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Moles and Stoichiometry Moles and Stoichiometry

Ch. 12Ch. 12

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The MoleThe Mole

OBJECTIVES:OBJECTIVES:– Describe the mole conceptDescribe the mole concept– Calculate the mass of a mole of Calculate the mass of a mole of

any substance.any substance.– Convert between moles, grams, Convert between moles, grams,

liters, and particle numberliters, and particle number

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What is a Mole What is a Mole 摩尔摩尔 ?? We measure mass in We measure mass in gramsgrams. . gg We measure volume in We measure volume in litersliters. . LL We count pieces inWe count pieces in MOLESMOLES. . molmol

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The Mole ConceptThe Mole ConceptA Carbon-12 A Carbon-12 atom atom

has a mass of has a mass of 12amu12amuC = 12amu

A mole of Carbon atoms has a mass of 12 grams

CC

C

CCC

C

C

CC

C

CC

CC

CC

CC

C

CC

C

C

CC

C

CCC

C

C

CC

C

C

C CC

C

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Gram Atomic MassGram Atomic Mass Equals the mass of 1 mole of an elementEquals the mass of 1 mole of an element Written on the Periodic Table Written on the Periodic Table 12.01 grams of C has the same number of 12.01 grams of C has the same number of

pieces as 1.008 grams of H and 55.85 pieces as 1.008 grams of H and 55.85 grams of iron.grams of iron.

We can write this as We can write this as 12.01 g C = 1 mole C 12.01 g C = 1 mole C

We can count things by weighing them.We can count things by weighing them.

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The Mole ConceptThe Mole Concept

Mole of atomsMole of atoms Atomic Mass in grams

A mole of aluminum A mole of aluminum = =

A mole of gold A mole of gold ==

A mole of silverA mole of silver ==

A mole of boronA mole of boron ==

27.0g197g

108g

10.8g

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The Mole ConceptThe Mole ConceptSo,So,

1.1. How many atoms are in a mole?How many atoms are in a mole?

2.2. Does a mole of H have the same Does a mole of H have the same number of atoms as a mole of He?number of atoms as a mole of He?

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He

If a Helium atom is 4 timesheavier than a Hydrogen atom,

H

then a dozen Helium atoms is 4 timesheavier than a dozen Hydrogen atoms.

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And a mole of Helium atoms is 4 timesheavier than a mole of Hydrogen atoms.

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So, the number of atoms in a mole is always the same

The number of atoms in a mole is called,Avogadro's Number

Avogadro's Number = 6.022 x 1023

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Mole – Particle Conversions Mole – Particle Conversions The mole concept allows us to count atoms, molecules,

formula units and ions.

1 mole of Al = 6.022 x 1023 atoms of Al

So how many atoms in 3 mol of Al?

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Mole – Particle ConversionsMole – Particle Conversions1 mole of Al = 6.022 x 1023 atoms of Al

So how many atoms in 3 mol of Al?

3 mol Al 6.022 x 1023 atoms of Al

1 mol Al

= 1.8066 x 1023 atoms of Al

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Conversions Conversions 1 mole of Al = 6.022 x 1023 atoms of Al

So how many moles are 3.0 x 1023 atoms of Al?

3.0 x 1023 atoms Al

6.022 x 1023 atoms of Al

1 mol Al

= .5 mol of Al

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Converting into Moles

How many moles of Na atoms are there in 46.0g of Na?

46.0g Na

Step 1: Write a grid and place the given number into the upper left hand part of the gridStep 2: Look up the atomic mass on the periodic table and find out how many grams = 1mole

Na has a mass of 23.023.0

23.0g Na

1 mol Na = 2 mol Na

Step 3: Place the units you need to cancel on the bottom, and multiply by the top and divide by the bottom

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Mole-Mass ConversationsMole-Mass Conversations

• Dimensional Analysis- converting between Dimensional Analysis- converting between physical properties using ratiosphysical properties using ratios

• How many grams are in 3.5 mol COHow many grams are in 3.5 mol CO22??

