Chapter 6Chapter 6

Chemical QuantitiesChemical Quantities

HomeworkHomework Assigned Problems (odd numbers only)Assigned Problems (odd numbers only) ““Questions and Problems” 6.1 to 6.53 Questions and Problems” 6.1 to 6.53

(begins on page 168)(begins on page 168) ““Additional Questions and Problems” Additional Questions and Problems”

6.59 to 6.77 (page 190-192)6.59 to 6.77 (page 190-192) ““Challenge Questions” 6.79, 6.81 (page Challenge Questions” 6.79, 6.81 (page

192)192)

Counting Particles By Counting Particles By WeighingWeighing If a person requests 500 quarter inch If a person requests 500 quarter inch

hexagonal nuts for purchasehexagonal nuts for purchase How would you count 500 hex nuts?How would you count 500 hex nuts?

a)a) You could count the hex nuts individually You could count the hex nuts individually

b)b) Or, count the number of hex nuts by weightOr, count the number of hex nuts by weight First, find the average weight by weighing out 10 First, find the average weight by weighing out 10

hex nuts and obtaining the total weight (10 hex hex nuts and obtaining the total weight (10 hex nuts weigh 105 g) nuts weigh 105 g)

nuthexgnutshex

g/5.10

10

105 Average

Weight

Counting Particles By Counting Particles By WeighingWeighing

What size (wt.) will What size (wt.) will contain 500 hex contain 500 hex nuts?nuts?

Calculate what Calculate what weight will contain weight will contain 500 hex nuts500 hex nuts

So, weigh out 5.25 So, weigh out 5.25 kg of the hex nuts kg of the hex nuts

gnuthex

gnutshex 5250

5.10500

Using Atomic Mass to Count Using Atomic Mass to Count AtomsAtoms

Can do the exact same thing with atomsCan do the exact same thing with atoms Too small to conveniently countToo small to conveniently count Atoms of the same element don’t always Atoms of the same element don’t always

have exactly the same mass (have exactly the same mass (isotopesisotopes) so ) so use an use an Average MassAverage Mass

Grams are too large to use to measure an Grams are too large to use to measure an atom so use atom so use Atomic Mass UnitsAtomic Mass Units ( (amuamu))

g 101.66amu 1 24

Atomic Mass and Formula MassAtomic Mass and Formula Mass To calculate the mass To calculate the mass

of a sample of atomsof a sample of atoms Each element exists Each element exists

as a mixture of as a mixture of isotopes isotopes

Use a “weighted Use a “weighted average” for the average” for the atomic massatomic mass

Number on the Number on the bottom of each bottom of each square in the periodic square in the periodic table is the table is the average average weightweight of the element of the element ((in amuin amu))

Atomic Mass and Formula MassAtomic Mass and Formula Mass

Atomic masses are Atomic masses are determined on a determined on a relative scalerelative scale

The standard scale The standard scale references the references the carbon-12 isotope carbon-12 isotope = 12.000 amu= 12.000 amu

All other atomic All other atomic masses are masses are determined determined relativerelative to carbon-12to carbon-12

Atomic Mass and Formula MassAtomic Mass and Formula Mass

Using Atomic Mass to Count AtomsUsing Atomic Mass to Count Atoms Calculating the number of atoms in a specific Calculating the number of atoms in a specific

massmass If you have a sample of an element, can If you have a sample of an element, can

calculate the number of atoms in that samplecalculate the number of atoms in that sample From the atomic mass per one atom a From the atomic mass per one atom a

conversion factor can be madeconversion factor can be made For example: One nitrogen atom has an atomic For example: One nitrogen atom has an atomic

mass of 14.01 amumass of 14.01 amu

amu14.01

atomN1and

atomN1

amu14.01

amu14.01atomN1

Calculating The Number of Atoms in a Calculating The Number of Atoms in a Specific Mass Specific Mass

You have a 1.00 g sample of lead. How You have a 1.00 g sample of lead. How many atoms of lead are present?many atoms of lead are present?

