate, MgCO33..

From previous slide:From previous slide:24.31 g + 12.01 g + 3(16.00 g) = 24.31 g + 12.01 g + 3(16.00 g) = 84.32 g84.32 g 24.31

100 28.83%84.32

Mg 12.01

100 14.24%84.32

C 48.00

100 56.93%84.32

O

100.00

FormulasFormulas

molecular formula = (empirical formula)n [n = integer]

molecular formula = C6H6 = (CH)6

empirical formula = CH

Empirical formula: the lowest whole number ratio of atoms in a compound.

Molecular formula: the true number of atoms of each element in the formula of a compound.

FormulasFormulas (continued)(continued)

Formulas for Formulas for ionic compoundsionic compounds are are ALWAYSALWAYS empirical (lowest whole empirical (lowest whole number ratio).number ratio).Examples:Examples:

NaCl MgCl2 Al2(SO4)3 K2CO3

FormulasFormulas (continued)(continued)

Formulas for Formulas for molecular compoundsmolecular compounds MIGHTMIGHT be empirical (lowest whole be empirical (lowest whole number ratio).number ratio).

Molecular:Molecular:

H2O

C6H12O6 C12H22O11

Empirical:

H2O

CH2O C12H22O11

Empirical Formula Empirical Formula DeterminationDetermination

Base calculation on 100 grams of compound.

Determine moles of each element in 100 grams of compound.

Divide each value of moles by the smallest of the values.

Multiply each number by an integer to obtain all whole numbers.


Adipic acid contains 49.32% C, 43.84% O, and 6.85% H by mass. What is the empirical formula of adipic acid?

49.32 14.107

12.01

g C mol Cmol C

g C

6.85 16.78

1.01

g H mol Hmol H

g H

43.84 12.74

16.00

g O mol Omol O

g O


(part 2)(part 2)

4.1071.50

2.74

mol C

mol O

6.782.47

2.74

mol H

mol O

2.741.00

2.74

mol O

mol O

Divide each value of moles by the smallest Divide each value of moles by the smallest of the values.of the values.

Carbon:Carbon:

Hydrogen:Hydrogen:

Oxygen:Oxygen:


(part 3)(part 3)Multiply each number by an integer to Multiply each number by an integer to obtain all whole numbers.obtain all whole numbers.

Carbon: 1.50Carbon: 1.50 Hydrogen: 2.50Hydrogen: 2.50 Oxygen: 1.00Oxygen: 1.00x 2 x 2 x 2

33 55 22

Empirical formula:C3H5O

2

Finding the Molecular Finding the Molecular FormulaFormula

The empirical formula for adipic acid The empirical formula for adipic acid is Cis C33HH55OO22. The molecular mass of . The molecular mass of adipic acid is 146 g/mol. What is the adipic acid is 146 g/mol. What is the molecular formula of adipic acid?molecular formula of adipic acid?

1. Find the formula mass of 1. Find the formula mass of CC33HH55OO22

3(12.01 g) + 5(1.01) + 2(16.00) = 3(12.01 g) + 5(1.01) + 2(16.00) = 73.08 g73.08 g



3(12.01 g) + 5(1.01) + 2(16.00) = 3(12.01 g) + 5(1.01) + 2(16.00) = 73.08 g73.08 g

2. Divide the molecular mass by 2. Divide the molecular mass by the mass given by the emipirical the mass given by the emipirical formula.formula.

1462

73



3(12.01 g) + 5(1.01) + 2(16.00) = 3(12.01 g) + 5(1.01) + 2(16.00) = 73.08 g73.08 g146

273

3. Multiply the empirical formula by 3. Multiply the empirical formula by this number to get the molecular this number to get the molecular formula.formula.

(C(C33HH55OO22) x 2 ) x 2 ==

CC66HH1010OO44

Chemistry Chapter 2

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