• How many moles are in 150g in NaBr?How many moles are in 150g in NaBr?

3.5 mol CO2

1 mol CO2

44.0 g CO2=154g CO2

150 g NaBr

102.9 g NaBr

1 mol NaBr= 1.5 mol NaBr

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ExamplesExamples How much would 2.34 moles of carbon How much would 2.34 moles of carbon

weigh?weigh?

How many moles of magnesium is How many moles of magnesium is 24.31 g of Mg?24.31 g of Mg?

How many atoms of lithium is 1.00 g of How many atoms of lithium is 1.00 g of Li?Li?

28.1 g C

1 mol Mg

8.60 x 1022 atoms Li

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What about compounds?What about compounds? In 1 mole of HIn 1 mole of H22O molecules there are 2 O molecules there are 2

moles of H atoms and 1 mole of O atomsmoles of H atoms and 1 mole of O atoms To find the mass of one mole of a To find the mass of one mole of a

compound compound

– determine the moles of the elements they determine the moles of the elements they havehave

– Find out how much they would weighFind out how much they would weigh

– add them upadd them up

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Types of Molar MassTypes of Molar Mass

• Gram Molecular Mass Gram Molecular Mass (GMM)- the total (GMM)- the total number of atoms in a number of atoms in a molecularmolecular compound compound

• ClCl22 = 2 x 35.4 g = 70.8 g = 2 x 35.4 g = 70.8 g

• CHCH44= =

• Gram Formula Mass Gram Formula Mass (GFM)- the total (GFM)- the total number of atoms in an number of atoms in an ionicionic compound compound

• NaCl = (1 x 23.0g) + (1 x 35.4g) = 58.4gNaCl = (1 x 23.0g) + (1 x 35.4g) = 58.4g• Ca(OH)Ca(OH)22= =

(1 x 12.0g) + (4 x 1.0g) = 16g

(1 x 40.0g) + (2 x (16.0g+1.0g))= 74g

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Molar MassMolar Mass Molar massMolar mass is the generic term for the is the generic term for the

mass of one mole of any substance (in mass of one mole of any substance (in grams) grams)

The same as: The same as:

– 1) gram molecular mass1) gram molecular mass

– 2) gram formula mass2) gram formula mass

– 3) gram atomic mass3) gram atomic mass

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ExamplesExamples Calculate the molar mass of the Calculate the molar mass of the

following and tell what type it is:following and tell what type it is:

NaNa22SS

NN22OO44

Ca(NOCa(NO33))22

CC66HH1212OO66

(NH(NH44))33POPO44

= 78.1 g= 92.0 g= 164.1 g= 180.0 g= 149.0 g

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ExamplesExamples How many moles is 4.56 g of COHow many moles is 4.56 g of CO22??

How many grams is 9.87 moles of How many grams is 9.87 moles of HH22O?O?

How many molecules is 6.8 g of CHHow many molecules is 6.8 g of CH44??

0.104 mol CO2

178 g H2O

0.425 mol CH4

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GasesGases Many of the chemicals we deal with are Many of the chemicals we deal with are

gases.gases.–They are difficult to They are difficult to weighweigh..

Need to know how many moles of gas we Need to know how many moles of gas we have.have.

Two things effect the volume of a gasTwo things effect the volume of a gas–Temperature and pressureTemperature and pressure

We need to compare them at the same We need to compare them at the same temperature and pressure.temperature and pressure.

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Standard Temperature and Standard Temperature and PressurePressure

0ºC and 1 atm pressure 0ºC and 1 atm pressure （（ 11 个个大气压大气压，，约为约为 101.325kPa101.325kPa ））00ooC = 32C = 32ooF= 273 KF= 273 K

1 atm= 101.3 kPa = 760 mmHg (torr)1 atm= 101.3 kPa = 760 mmHg (torr) abbreviated abbreviated STP STP 标准状况标准状况 At STP 1 mole of gas occupies At STP 1 mole of gas occupies 22.4 L22.4 L Called the Called the molar volume molar volume 摩尔体积摩尔体积 1 mole = 22.4 L of any gas at STP1 mole = 22.4 L of any gas at STP

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ExamplesExamples What is the volume of 4.59 mole of What is the volume of 4.59 mole of

COCO22 gas at STP? gas at STP?

