3. the Mole Concept and Atoms

Chapter 3: Calculations Chapter 3: Calculations and the Chemical Equationand the Chemical Equation

The Mole Concept and Atoms

Atomic mass unitAtomic mass unit

1 amu = 1.661 X 101 amu = 1.661 X 10-24-24 g g

Because the mass of one amu is so small, Because the mass of one amu is so small, chemists deal with a much larger number chemists deal with a much larger number of atoms while working with chemicalsof atoms while working with chemicals

Mole Mole

One mole is defined as 6.022 X 10One mole is defined as 6.022 X 102323. . This refers to one mole of anything, eggs, This refers to one mole of anything, eggs, paperclips, atoms. One mole of anything paperclips, atoms. One mole of anything is 6.022 X 10is 6.022 X 1023 23 items. Much like one items. Much like one dozen of something is 12.dozen of something is 12.This number, 6.022 X 10This number, 6.022 X 102323 is called is called Avogadro’s number, named after the Avogadro’s number, named after the scientist who conducted a series of scientist who conducted a series of experiments leading to the “mole concept”.experiments leading to the “mole concept”.

The mole conceptThe mole concept

The mole and the amu are related. For The mole and the amu are related. For atoms, the atomic mass of an element atoms, the atomic mass of an element corresponds to the average mass of a corresponds to the average mass of a single atom in amu single atom in amu

AndAnd

The mass of a mole of atoms in grams.The mass of a mole of atoms in grams.

For example:For example:

The atomic mass of oxygen is 16.00 amu.The atomic mass of oxygen is 16.00 amu.

AndAnd

One mole of oxygen atoms (6.022 X 10One mole of oxygen atoms (6.022 X 102323 oxygen atoms) has a mass of 16.00 gramsoxygen atoms) has a mass of 16.00 grams

Another exampleAnother example

The atomic mass of iron (Fe) is 55.85 The atomic mass of iron (Fe) is 55.85 amu.amu.

AndAnd

One mole of iron atoms (6.022 X 10One mole of iron atoms (6.022 X 102323 oxygen atoms) has a mass of 55.85 gramsoxygen atoms) has a mass of 55.85 grams

And yet another exampleAnd yet another example

The atomic mass of radium (Ra) is 226 The atomic mass of radium (Ra) is 226 amu.amu.

AndAnd

One mole of radium atoms (6.022 X 10One mole of radium atoms (6.022 X 102323 radium atoms) has a mass of 226 gramsradium atoms) has a mass of 226 grams

Molar massMolar mass

The mass of one mol (mole) of atoms in The mass of one mol (mole) of atoms in gramsgrams

NoteNote

One mole of atoms of any element One mole of atoms of any element contains 6.022 X 10contains 6.022 X 102323 atoms, regardless of atoms, regardless of the type of element.the type of element.The mass of one mole of an element The mass of one mole of an element depends on what that element is, and is depends on what that element is, and is equal to the atom mass of that element in equal to the atom mass of that element in grams.grams.

This meansThis means

There are several “conversions” regarding There are several “conversions” regarding atoms, moles, and massatoms, moles, and mass

Converting moles to atomsConverting moles to atoms

How many atoms are in 4 moles of H?How many atoms are in 4 moles of H?

4 moles H X 6.022 X 104 moles H X 6.022 X 102323 atoms/mole = atoms/mole = 24.088 X 1024.088 X 102323 atoms of hydrogen or 2.409 atoms of hydrogen or 2.409

X 10X 102424 atoms atoms

In this case you multiply the number of In this case you multiply the number of moles X the number of atoms in each moles X the number of atoms in each mole.mole.

Converting atoms to molesConverting atoms to molesCalculate the number of moles of copper represented by Calculate the number of moles of copper represented by 3.26 X 103.26 X 102424 atoms. atoms.

3.26 X 103.26 X 1024 24 = 32.6 X 10 = 32.6 X 102323 (ok, I did this step to make the (ok, I did this step to make the math easier.)math easier.)

32.6 X 1032.6 X 102323 / 6.022 X 10 / 6.022 X 102323 = 5.413 X 10 = 5.413 X 102323 moles of copper. moles of copper.

In this case, to convert atoms to moles, I divide the In this case, to convert atoms to moles, I divide the number of atoms by the number of atoms in one mol (by number of atoms by the number of atoms in one mol (by 6.022 X 106.022 X 102323 ) )

Converting moles of a substance to Converting moles of a substance to mass in grams.mass in grams.