1.00 g Pb1 atom Pb = 207.2 amu

1.6610-24 g = 1 amu

2.91021 atoms Pb

1.00 g Pb 1 amu

1.66 x 1024

g 1 atom Pb207.2 amu

Calculating Mass ExampleCalculating Mass Example Calculate the mass (Calculate the mass (in amuin amu) of 1.0 ) of 1.0 хх

101044 carbon atoms carbon atoms

amu12.01

atomC1

atom C1

amu12.01and

C atoms 101.0 4

amu 12.01= C atom 1

amu101.2 5

1) Given: 2) Plan: Convert from atoms to amu

3) CF

atomC1

amu12.01atomC101.0 4

4) Set Up Problem

Formula MassFormula Mass

The sum of atomic masses of all The sum of atomic masses of all atoms in its formulaatoms in its formula

Important role in nearly all chemical Important role in nearly all chemical calculationscalculations

Can be calculated for compounds Can be calculated for compounds and diatomic elements and diatomic elements

Calculating Formula MassCalculating Formula Mass Calculate the formula mass of calcium chlorideCalculate the formula mass of calcium chloride Write the formula from the name givenWrite the formula from the name given CaCa2+ 2+ (from group II) and Cl(from group II) and Cl- - (from group VII)(from group VII) Formula is CaClFormula is CaCl2 2 due to charge balancedue to charge balance Formula mass: Sum of the atomic masses of Formula mass: Sum of the atomic masses of

atoms in the formula (1 Ca atom + 2 Cl atoms)atoms in the formula (1 Ca atom + 2 Cl atoms)

atomCl1

amu35.45atomCl 2

atomCa1

amu 40.08atomCa1

amu110.98

= 40.08 amu

= 70.90 amu

Formula mass of CaCl2

Counting Large QuantitiesCounting Large Quantities Many chemical calculations require counting Many chemical calculations require counting

atoms and moleculesatoms and molecules It is difficult to do chemical calculations in It is difficult to do chemical calculations in

terms of atoms or formula unitsterms of atoms or formula units Since atoms are so small, extremely large Since atoms are so small, extremely large

numbers are needed in calculationsnumbers are needed in calculations Need to use a special counting unit just as Need to use a special counting unit just as

used for other itemsused for other items A A reamream of paper of paper One One dozendozen donuts donuts A A pairpair of shoes of shoes

The MoleThe Mole It is more convenient to use a special counting It is more convenient to use a special counting

unit for such large quantities of particles unit for such large quantities of particles MoleMole: A unit that contains : A unit that contains 6.022 6.022 хх 10 1023 23 objectsobjects It is used due to the extremely small size of It is used due to the extremely small size of

atoms, molecules, and ionsatoms, molecules, and ions 6.022x106.022x102323 particles in 1 mole particles in 1 mole Called Called Avogadro’s NumberAvogadro’s Number

Periodic TablePeriodic Table The The average atomic massaverage atomic mass inin amuamu (one atom)(one atom) The The weight of 1 moleweight of 1 mole of the element in of the element in gramsgrams Avogadro’s number provides the connecting Avogadro’s number provides the connecting

relationship between molar masses and relationship between molar masses and atomic massesatomic masses

Calculating the Number of Calculating the Number of Molecules in a MoleMolecules in a Mole

How many molecules of bromine are present in How many molecules of bromine are present in 0.045 mole of bromine gas? 0.045 mole of bromine gas?

223

2

2

223

10022.6

10022.6

Brmolecules

Brmoland

Brmol

Brmolecules

223

2 Br molecules 10022.6Br mol 1

222 Br molecules 107.2

Given: 0.045 mol Br2 Need: molecules of Br2

Avogadro’s number

2

223

2 10022.6045.0

Brmol

BrmoleculesBrmol

Conversion factors:

Equality:

Set Up Problem:

Subscripts State Moles of Subscripts State Moles of ElementsElements

The subscripts in a chemical formula indicate The subscripts in a chemical formula indicate the number of atoms of each element present the number of atoms of each element present in a compoundin a compound

