STOICHIOMETRYSTOICHIOMETRY

Chapter 3

Law of conservation of massLaw of conservation of mass

The balance became an important instrument in the eighteen century.

Balances measure mass, which is the quantity of matter in a material.

You should note the distinction You should note the distinction between the terms between the terms massmass and and weightweight in precise usage. in precise usage.

By weighing substances before and after chemical change, Lavoisier (1743-1794) demonstrated the law of conservation of mass which states that:

the total mass remains constant during a chemical change (chemical reaction).

Using the Law of Conservation of MassUsing the Law of Conservation of MassYou heat 2.53 g of metallic mercury in air, which produces 2.73 g of a red-orange residue. Assume that the chemical change is the reaction of the metal with oxygen in air.

Mercury + oxygen red-orange residue

What is the mass of oxygen that reacts?

When you strongly heat the red-orange residue, it decomposes to give back mercury and releases the oxygen, which you collect.

What is the mass of oxygen you collect?

Solution:

Total mass of substances before reaction

= Total mass of substance after reaction

From the law of conservation of mass:

Chemical EquationsChemical Equations

A chemical equation is a symbolic representation of a chemical reaction in terms of chemical formulas.

eg. 2Na + Cl2 2NaCl

A reactant is a starting substance in a chemical reaction

A product is a substance that results from a reaction.

Balancing Chemical Equations Balancing Chemical Equations

A chemical equation is said to be balanced, when the numbers of atoms of each element are equal on either side of the arrow.

Consider the burning of natural gas:

CH4 + O2 CO2 + H2O

The state or phase of a substance may be indicated with one of the following labels:

(g) ; (I) ; (s) ; (aq)

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

You can also indicate the conditions under which a reaction takes place, as well as the presence of a catalyst.

eg. 2H2O2(aq) Pt 2H2O(l) + O2(g)

Consider the burning or propane gasConsider the burning or propane gas

C3H8 + O2 CO2 + H2O

To balance the equation, you select coefficients that will make the numbers of atoms of each element equal on both sides of the equation.

Balancing Simple EquationsBalancing Simple Equations

Balance the following equations:

CS2 + O2 CO2 + SO2

C2H5OH + O2 CO2 + H2O

NH3 + O2 NO + H2O

Atomic Weights & Molecular WeightsAtomic Weights & Molecular Weights

Central to Dalton’s atomic theory was the idea that each atom had a characteristic mass.

We now know that each isotope has its own characteristic mass. Dalton actually calculated the average atomic mass, based on the relative abundance of each isotope.

Dalton could not weigh individual atoms, instead he could find the average mass of one atom relative to the average mass of another. (using H as a base)

Atomic mass unit - amuAtomic mass unit - amu

The atomic weight of an element, is the average atomic mass for the naturally occurring element, expressed in atomic mass units.

Today based on carbon-12

Mass of 12C = 12 amu

1 amu = 12 mass of 12C 1

Fractional AbundanceFractional Abundance

The fractional abundance of an isotope is the fraction of the total number of atoms that is composed of a particular isotope

An element has four naturally occurring isotopes. The mass and percentage abundance of each isotope are as follows:

Percentage abundance Mass

1.50 203.973

23.6 205.9745

22.6 206.9745

52.3 207.9766

What is the atomic weight and the name of the element?

Alternate Example

The mass percentages sums to 100

ie. 1.48 + 23.6 + 22.6 + 52.3 = 99.98= 100 (SIG FIG’S)

PPercentage ercentage CompositionComposition

The percentage of element B Is defined as:

Mass % B =(Atoms of B)(AW of B)mass of the whole x 100%

Remember the sum of the percentages of each element in the substance add up to 100%

Percentage composition of a compound = the percentage by mass contributed by each element in the substance

ExampleExample

Lead(II)chromate is used as a paint pigment (chrome yellow). What is the percentage composition of lead(II)chromate?

Lead(II)chromate = PbCrO4

Ar(Pb) = 207.2 g/mol

Ar(Cr) = 51.9961 g/mol

Ar(O) = 15.9994 g/mol

The chemical name for table sugar is sucrose, C12H22O11. How many grams of carbon are in 61.8 g of sucrose?

ExampleExample

Mass and Moles of SubstanceMass and Moles of Substance

We have seen so far that atoms / molecules react in simple ratios.

Atoms and molecules are too small to count. We need find another way of expressing

such large numbers

In pursuit of this end we are going to consider the following concepts:

Molecular weight Formula weight the Chemical Mole

Formula and Molecular WeightFormula and Molecular Weight

The formula weight of a substance is the sum of the atomic weights of all atoms in a formula unit of the compound.

The molecular weight of a substance is the sum of the atomic weights of all the atoms in a molecule of the substance.

Note: the formula weight is applicable to both molecular and ionic compounds.

Example Example

Calculate the formula weight of the following compounds from their formulae:

a) calcium hydroxide

b) methylamine = CH3NH2

The MoleThe MoleChemists have adopted the mole concept as a convenient way to deal with the enormous numbers of atoms, molecules or ions in the samples they work with.

Definition of Mole:A mole (symbol mol) = the amount of matter that contains as many Objects (atoms, molecules etc) as the number of atoms in exactly 12 grams of carbon-12.

The number of atoms in a 12 gram sample of carbon-12 is called Avogadro’s number (NA)

The term mole, just like a dozen or gross, refers to a particular number of things.

one dozen = 12one gross = 144one mole = 6.0221367 x 1023

When using the term mole it is important to specify what is being referred to!

eg : 1 mol of CH3COOH molecules contains 2 moles of C atoms etc.

Avogadro’s number (NA)

The molar mass of a substance is the mass of one mole of the substance

For all substances, the molar mass in grams per mole is numerically equal to the formula weight in atomic mass units.