How many moles is 5.67 L of OHow many moles is 5.67 L of O2 2 at at

STP?STP?

4.59 mol CO2

1 mol CO2

22.4 L CO2=103 L CO2

5.67 L O2

22.4 L O2

1 mol O2=0.253 mol O2

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Ideal Gas LawIdeal Gas Law Connection between the number of particles (Connection between the number of particles (nn) and ) and

the pressure (P), volume (V), and temperature (T) of the pressure (P), volume (V), and temperature (T) of a gasa gas

PV=PV=nnRTRT R= 8.31 kPa∙L/ mol∙KR= 8.31 kPa∙L/ mol∙K T= ALWAYS in Kelvin, so convert T= ALWAYS in Kelvin, so convert ooC to KC to K

-50-50ooC + 273 = 223KC + 273 = 223K How many moles of helium are contained in a 5.00-L How many moles of helium are contained in a 5.00-L

canister at 101 kPa and 30canister at 101 kPa and 30ooC?C?nn= PV/RT= PV/RT

n= n= 101kPa x 5.00-L101kPa x 5.00-L

8.31 kPa∙L/mol∙K x 303K8.31 kPa∙L/mol∙K x 303K

n= n= 0.2 mol0.2 mol

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StoichiometryStoichiometry 化学计量法化学计量法““Stoichiometry” is Greek for “Measuring Stoichiometry” is Greek for “Measuring

Elements”Elements”

It starts with a balanced equationIt starts with a balanced equation

2H2H2 2 + O+ O22 2H2H22OO

2 moles of hydrogen reacts with2 moles of hydrogen reacts with 1 mole of oxygen 1 mole of oxygen Forming 2 moles of water.Forming 2 moles of water.

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StoichiometryStoichiometryThe The coefficientscoefficients tell us how many tell us how many molesmoles of of

each substance. Not Grams!each substance. Not Grams!

For example: For example:

2H2H2 2 + O+ O22 2H2H22OO

2 g of H2 g of H22 + 1 g of O + 1 g of O22 == 2 g of H 2 g of H22OO

3 g of reactants can’t make only 2 g of products3 g of reactants can’t make only 2 g of products

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Mass of a ProductMass of a Product

The Law of Conservation of Mass appliesThe Law of Conservation of Mass applies

Convert the moles to grams and the equation does Convert the moles to grams and the equation does work.work.

2H2H2 2 + O+ O22 2H2H22OO2 moles H2

2.02 g H2

1 mole H2

= 4.04 g H2

1 mole O232.00 g O2

1 mole O2

= 32.00 g O2

36.04 g H2+O2

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Mass of a ProductMass of a Product

2H2H2 2 + O+ O22 2H2H22OO

2 moles H2O 18.02 g H2O

1 mole H2O= 36.04 g H2O

2H2 + O2 2H2O

36.04 g H2 + O2= 36.04 g H2O

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2Na + Cl2Na + Cl22 2NaCl 2NaClHow many grams of sodium are needed How many grams of sodium are needed

to react with .071g of chlorine gas?to react with .071g of chlorine gas?

Mole Ratio 2 1 2

Mass Ratio 35.5 x 2 x 1=71

23 x 2=46

58.5 x 2=117

0.071 g Cl2

71 g Cl2

1 mol Cl2

= 0.046 g Na

2Na (s) + Cl2(g) 2NaCl (s)

1 mol Cl2

2 mol Na

2 mol Na

46 g Na

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Chemical Yield Chemical Yield The amount of product made in a The amount of product made in a

chemical reaction.chemical reaction.