The subscripts in a chemical formula can also The subscripts in a chemical formula can also indicate the indicate the number of molesnumber of moles of atoms of each of atoms of each element present in element present in one moleone mole of a compound of a compound

i.e. In one molecule of glucose (Ci.e. In one molecule of glucose (C66HH1212OO66) there ) there are are 66 atoms of carbon, atoms of carbon, 1212 atoms of hydrogen, atoms of hydrogen, and and 66 atoms of oxygen atoms of oxygen

Calculating the Moles of an Calculating the Moles of an Element in a CompoundElement in a Compound

How many moles of carbon atoms are How many moles of carbon atoms are present in 1.85 moles of glucose?present in 1.85 moles of glucose?

Plan: moles of glucose moles of C atomssubscript

(One) mol C6H12O6 = 6 mols C atomsEquality:

Conversion Factors:

Set Up Problem:

atomsCmoles6

OHCmol

OHCmol

atomsCmoles6 6126

6126

and

6126

6126

OHCmol

atomsCmols6OHCmol1.8511.1 mol C atoms

Molar MassMolar Mass The atomic mass of a carbon-12 atom is The atomic mass of a carbon-12 atom is

12.00 amu12.00 amu The atomic mass of The atomic mass of one moleone mole of carbon- of carbon-

12 atoms 12.00 g12 atoms 12.00 g One mole of any element is the amount One mole of any element is the amount

of atoms (molecules or ions) that is of atoms (molecules or ions) that is equal to its atomic mass (in grams)equal to its atomic mass (in grams)

This mass contains 6.022 This mass contains 6.022 хх 10 1023 23 particles particles of that elementof that element

Use the periodic table to obtain the Use the periodic table to obtain the molar mass of any elementmolar mass of any element

Molar MassMolar Mass When the number of grams (weighed out) When the number of grams (weighed out)

of a substance equals the formula mass of of a substance equals the formula mass of that substance, that substance, Avogadro’s numberAvogadro’s number of of molecules of that substance are presentmolecules of that substance are present

Molar Mass of a CompoundMolar Mass of a Compound Calculate the molar mass of Calculate the molar mass of iron (II) sulfateiron (II) sulfate Formula is Formula is FeSOFeSO44

1)1) Calculate the molar mass of each element Calculate the molar mass of each element 2)2) Each element is multiplied by its Each element is multiplied by its

respective subscript: respective subscript: (number of moles of (number of moles of each element)each element)

3)3) The molar mass is calculated by the sum of The molar mass is calculated by the sum of the molar masses of each element the molar masses of each element

Moles of Element in Compound

Moles of Compound

Formula Subscript

Molar Mass of a CompoundMolar Mass of a Compound

Omol

Og16.00

Smol

Sg32.00

Femol

Feg55.851) Formula is FeSOFormula is FeSO44: : The molar masses of iron, sulfur, and oxygen are

2) Multiply each molar mass by its subscript

Og64.00Omol

Og16.00Omol4

Sg32.00Smol

Sg32.00Smol1Feg55.85

Femol

Feg55.85Femol1

3) Find the molar mass of the compound by adding the mass of each element

g151.85g64.00g32.00g 55.85

Calculations Using Molar Calculations Using Molar MassMass

The three quantities most often The three quantities most often calculated calculated Number of particlesNumber of particles Number of moles Number of moles Number of gramsNumber of grams

Using molar mass as a conversion factor Using molar mass as a conversion factor is one of the most useful in chemistryis one of the most useful in chemistry Can be used for g to mole and mole to g Can be used for g to mole and mole to g

conversions conversions

Relationship between Moles, Relationship between Moles, Molar Mass and Avogadro’s Molar Mass and Avogadro’s

numbernumber

Moles of substance

Particles of substance

Moles of substance

Grams of substance

Avogadro’sNumber

Molar Mass

Moles of substance

Avogadro’sNumber

Moles of substance

Avogadro’sNumber

Particles of substance

Moles of substance

Avogadro’sNumber

Converting Mass of a Compound to MolesConverting Mass of a Compound to Moles International Foods Coffee contains 3 mg of sodium International Foods Coffee contains 3 mg of sodium

chloride per cup of coffee. How many moles of chloride per cup of coffee. How many moles of sodium chloride are in each cup of coffee?sodium chloride are in each cup of coffee?