What is the mass in grams of 5.6 mol of What is the mass in grams of 5.6 mol of Neon?Neon?

The mass of one mole of Ne is the same The mass of one mole of Ne is the same as the atomic mass in g (20.18 g)as the atomic mass in g (20.18 g)

5.6 mol X 20.18 g/mol = 100.9 g of Ne5.6 mol X 20.18 g/mol = 100.9 g of Ne

Converting grams to numbers of Converting grams to numbers of atoms.atoms.

How many atoms would be in a gold ring How many atoms would be in a gold ring that weighs 25 g?that weighs 25 g?First, find the number of moles of Gold in First, find the number of moles of Gold in 25 g. Gold has an atomic mass of 107.9. 25 g. Gold has an atomic mass of 107.9. So, 25 g / 107.9 g/mol = 0.2317 mol of So, 25 g / 107.9 g/mol = 0.2317 mol of gold are in the ring.gold are in the ring.Next, 0.2317 mol X (6.022 X 10Next, 0.2317 mol X (6.022 X 102323) ) atoms/mol =1.395 X 10atoms/mol =1.395 X 1023 23 atomsatoms

When dealing with molecules. . .When dealing with molecules. . .

Like OLike O2 2 or Hor H2 2 , double the number of atoms,

because there are 2 atoms per molecule.Remember, one mole of something is 6.022 X X 101023 23 of whatever it is. If it is molecules, it’sof whatever it is. If it is molecules, it’s 6.022 X 10 1023 23 of themof them.. If it is atoms, it’s 6.022 x10 If it is atoms, it’s 6.022 x1023 23

atoms. atoms. If there are 2 atoms per molecule you need to If there are 2 atoms per molecule you need to double the number of moles. double the number of moles. 2 X (2 X (6.022 X 10X 1023 23 ) = 12.044 X 10) = 12.044 X 1023 23 or 1.204 X or 1.204 X 10102424


Section 4.2: The Chemical Section 4.2: The Chemical Formula, Formula Weight, and Formula, Formula Weight, and

Molar MassMolar Mass

Chemical FormulaChemical Formula

A combination of symbols of the various A combination of symbols of the various elements that make up the compound.elements that make up the compound.

Formula UnitFormula Unit

The smallest amount of atoms that The smallest amount of atoms that provides the following informationprovides the following information The identity of atoms in the compoundThe identity of atoms in the compound The relative numbers of each type of atomThe relative numbers of each type of atom ExamplesExamples

Molecule vs ion pairMolecule vs ion pair

Covalent compounds form molecules, and Covalent compounds form molecules, and when calculating formula weight all of the when calculating formula weight all of the atoms in the compound are added atoms in the compound are added together.together.Ion pairs (ionic compounds) form Ion pairs (ionic compounds) form crystalline structures. It’s the smallest crystalline structures. It’s the smallest group of ions that are listed in the formula group of ions that are listed in the formula for these types of chemicals.for these types of chemicals.

Formula weight vs Molecular Formula weight vs Molecular WeightWeight

The sum of all of the atomic weights in the The sum of all of the atomic weights in the compound in an ionic compound it’s the compound in an ionic compound it’s the formula weight. In a covalent compound formula weight. In a covalent compound it’s the molecular weight.it’s the molecular weight.

Molar MassMolar Mass

The mass of one mole of the compound or The mass of one mole of the compound or the formula weight in grams.the formula weight in grams.ExamplesExamples

Conversions using Formula WeightConversions using Formula Weight

Finding the number of moles Finding the number of moles corresponding to a certain number of corresponding to a certain number of grams.grams.

Conversions using Formula WeightConversions using Formula Weight

Finding grams corresponding to a certain Finding grams corresponding to a certain number of moles.number of moles.


Section 3: The Chemical Section 3: The Chemical Equation and the Information it Equation and the Information it

ConveysConveys

Chemical equationChemical equation

The shorthand notation for a chemical The shorthand notation for a chemical reaction, where one substance changes reaction, where one substance changes chemically into another substance.chemically into another substance.An example: burning sugarAn example: burning sugar

ReactantsReactants

The starting materials that undergo a The starting materials that undergo a chemical changechemical change

ProductsProducts

The ending materials that are produced by The ending materials that are produced by a chemical reaction.a chemical reaction.