There are three types:There are three types:

1.Theoretical yield 1.Theoretical yield 理论产量 理论产量 - the amount - the amount of Product that should be made (of Product that should be made (from from calculationscalculations))

2. Actual yield 2. Actual yield 实际产量实际产量 - the amount of - the amount of Product formed in the laboratory (Product formed in the laboratory (always always givengiven))

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Chemical Yield Chemical Yield

3. Percent yield3. Percent yield – – a percentagea percentage//ratio between ratio between the actual yield and the theoretical yield. the actual yield and the theoretical yield.

% Yield = % Yield =

% yield tells us how “efficient” a reaction is.% yield tells us how “efficient” a reaction is. % yield can not be bigger than 100 %.% yield can not be bigger than 100 %.

Actual YieldTheoretical Yield

x 100

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ExampleExample According to your calculations the According to your calculations the

theoretical yield for the production of theoretical yield for the production of NaCl is 13.6 grams. In the laboratory NaCl is 13.6 grams. In the laboratory your actual yield is 11.8 grams of NaCl. your actual yield is 11.8 grams of NaCl. What is the percent yield? What is the percent yield?

13.6 g NaCl

11.8 g NaClx 100

Answer = 86.7 %

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Calculating Percent CompositionCalculating Percent Composition 质质量分数量分数 of a Compoundof a Compound

Like all percent problems:Like all percent problems:

Part Part wholewhole

Find the mass of each component,Find the mass of each component, then divide by the total mass.then divide by the total mass.

x 100 %

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Calculating Percent CompositionCalculating Percent Composition 质质量分数量分数 of a Compoundof a Compound

Find the mass percent for the elements in Find the mass percent for the elements in Sodium hydrogen carbonate:Sodium hydrogen carbonate:

NaHCONaHCO33

-molar mass is 84 g/mol-molar mass is 84 g/mol

-mass of: Na= 23g-mass of: Na= 23g H= 1gH= 1g

C= 12gC= 12g O= 3 x 16= 48gO= 3 x 16= 48g

%C = (12g/84g) x 100= 14.3%%C = (12g/84g) x 100= 14.3%

%Na = (23g/84g) x 100= 27.4%%Na = (23g/84g) x 100= 27.4%

%H = (1g/84g) x 100= 1.2%%H = (1g/84g) x 100= 1.2%

%O = (48g/84g) x 100= 57.1%%O = (48g/84g) x 100= 57.1%

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The Empirical Formula The Empirical Formula 经验式经验式 The lowest The lowest whole number ratiowhole number ratio of of

elements in a compound.elements in a compound. The The molecular formula molecular formula = the = the actualactual

ratio of elements in a compound.ratio of elements in a compound. The two The two cancan be the same. be the same. CHCH22 is an empirical formula is an empirical formula CC22HH44 is a molecular formula is a molecular formula CC33HH66 is a molecular formula is a molecular formula HH22O is both empirical & molecularO is both empirical & molecular

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Calculating EmpiricalCalculating Empirical Just find the lowest whole number ratioJust find the lowest whole number ratio CC66HH1212OO66 CHCH44NN It is not just the ratio of atoms, it is also It is not just the ratio of atoms, it is also

the ratio of moles of atoms.the ratio of moles of atoms. In 1 mole of COIn 1 mole of CO22 there is 1 mole of carbon there is 1 mole of carbon

and 2 moles of oxygen.and 2 moles of oxygen. In one molecule of COIn one molecule of CO22 there is 1 atom of there is 1 atom of

C and 2 atoms of O.C and 2 atoms of O.

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Calculating EmpiricalCalculating Empirical We can get a ratio from the percent We can get a ratio from the percent

composition.composition. Assume you have a 100 g.Assume you have a 100 g. The percentages become grams.The percentages become grams. Convert grams to moles. Convert grams to moles. Find lowest whole number ratio by Find lowest whole number ratio by

dividing by the smallest mole valuedividing by the smallest mole value

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ExampleExample Calculate the empirical formula of a compound Calculate the empirical formula of a compound

composed of 38.67 % C, 16.22 % H, and 45.11 composed of 38.67 % C, 16.22 % H, and 45.11 %N.%N.