NaCl mg 1000

NaCl 1gNaCl mg 3

1(35.45)1(22.99)1(Cl)1(Na)NaCl MM 58.44g

mol NaCl

5.1310 -5 mol NaCl0.003 g NaCl 1mol NaCl

58.44 g NaCl

Equality:NaCl g 58.44

NaCl mol

NaCl mol

NaCl g 58.44and1 mol NaCl = 58.44 g

3 mg NaCl moles of NaCl

= 0.003 g NaCl

Converting Grams to Converting Grams to ParticlesParticles

Ethylene glycol (antifreeze) has the formula CEthylene glycol (antifreeze) has the formula C22HH66OO22. How . How many molecules are present in a 3.86 many molecules are present in a 3.86 × 10× 10-20 -20 g sample?g sample?

Plan: convert g moles molecules of ethylene glycol

Equality 1: ConversionFactor 1

Equality 2:

262

262

262

262

OHCg62.05

OHCmoland

OHCmol

OHCg62.05

molecules106.022OHCmol1 23262

ConversionFactor 2 molecules106.022

OHC1molor

OHC 1mol

molecules106.02223

262

262

23

262

23

262

262262

20

OHCmol

molecules106.022

OHC g62.05

OHCmolOHCg103.86 375 molecules

262262 OHCg62.05OHCmol1

Molarmass

AvogNumber

Percent CompositionPercent Composition

Sometimes it’s useful to know the Sometimes it’s useful to know the composition of a compound in terms of composition of a compound in terms of what what percentagepercentage of the total is each of the total is each elementelement

PercentPercent ““Parts per 100”Parts per 100” The number of specific items per a group of The number of specific items per a group of

100 items100 items 50% of $100 is $50 (50 items/100 total 50% of $100 is $50 (50 items/100 total

items)items)

Percent ExamplePercent Example You have 4 oranges and 5 apples. What percent of the total is oranges?You have 4 oranges and 5 apples. What percent of the total is oranges?

In “parts per 100”In “parts per 100”

oranges 44%100% total9

oranges 4

oranges 44%100% total100

oranges 44

Percent CompositionPercent Composition It is the percent by mass of each element in a It is the percent by mass of each element in a

compoundcompound Can be determined Can be determined

By its chemical formulaBy its chemical formula Molar masses of the elements that compose Molar masses of the elements that compose

the compound the compound The percent of each element contributes to the The percent of each element contributes to the

mass of the compoundmass of the compound

compoundainelement100%

compoundtheofmassmolarelementeachofmasseachofpercentmass

Calculating Percent Composition Calculating Percent Composition ExampleExample

What is the percent composition of each What is the percent composition of each element in NHelement in NH44OH?OH?

g14.01 = g14.011:N g5.04 = g0078.15:H g16.00 = g00.611:O

g35.05 = %100

g35.05

g14.01 :N

%100g35.05

g5.04 :H

%100g35.05

g16.00 :O

N 39.97%

H 14.38%

O 45.65%

Determine the contribution of each element

Molar mass

Empirical FormulasEmpirical Formulas

The simplest ratio of elements in a The simplest ratio of elements in a compoundcompound

It uses the smallest possible whole It uses the smallest possible whole number ratio of atoms present in a number ratio of atoms present in a formula unit of a compoundformula unit of a compound

If the percent composition is known, If the percent composition is known, an empirical formula can be an empirical formula can be calculatedcalculated

Empirical FormulasEmpirical Formulas To Determine the empirical To Determine the empirical

formula:formula:1)1) Calculate the moles of each Calculate the moles of each

elementelement Use molar mass (atomic mass)Use molar mass (atomic mass)

2)2) Calculate the ratios of the elements Calculate the ratios of the elements to each otherto each other

