Chapter 5

Calculations and the Chemical Equation

Denniston Topping Caret

4th Edition

Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

5.1 The Mole Concept and AtomsThe Mole and Avogadro’s Number• atomic mass unit (amu) - unit of measure for the

mass of atoms.– carbon-12 assigned the mass of exactly 12 amu– 1 amu = 1.66 x 10-24 g – periodic table gives atomic weights in amu.

• Chemists usually work with much larger quantities.– It is more convenient to work with grams than amu.

• To make the connection we must define the mole.

The mole is abbreviated mol.

• Avogadro’s number

1 mol of atoms = 6.022 x 1023 atoms of an element

• A mole is simply a unit that defines an amount of something– Just as a dozen defines 12– Just as a gross defines 144

• Molar mass - The mass in grams of 1 mole of atoms.

• What is the molar mass of carbon? 12.01 g/mol

• This means if you counted out a mole of Carbon atoms (i.e, 6.022 x 1023 of them) they would have a mass of 12.01 g.

• The average mass of one atom of an element in amu is numerically equivalent to the mass of one mole of an element expressed in grams.

– That is, 1 atom F is 19.00 amu and 1 mole of F is 19.00 g. Or,

– 19.00 amu/atom F and 19.00 g/mole F

F mol 1

F atom10022.6

Famu 1

F g1066.1

F atom 1

Famu 00.19 2324

=19.00 g F/mol F or 19.00 g/mol F

Calculating Atoms, Moles, and Mass• We now know the following conversion factors:

Conversion Tool

g ml density

amu g 1 amu = 1.661 x 10-24 g

6.022 x 1023 amu = 1g

moleactual number Avegadro’s No.

g mole Molar Mass

5.2 Compounds

The Chemical Formula• Chemical Formula - a combination of symbols of

the various elements that make up the compound.• Formula unit - the smallest collection of atoms that

provide two important pieces of information– the identity of the atoms and– the relative number of each type of atom

• Let’s look closely at the following formulas:

• H2O, NaCl, Fe(CN)3, (NH4)3PO4, CuSO4.5H2O

– This is an example of a hydrate - compounds containing one or more water molecules as an integral part of their structure.

5.3 The Mole Concept Applied to Compounds

• Formula weight - the sum of the atomic weights of all atoms in the compound, as represented by its formula.– expressed in amu

• Molar mass applies to compounds also.

• What is the formula weight of H2O?– 16.00 amu + 2(1.008 amu) = 18.02 amu

• What is the molar mass of H2O?

– 18.02 g/mol H2O

• When calculating the formula weight (or molar mass of an ionic compound, use the smallest unit of the crystal)

• What is the molar mass of (NH4)3PO4?

• 149.10 g/mol (NH4)3PO4

5.4 The Chemical Equation and the Information It Conveys

A Recipe For Chemical Change• Chemical Equation - shorthand notation of a

chemical reaction.• Reactants - (starting materials) - the substances

that undergo change in the reaction.• Products - substances produced by the reaction.• Law of Conservation of Mass - matter cannot be

either gained or lost in the process of a chemical reaction.– The total mass of products must equal the total mass of

the reactants.

Features of a Chemical Equation

)(O )2Hg( )2HgO( 2 gls

Products - written on the right

Reactants- written on the left of arrow

Products and reactants must be specified using chemical symbols

Physical states are shown in parentheses

- means heat is needed.

)(O )2Hg( )2HgO( 2 gls

• The equation must be balanced. – All the atoms of every reactant must also

appear in the products.

• How many Hg’s on left?

• on right?

• How many O’s on left?

• on right?

Coefficient - how many of the substance are in the reaction

We know that a chemical equation represents a chemical change. The following is evidence for a reaction:

• Release of a gas.– CO2 is released when acid is placed in a solution

containing CO32- ions.

– H2 is released when Na is placed in water.

• Formation of a solid (precipitate.)

– A solution containing Ag+ ions is mixed with a solution containing Cl- ions.

• Heat is produced or absorbed (temperature changes)– Acid and base are mixed together

• The color changes

• Light is absorbed or emitted

• Changes in the way the substances behave in an electrical or magnetic field

• Changes in electrical properties.

5.5 Balancing Chemical Equations• Consider the following reaction:

hydrogen reacts with oxygen to produce water• Write the above reaction as a chemical equation.• You probably wrote the following:

H2 + O2 H2O

• Don’t forget the diatomic elements.• Is the law of conservation of mass obeyed as

written? NO!• Balancing chemical equations uses coefficients to

ensure that the law of conservation of mass is obeyed.

H2 + O2 H2O

•You may not change subscripts!

•WRONG: H2 + O2 H2O2

Using the equation below, let’s see the steps to balancing:

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

Reactants Products2 mol H 2 mol H2 mol O 1 mol O

Step 2. Determine which elements are not balanced. Oxygen is not balanced.

Step 3. Balance one element at a time using coefficients.

H2 + O2 2H2O

This balances oxygen, but is hydrogen still balanced? How will we balance hydrogen?

2H2 + O2 2H2O

Step 4. Check! Make sure the Law of conservation of mass is obeyed.

5.6 Calculations Using the Chemical Equation

• We will learn in this section to calculate quantities of reactants and products in a chemical reaction.

• Need a balanced chemical equation for the reaction of interest.

• Keep in mind that the coefficients represent the number of moles of each substance in the equation.

• Let’s examine the reaction:

2H2 + O2 2H2O

7

• What do the coefficients tell us?

• 2 mol H2 reacts with 1 mol O2 to produce 2 mol H2O.

• What if 4 moles of H2 reacts with 2 moles of O2?

• It yields 4 moles of H2O

• The coefficients of the balanced equation are used to convert between moles of substances.

• How many moles of O2 are needed to react with 4.26 moles of H2?

• You may be able to do this in your head, but let’s see how to use the factor label method.

2

22 H mol__

O __molH mol 26.4

1

22.13 mol O2

Comes from the balanced equation.

Plan your route before calculating.

Theoretical and Percent Yield

• Theoretical yield - the maximum amount of product that can be produced – Pencil and paper yield

• Actual yield - the amount produced when the reaction is performed– Laboratory yield

• Percent yield:

%100yield ltheoretica

yield actual yield %