Additional information in a chemical Additional information in a chemical reactionreaction

Physical state of the substance (solid, Physical state of the substance (solid, liquid, or gas)liquid, or gas)If the reaction occursIf the reaction occursIdentifies the solvent, if there is one. (A Identifies the solvent, if there is one. (A solvent is the solution the materials are solvent is the solution the materials are dissolved in, such as water.)dissolved in, such as water.)Experimental conditions such as heat, Experimental conditions such as heat, light, or electrical energy addedlight, or electrical energy added

Most importantlyMost importantly

The chemical equation identifies the The chemical equation identifies the relative number of moles of reactants and relative number of moles of reactants and products.products.

According to the Law of According to the Law of Conservation of MassConservation of Mass

Matter cannot be gained or lost in the Matter cannot be gained or lost in the process of a chemical reactionprocess of a chemical reactionThe total mass of the products must equal The total mass of the products must equal the total mass of the reactantsthe total mass of the reactantsThe chemical equation must be balanced.The chemical equation must be balanced.

Features of a chemical reaction.Features of a chemical reaction.

CaCOCaCO33(s) (s) →→∆ ∆ CaO(s) + COCaO(s) + CO22(g)(g)

Reactants are on the left of the

arrow.

The arrow indicates the

reaction occurs in one

direction.

The products

are on the right of the

arrow.



“s” indicates the chemical

is a solid substance

“g” indicates the substance

is a gas

“l” would indicate the

substance

were a liquid.



The ∆ indicates that energy was necessary for the chemical reaction to

occur



The main feature of a chemical equation is that it is balanced, with the same number of elements in

compounds on both sides of the arrow.

The experimental basis of a The experimental basis of a chemical equationchemical equation

Evidence for a chemical reaction includes:Evidence for a chemical reaction includes:

The release of a gas resulting in bubblesThe release of a gas resulting in bubbles

The formation of a solid (precipitate) in solutionThe formation of a solid (precipitate) in solution

The production of heat resulting in an increase in The production of heat resulting in an increase in temperaturetemperature

A change in color of a substanceA change in color of a substance

The experimental basis of a The experimental basis of a chemical equationchemical equation

Sometimes instruments must be used to Sometimes instruments must be used to measure subtle changes that indicate a measure subtle changes that indicate a chemical reaction.chemical reaction.

Heat or light absorbed or emittedHeat or light absorbed or emitted

Changes in the way a sample behaves in an electrical Changes in the way a sample behaves in an electrical or magnetic fieldor magnetic field

Changes in electrical propertiesChanges in electrical properties

Writing Chemical ReactionsWriting Chemical Reactions

Most reactions follow a few simple Most reactions follow a few simple patternspatterns

Combination reactionsCombination reactions

Decomposition reactionsDecomposition reactions

Replacement reactionsReplacement reactions


Involve the joining or combining of two or Involve the joining or combining of two or more compoundsmore compoundsThe general form of the reaction is The general form of the reaction is

A + B A + B → AB→ AB


Examples include:Examples include: Combination of a metal and non-metal to form a saltCombination of a metal and non-metal to form a salt

Ca(s) Ca(s) + Cl+ Cl22(g)(g) → CaCl→ CaCl22(s)(s)

Reaction of magnesium oxide and carbon dioxide to Reaction of magnesium oxide and carbon dioxide to produce magnesium carbonateproduce magnesium carbonate

MgO(s) + COMgO(s) + CO22(g) →MgCO(g) →MgCO33(s)(s)

Decomposition ReactionsDecomposition Reactions

Reactions that produce two or more Reactions that produce two or more products from a single reactant.products from a single reactant.The general form for the reaction is The general form for the reaction is

AB AB → A + B→ A + B

Decomposition reactionsDecomposition reactions

Examples includeExamples include The removal of water from a hydrate (a substance The removal of water from a hydrate (a substance

that has water molecules linked in it’s structure)that has water molecules linked in it’s structure)

CuSOCuSO44·5H·5H22O(s) →O(s) →CuSOCuSO44(s) + (s) + 5H5H22O(g)O(g)

The heating of calcium carbonate to produce calcium The heating of calcium carbonate to produce calcium oxide and carbon dioxide gasoxide and carbon dioxide gas

CaCOCaCO33(s) → CaO(s) + CO(s) → CaO(s) + CO22(g)(g)

Replacement Reactions—Single Replacement Reactions—Single ReplacementReplacement

Single replacement reactions is where one Single replacement reactions is where one atom replaces another in the compoundatom replaces another in the compoundThe general formula is The general formula is

A + BC A + BC → AC + B→ AC + B

Replacement ReactionsReplacement Reactions

Examples includeExamples include

The replacement of copper by zinc in The replacement of copper by zinc in copper sulfate forming zinc sulfatecopper sulfate forming zinc sulfate