Calculating the Mass of an Atom or Molecule

What is the mass of a nitric acid molecule?

Mole CalculationsMole Calculations

Because molar mass is the mass per mole we have the formula:

Molar Mass = Mass

Molesor Mr =

m

n

Remember that mass must be expressed in grams here!

Example

Converting Grams of Substance to Moles

Calcite is a mineral composed of calcium carbonate, CaCO3. A sample of calcite composed of pure CaCO3 weighs 23.6 g. How many moles of calcium carbonate is this?

Converting Moles of Substance to Grams

A sample of nitric acid contains 0.253 mol HNO3. How many grams is this?

Mr(HNO3) = 63.013 g.mol-1 (see previous example)

Example

Example

Calculating the Number of Molecules in a Given Mass

The daily requirement of chromium in the human diet is 1.0x10-6 g. How many atoms of chromium does this represent?

Determining formulaDetermining formulaee

The percentage composition of a compound leads directly to its empirical formula.

Recall: An empirical formula for a compound is the formula of a substance written with the smallest integer subscripts.

Eg. Consider hydrogen peroxide:

Molecular formula = H2O2

Empirical formula =

Compounds with different molecular formulae can have the same empirical formula, and such substances will have the same percentage composition.

Eg. acetylene = C2H2

benzene = C6H6

both have the empirical formula =

Empirical formula from CompositionEmpirical formula from CompositionConsider the following flow-diagram:

Percent composition

Mass Composition

Number of moles of each element

Divide by smallest number of moles to find the molar ratios

Multiply by appropriate number to get whole number subscripts

Example

Determining the Empirical Formula from the Masses of Elements (Binary Compound)

We have determined the percentage composition of benzene: 92.3% C and 7.7% H. What is the empirical formula of benzene?

Example

Determining The Empirical Formula from Percentage Composition.

Sodium pyrophosphate is used in detergent preparations. The mass percentages of the elements in this compound are 34.6% Na, 23.3% P and 42.1%O. What is the empirical formula of sodium pyrophosphate?

Hint: Consider a 100 g sample.

Molecular Formula from Empirical Molecular Formula from Empirical FormulaFormula

The molecular formula of a compound is a multiple of its empirical formula.

Molecular weight = n x empirical formula weight

where n = number of empirical formula units in the molecule.

Determining the Molecular Formula from the Percentage Composition and Molecular Weight.

We have already determined the mass composition and empirical formula of benzene. In a separate experiment, the molecular weight of benzene was determined to be 78.1. What is the molecular formula of benzene

Example

StoichiometryStoichiometry

Stoichiometry is the calculation of the quantities of reactants and products involved in a chemical reaction

It is based on the chemical equation and the relationship between mass and moles.

We can interpret a chemical equation in terms of number of molecules (or ions or formula units) or in terms of number of moles of molecules etc. depending on our needs.

Remember that because moles can be converted to mass, we can also produce a mass interpretation of a chemical equation.

Molecular Interpretation:

Molar interpretation:

Mass interpretation:

1 molecule N2 + 3 molecules H2 2 molecules NH3

1 mol N2 + 3 mol H2 2 mol NH3

28.0 g N2 + 3 x 2.02 g H2 2 x 17.0 g NH3

N2(g) + 3H2(g) 2NH3(g)Consider the reaction:

Notice that : The number of moles involved in a reaction is proportional to the coefficients in the balanced chemical equation.

Example

Find the amount of water produced when 3.68 mol of NH3 is consumed according to the following equation:

4NH3 + 5O2 4NO + 6H2O

We assume that sufficient O2 is present.

Amounts of Substance in a Chemical Reaction

The Steps in a Stoichiometric The Steps in a Stoichiometric CalculationCalculation

Mass of substance A

Moles of substance A

Moles of substance B

Mass of substance B

Use molar mass of AUse molar mass of A

Use molar mass of BUse molar mass of B

Use coefficients of A & B in Use coefficients of A & B in balanced eqnbalanced eqn

ExampleExample

Calculate the mass of sulfur dioxide (SO2) produced when 3.84 mol O2 is reacted with FeS2 according to the equation:

4FeS2 + 11O2 2Fe2O3 + 8SO2

Another Another Example

One of the most spectacular reactions of aluminium, the thermite reaction, is with iron oxide, Fe2O3, by which metallic iron is made.

The equation is :

2Al(s) + Fe2O3(s) Al2O3(s) + 2Fe(l)

A certain welding operation, requires that at least 86.0 g of Fe be produced. What is the minimum mass in grams of Fe2O3 that must be used for the operation?

Calculate also how many grams of aluminium are needed.

Strategy:

Limiting ReactantsLimiting Reactants

The limiting reactant (or limiting reagent) is the reactant that is entirely consumed when a reaction goes to completion.

The moles of product are always determined by the starting moles of the limiting reactant.

The Cheese Sandwich AnalogyThe Cheese Sandwich Analogy

Which is the limiting reactant? Which is the limiting reactant?

Use the relationships from the balanced chemical equation

You take each reactant in turn and ask how much product would be obtain, if each were totally consumed.

The reactant that gives the smaller amount of product is the limiting reactant.

Strategy:

When 100.0 g mercury is reacted with 100.0 g bromine to form mercuric bromide, which is the limiting reagent?

Hg + Br2 HgBr2

Example

ExampleMore Challenging!!

Iron can be obtained by reacting the ore haematite (Fe2O3) with coke (C). The latter is converted to CO2. As manager of a blast furnace you are told that you have 20.5 Mg of Fe2O3 and 2.84 Mg of coke on hand.

(a) Which should you order first - another shipment of iron ore or coke?

(b) How many megagrams of iron can you make with the materials you have?

2Fe2O3 + 3C 4Fe + 3CO2