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 of atoms of each element present in each element present in one moleone mole of a of a compoundcompound
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