Zn(s) + CuSOZn(s) + CuSO44(aq) (aq) → Zn → Zn SOSO44(aq) + Cu(s)(aq) + Cu(s)

Replacement Reactions—Double Replacement Reactions—Double ReplacementReplacement

Two compounds that “switch” atoms with Two compounds that “switch” atoms with each othereach otherThe general formula isThe general formula is

AB + CD AB + CD → AD + CB→ AD + CB

Replacement Reactions—Double Replacement Reactions—Double ReplacementReplacement

Examples includeExamples includeThe formation of salt and water with the The formation of salt and water with the reaction of a base and an acidreaction of a base and an acid

HCl(aq) + NaOH(aq) HCl(aq) + NaOH(aq) →H→H22O(l) + NaCl(aq)O(l) + NaCl(aq)

Types of Chemical ReactionsTypes of Chemical Reactions

There are four main types of chemical There are four main types of chemical reactionsreactions Precipitation reactionsPrecipitation reactions

Reactions with OxygenReactions with Oxygen

Acid-base reactionsAcid-base reactions

Oxidation-reduction reactionsOxidation-reduction reactions

Precipitation reactionsPrecipitation reactions

A chemical change that produces an A chemical change that produces an insoluble product that will form a solid. insoluble product that will form a solid. Usually the solid can be seen “falling out” Usually the solid can be seen “falling out” of the solution, hence, called precipitation. of the solution, hence, called precipitation. At other times the solid makes the solution At other times the solid makes the solution turn from clear to cloudy.turn from clear to cloudy.

Solubility predictionsSolubility predictionsNa, K, and ammonium compounds are generally soluble.Na, K, and ammonium compounds are generally soluble.

Nitrates and acetates are generally solubleNitrates and acetates are generally soluble

Chlorides, bromides, and iodides are generally soluble. However, Chlorides, bromides, and iodides are generally soluble. However, iodine compounds that contain lead, silver, and mercury are iodine compounds that contain lead, silver, and mercury are insoluble.insoluble.

Carbonates and phosphates are generally insoluble. Sodium, Carbonates and phosphates are generally insoluble. Sodium, potassium, and ammonium carbonates and phosphates are soluble.potassium, and ammonium carbonates and phosphates are soluble.

Hydroxides and sulfides are generally insoluble. Sodium, Hydroxides and sulfides are generally insoluble. Sodium, potassium, calcium, and ammonium compounds are however potassium, calcium, and ammonium compounds are however soluble. soluble.

Reactions with oxygenReactions with oxygen

Many substances react with oxygen. If the Many substances react with oxygen. If the substance contains carbon, then carbon substance contains carbon, then carbon dioxide is usually produced. If the dioxide is usually produced. If the substance contains hydrogen, then water substance contains hydrogen, then water is usually produced.is usually produced.An example is iron turning to rustAn example is iron turning to rust

4Fe(s) + 3O4Fe(s) + 3O22(g) (g) → 2Fe→ 2Fe22OO33(s)(s)This number is called a coefficient, and indicates the

number of molecules or moles that reacts with the other compounds.

Acid-base ReactionsAcid-base ReactionsThis involves an acid combining with a This involves an acid combining with a base to form a salt.base to form a salt.An example would beAn example would be

HCl(aq) + NaOH(aq) HCl(aq) + NaOH(aq) → NaCl(aq) + H→ NaCl(aq) + H22O(aq)O(aq)

Oxidation Reduction ReactionsOxidation Reduction Reactions

Involves the transfer of negative charge Involves the transfer of negative charge from one reactant to another.from one reactant to another.The reaction of zinc with copper would be The reaction of zinc with copper would be an example.an example.

Zn(s) + CuZn(s) + Cu2+2+ (aq) (aq) → → ZnZn2+2+ (aq) + Cu (s) (aq) + Cu (s)

These specific reactions will be discuss in These specific reactions will be discuss in further detail at a later time.further detail at a later time.

Homework Assignment #12Homework Assignment #12

p. 147 Answer questions 59-68p. 147 Answer questions 59-68Read p. 126-136. Answer the exercises in Read p. 126-136. Answer the exercises in

the reading that were not answered in the reading that were not answered in class as examples.class as examples.