Assume 100 g soAssume 100 g so 38.67 g C x 1mol C = 3.220 mole C 38.67 g C x 1mol C = 3.220 mole C

12.01 g C 12.01 g C 16.22 g H x 1mol H = 16.09 mole H 16.22 g H x 1mol H = 16.09 mole H

1.01 g H 1.01 g H 45.11 g N x 1mol N = 3.219 mole N 45.11 g N x 1mol N = 3.219 mole N

14.01 g N 14.01 g N

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ExampleExample The ratio is 3.220 mol C = 1 mol CThe ratio is 3.220 mol C = 1 mol C

3.219 mol N 1 mol N 3.219 mol N 1 mol N The ratio is 16.09 mol H = 5 mol HThe ratio is 16.09 mol H = 5 mol H

3.219 mol N 1 mol N 3.219 mol N 1 mol N

= C= C11HH55NN11 = CH = CH55NN

Caffeine is 49.48% C, 5.15% H, 28.87% N Caffeine is 49.48% C, 5.15% H, 28.87% N and 16.49% O. What is its empirical and 16.49% O. What is its empirical formula?formula?

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Empirical to molecularEmpirical to molecular Since the empirical formula is the lowest ratio, Since the empirical formula is the lowest ratio,

the actual molecule would weigh more.the actual molecule would weigh more. By a whole number multiple.By a whole number multiple. Divide the actual molar mass by the empirical Divide the actual molar mass by the empirical

formula mass.formula mass. Caffeine has a molar mass of 194 g. what is its Caffeine has a molar mass of 194 g. what is its

molecular formula?molecular formula?

CC44HH55ONON22 = 97.11g = 97.11g

Ratio= 194g/ 97.11g = 2Ratio= 194g/ 97.11g = 2

2(C2(C44HH55ONON22) = C) = C88HH1010OO22NN4;4; molecular formula molecular formula

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ExampleExample A compound is known to be A compound is known to be

composed of 71.65 % Cl, 24.27% C composed of 71.65 % Cl, 24.27% C and 4.07% H. Its molar mass is and 4.07% H. Its molar mass is known (from gas density) to be 98.96 known (from gas density) to be 98.96 g. What is its molecular formula?g. What is its molecular formula?

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Final ExamFinal Exam What is matter?What is matter? Compounds; elements; substances vs. mixtures (Homogeneous Compounds; elements; substances vs. mixtures (Homogeneous

and Heterogeneous)and Heterogeneous) Atomic symbols; Naming compoundsAtomic symbols; Naming compounds Periodic table trends: Electronegativity, Atomic Radius, Ion Size, Periodic table trends: Electronegativity, Atomic Radius, Ion Size,

etc…etc… Reaction energy; exothermic vs. endothermic; activation energyReaction energy; exothermic vs. endothermic; activation energy Solvents, solutes, and solutionsSolvents, solutes, and solutions Balancing EquationsBalancing Equations Valence electronsValence electrons Structure of an Atom; Molecular structuresStructure of an Atom; Molecular structures Alpha, Beta, and Gamma DecayAlpha, Beta, and Gamma Decay Group names: Halogens, transition metals, alkali metals, etc…Group names: Halogens, transition metals, alkali metals, etc… Properties of metals, non-metals, metalloids, and semiconductorsProperties of metals, non-metals, metalloids, and semiconductors

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Final ExamFinal Exam Lewis Dot StructuresLewis Dot Structures Types of reactionsTypes of reactions Orbitals and sub-orbitalsOrbitals and sub-orbitals Ionic vs. Covalent bondingIonic vs. Covalent bonding Temperature and Kinetic motionTemperature and Kinetic motion Equilibrium and shifting the direction of reactionsEquilibrium and shifting the direction of reactions Calculate:Calculate:

– DensityDensity

– Wavelength and FrequencyWavelength and Frequency

– Atomic MassAtomic Mass

– Half lifeHalf life

– Radioactive decayRadioactive decay

– Moles; Mass percent, Percent yield, Mass-Mole Moles; Mass percent, Percent yield, Mass-Mole conversionsconversions