3)3) Find the lowest whole number ratioFind the lowest whole number ratio Divide each number of moles by the Divide each number of moles by the

smallest number of moles presentsmallest number of moles present

Empirical Formula: Converting Decimal Empirical Formula: Converting Decimal Numbers to Whole NumbersNumbers to Whole Numbers

The subscripts in a formula are The subscripts in a formula are expressed as whole numbers, not expressed as whole numbers, not as decimalsas decimals

The resulting numbers from a The resulting numbers from a calculation represent each calculation represent each element’s subscriptelement’s subscript

If the number(s) are If the number(s) are NOTNOT whole whole numbers, multiply each number numbers, multiply each number by the same small integer (2, 3, 4, by the same small integer (2, 3, 4, 5, or 6) until a whole number is 5, or 6) until a whole number is obtainedobtained

Relating Empirical and Relating Empirical and Molecular FormulasMolecular Formulas

nn represents a whole number multiplier represents a whole number multiplier from 1 to as large as necessaryfrom 1 to as large as necessary

Calculate the empirical formula and the Calculate the empirical formula and the mass of the empirical formulamass of the empirical formula

Divide the given molecular mass by the Divide the given molecular mass by the calculated empirical masscalculated empirical mass Answer is a whole number Answer is a whole number multipliermultiplier

)/(

)/(

molgmassformulaempirical

molgmassmolarn

Relating Empirical and Relating Empirical and Molecular FormulasMolecular Formulas

Multiply each Multiply each subscriptsubscript in the empirical in the empirical formula by the formula by the whole number multiplierwhole number multiplier to to get the molecular formulaget the molecular formula

Calculate Empirical Formula Calculate Empirical Formula from Percent Compositionfrom Percent Composition

Lactic acid has a molar mass of 90.08 Lactic acid has a molar mass of 90.08 g and has this percent composition:g and has this percent composition:

40.0% C, 6.71% H, 53.3% O40.0% C, 6.71% H, 53.3% O What is the What is the empiricalempirical and and molecularmolecular

formula of lactic acid?formula of lactic acid? Assume a 100.0 g sample sizeAssume a 100.0 g sample size

Convert percent numbers to gramsConvert percent numbers to grams

Calculate Empirical Formula from Calculate Empirical Formula from Percent CompositionPercent Composition

Convert mass of each element to molesConvert mass of each element to moles Divide each mole quantity by the smallest Divide each mole quantity by the smallest

number of molesnumber of moles

CmolCg

CmolCg 33.3

0.120.40

HmolHg

HmolHg 66.6

008.171.6

OmolOg

OmolOg 33.3

00.163.53

00.13.33

3.33 :C

00.23.33

6.66 :H

00.13.33

3.33 :O

The ratio of C to H to O is 1 to 2 to 1Empirical formula is

Empirical formula mass = 12.01 + 2 (1.008) + 16.00 = 30.03 g/mol

CH2O

Determination of the Determination of the Molecular Formula Molecular Formula

Obtain the value of n (whole number multiplier)Obtain the value of n (whole number multiplier) Multiply the empirical formula by the multiplierMultiply the empirical formula by the multiplier

)/(

)/(

molgmassformulaempirical

molgmassmolarn 3

/03.30

/08.90

molg

molg

Molecular formula = n х empirical formula

Molecular formula = 3 (CH2O) C3H6O

3

Formulas for CompoundsFormulas for Compounds Empirical FormulaEmpirical Formula

Smallest possible set of subscript numbers Smallest possible set of subscript numbers Smallest whole number ratioSmallest whole number ratio All ionic compounds are given as empirical All ionic compounds are given as empirical

formulasformulas Molecular FormulasMolecular Formulas The actual formulas of moleculesThe actual formulas of molecules It shows all of the atoms present in a It shows all of the atoms present in a

moleculemolecule It may be the same as the EF or a whole- It may be the same as the EF or a whole-

number multiple of its EFnumber multiple of its EF

Molecular formula = n х Empirical formula

endend