Section 4: Balancing Chemical Section 4: Balancing Chemical EquationsEquations

The chemical equationThe chemical equation

Shows the molar quantity of reactants Shows the molar quantity of reactants needed to produce a certain molar needed to produce a certain molar quantity of products.quantity of products.

sincesince

The number of atoms in a molecule cannot The number of atoms in a molecule cannot be changed (it would make an entirely be changed (it would make an entirely different compound)different compound)

coefficientscoefficients

(whole numbers that show the numbers of (whole numbers that show the numbers of entire molecules) are used to balance a entire molecules) are used to balance a chemical equationchemical equation

For example, in the equationFor example, in the equation


On the reactant sideOn the reactant side On the product sideOn the product side

1 mole Ca1 mole Ca 1 mole Ca1 mole Ca1 mole C1 mole C 1 mole C1 mole C3 moles of O3 moles of O 3 moles of O3 moles of O

Since there are the same numbers of each type of molecules on both sides of the arrow, the equation is balanced.

HCl(aq) + Ca(s) HCl(aq) + Ca(s) CaClCaCl22(s) + H(s) + H22(g)(g)

On the reactant sideOn the reactant side On the product sideOn the product side

1 mole H1 mole H 2 mole H2 mole H

1 mole Cl1 mole Cl 2 moles Cl2 moles Cl

1 mole Ca1 mole Ca 1 mole Ca1 mole Ca

Since there are not the same number of moles on both sides of this equation, the equation is not balanced.

HCl(aq) + Ca(s) HCl(aq) + Ca(s) CaClCaCl22(s) + H(s) + H22(g)(g)

2HCl(aq) + Ca(s) 2HCl(aq) + Ca(s) CaCl CaCl22(s) + H(s) + H22(g)(g)

To balance the equation, place a coefficient of 2 in front of the HCl.

Steps to balancing a chemical Steps to balancing a chemical equationequation

Step 1: Count the number of moles of Step 1: Count the number of moles of atoms of each element on both product atoms of each element on both product and reactant sideand reactant side

H2(g) + O2(g) H2O(l)

On the reactant side:

2 moles of H2 moles of O

On the product side:

2 moles of H1 mole of O


Step 2: Determine which elements are not Step 2: Determine which elements are not balanced.balanced.

H2(g) + O2(g) H2O(l)

The oxygen atoms are not balanced in

this equation.


Step 3: Balance one element at a Step 3: Balance one element at a time. time.

H2(g) + O2(g) H2O(l)

First: H2(g) + O2(g) 2H2O(l)

Then 2H2(g) + O2(g) 2H2O(l)


Step 4: After you believe you have Step 4: After you believe you have successfully balanced the equation, check successfully balanced the equation, check to make sure you have the same number to make sure you have the same number of atoms on both sides of the equation.of atoms on both sides of the equation.

2H2(g) + O2(g) 2H2O(l)



Homework Assignment #13Homework Assignment #13

p. 147 Answer questions 69-84p. 147 Answer questions 69-84Read p. 136-145. Answer the exercises in Read p. 136-145. Answer the exercises in

the reading that were not answered in the reading that were not answered in class as examples.class as examples.


Section 4.5: Calculations Using Section 4.5: Calculations Using the Chemical Equationthe Chemical Equation

Calculations Using Chemical Calculations Using Chemical EquationsEquations

Using the chemical formulas to calculate Using the chemical formulas to calculate amounts of materials needed or produced amounts of materials needed or produced can be done once you have a balanced can be done once you have a balanced chemical equation.chemical equation.

In order to carry out In order to carry out chemical calculations the chemical calculations the following guidelines must following guidelines must

be followed.be followed.The chemical formulas of ALL the The chemical formulas of ALL the products and reactants must be products and reactants must be knownknown

The basis for the calculations is the The basis for the calculations is the balanced chemical equation. Be balanced chemical equation. Be sure all of the equations are sure all of the equations are balanced first.balanced first.The calculations are performed in The calculations are performed in terms of moles.terms of moles.

Use of Conversion Factors--Use of Conversion Factors--conversion between moles and conversion between moles and

grams.grams.

Example: convert 10 moles of NaCl to gramsExample: convert 10 moles of NaCl to grams

The formula mass of NaCl is the molecular The formula mass of NaCl is the molecular mass of Na + the molecular mass of Cl mass of Na + the molecular mass of Cl (22.99 + 35.45 = 58.44 grams per mole.(22.99 + 35.45 = 58.44 grams per mole.

10 moles NaCl X 10 moles NaCl X 55.44 grams 55.44 grams = 554.4 grams of NaCl = 554.4 grams of NaCl1 mole1 mole

Use of Conversion Factors--conversion Use of Conversion Factors--conversion between moles and grams.between moles and grams.

Example: How many moles of CaClExample: How many moles of CaCl22 would would 23 grams contain?23 grams contain?

The formula mass of CaClThe formula mass of CaCl22 equals the equals the atomic mass of Ca and 2 X the atomic mass atomic mass of Ca and 2 X the atomic mass of Cl (40.08 + 2(35.45) = 110.98)of Cl (40.08 + 2(35.45) = 110.98)

23 grams X 23 grams X 1 mole1 mole = 0.207 moles = 0.207 moles 110.98 grams 110.98 grams

Use of Conversion Factors—Use of Conversion Factors—Conversion of moles of reactants Conversion of moles of reactants

to moles of products.to moles of products.

Once you have a balanced chemical Once you have a balanced chemical equation, develop a conversion equation, develop a conversion factor of reactants to products. After factor of reactants to products. After you have done that you can:you have done that you can: Calculate reacting quantitiesCalculate reacting quantities Calculate grams of product producedCalculate grams of product produced Relate the mass of reactants and Relate the mass of reactants and

productsproducts

Converting moles of reactants to Converting moles of reactants to moles of productmoles of product

2H2H22(g) + O(g) + O22(g) (g) 2H 2H22O(l)O(l)

In this equation: 2 moles of HIn this equation: 2 moles of H2 2 will react with will react with 1 mole of O1 mole of O22 to produce 2 moles of H to produce 2 moles of H22O.O.

2H2H22(g) + O(g) + O22(g) (g) 2H 2H22O(l)O(l)

To calculate the number of grams of HTo calculate the number of grams of H22O O produced by 1 mole of Oproduced by 1 mole of O22

1.1. Convert from moles of OConvert from moles of O2 2 to moles of Hto moles of H22OO

1 mole O2 x 2 moles H2O = 2 moles H2O produced

2. Convert the moles of H2. Convert the moles of H22O to grams of O to grams of HH22OO

2 moles X 18.016 grams = 1 mole36.032 grams

Relating masses of reactants Relating masses of reactants and productsand products


How many grams of Ca0 will be produced How many grams of Ca0 will be produced by 100.0 grams of by 100.0 grams of CaCOCaCO33??

First, determine how many moles First, determine how many moles will be produced.will be produced.


One mole of CaCO3 will produce one mole of

CaO

Next, determine how many grams of Next, determine how many grams of each are in each mole of substance.each are in each mole of substance.

CaCO3(s) →∆ CaO(s) + CO2(g)

1 mole of CaCO3 has a formula mass

of 100.09 grams

1 mole of CaO has a

mass of 56.06 grams

0.9991 moles CaCO3 will produce 0.9991 moles CaO0.9991 moles CaCO3 will produce 0.9991 moles CaO

0.9991 moles CaO X 0.9991 moles CaO X 56.06 grams56.06 grams = 56.00 grams = 56.00 grams CaOCaO

1 mole1 mole

100 grams CaCO3 X 1 mole CaCO3 = 0.9991 moles CaCO3

100.09 grams CaCO3

Theoretical and percent yieldTheoretical and percent yield

If a chemical reaction occurs, in theory you If a chemical reaction occurs, in theory you can calculate how much of the product is can calculate how much of the product is created. This would be the maximum created. This would be the maximum amount that is produced. However, in the amount that is produced. However, in the real world often not all the possible real world often not all the possible product are produced in a chemical product are produced in a chemical reaction.reaction.

Theoretical yieldTheoretical yield

The maximum amount of product that The maximum amount of product that could be produced determined by could be produced determined by calculations using the chemical equation.calculations using the chemical equation.

Percent yieldPercent yield

The ratio of the actual and theoretical The ratio of the actual and theoretical yields determined by the formulayields determined by the formula

%yield = %yield = actual yieldactual yield X 100% X 100%Theoretical yieldTheoretical yield

Example:Example:

2HCl(aq) + Ca(s) 2HCl(aq) + Ca(s) CaCl CaCl22(s) + H(s) + H22(g)(g)

Assume the theoretical yield of CaClAssume the theoretical yield of CaCl2 2 in in this equation were 30 g. If the actual this equation were 30 g. If the actual yield of CaClyield of CaCl2 2 were 25 g, calculate the were 25 g, calculate the percentage yield.percentage yield.

%yield = %yield = actual yieldactual yield X 100% X 100%Theoretical yieldTheoretical yield

25 g 25 g X 100 = 83.3% X 100 = 83.3% 30g30g

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3. the Mole Concept and Atoms