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Mark S. CracoliceEdward I. Peters

Mark S. Cracolice • The University of Montana

Chapter 7Chemical Formula Relationships

Number of Atoms in a Formula

In writing the formula of a substance, subscript numbers are used to indicate the number of atoms or groups of atoms of each element in

the formula unit.

Number of Atoms in a Formula

How many atoms of each element are in a formula unit of ammonium carbonate?

The formula of the ammonium ion is NH4+

The formula of carbonate is CO32–

The formula of the ammonium carbonate is (NH4)2CO3.Each element in the parentheses is multiplied by two.

Total number of atoms of each element:2 nitrogen atoms, 8 hydrogen atoms,

1 carbon atom, 3 oxygen atoms

Atomic Mass

Atomic MassThe average mass of atoms of an element

By definition the mass of a carbon-12 atom is 12 u.

Molecular & Formula Mass

Molecular MassThe sum of the atomic masses of each atom in

the molecule.

Formula mass The sum of atomic

masses in the formula unit

Molecular & Formula MassWhat is the formula mass of calcium phosphate?

Calcium ion: Ca2+ Phosphate ion: PO43–

Calcium phosphate: Ca3(PO4)2

Ca 3 × 40.08 u = 120.24 uP 2 × 30.97 u = 61.94 uO 8 × 16.00 u = 128.00 u

Ca3(PO4)2 310.18 u

Defenition of Mole

The mole is the amount of substance that contains as many elementary entities as there are atoms in exactly 12 grams of carbon-12.

In 12 g of carbon-12 there are 6.022 x 10 23 atoms 1 mole of any substance = 6.022 x 10 23 units

of that substance. When the mole is used the elementary entities must

be specified: atoms, molecules, ions…

Avogadro’s Number NA

The number of elementary units in one mole

6.02214179 1023 units/mol

The Avogadro constant is a conversion factor between units and mole.

Conversion of Mole to MoleculesHow many carbon dioxide molecules are in 2.0 moles of carbon

dioxide?

2.0 mol CO2 × =

1.2 × 1024 molecules CO2

Molar Mass

Molar mass of a substance is the mass in grams of one mole of the substance.

Units: g/mol

Molar mass of an element is the mass of the element per mole of its atoms.

Atomic mass unit and gramThe mass of one atom of carbon-12 is exactly 12

atomic mass units.

The mass of one mole of carbon-12 atoms (6.022 x 1023 atoms of carbon-12) is exactly 12 grams

(6.022 x 1023 atoms) x (12 u/atom) = 12 grams6.022 x 1023 u = 1 gram

Molar MassThe mass of one atom of carbon-12 is exactly 12

atomic mass units.The mass of one mole of carbon-12 atoms is exactly 12

grams.This leads to the conclusion:

The molar mass of any substance in grams per mole is numerically equal to the atomic, molecular or formula mass of that substance in atomic mass units.

Molar Mass

Calculate the mass of one NH3 molecule and the mass of one mole of NH3 molecules.

14.01 u + 3x1.008 u = 17.03 uThe mass of one ammonia molecule is 17.03 u.To change from molecular mass to molar mass, change

the units from u to g/mol: 17.03 g/mol.One mole of ammonia molecules has a mass of 17.03 g.

Molar Mass

Mass, # of Moles, # of Units

Molar mass, MM, links mass in grams with the number of moles.

Avogadro’s number, NA, links the number of moles with the number of particles.

Mass, # of Moles, # of Units

How many molecules are in 454 g of water?

g moles molecules

454g x x

= 1.52 x 1025 molecules H2O

OO

2

223

H molH molecules 10 6.02

OO

2

2H g 18.02

H mol 1

Mass↔Moles↔ UnitsHow many hydrogen atoms are in 1.0 kg of ammonia?

1.0 kg NH3 × × ×

× =

1.1 × 1026 atoms H

Percentage Composition

Percentage

% A = × 100%

The percentage composition of a compound is thepercentage by mass of each element in the compound.

Percentage Composition

Determine the percentage composition of calcium fluoride Ca F2.

Solution:In one mole of Ca F2

1x(40.08 g Ca) + 2x(19.00 g F) = 78.08 g CaF2

(Solution continued on the next slide)

Percentage Composition

100 = 51.33 % Ca2CaF g 78.08

Ca) g (40.08

2CaF g 78.08F) 2x(19.00g 100 = 48.67% F

Check: 51.33% + 48.67% = 100.00%

Empirical FormulaEmpirical Formula

The simplest ratio of atoms of the elements in a compound.

The empirical formula of C2H4 is CH2.Likewise, the empirical formula of C3H6 is CH2.All compounds with the general formula CnH2n

have the same empirical formula andtherefore the same percentage composition.

Empirical Formula

Write the empirical formulas of benzene, C6H6, and octane, C8H18.

Look for the simplest whole-number ratio of elements:

For C6H6, the 6/6 ratio can be reduced to 1/1: CH.

For C8H18, the 8/18 ratio can be divided by 2 on top and bottom to be reduced to 4/9: C4H9.

Find Empirical Formula

To find empirical formula, you need to find the ratio of atoms of the elements

ratio of atoms = ratio of moles of atoms

How to Find an Empirical Formula

1. Find the masses of different elements in a sample of the compound.

2. Convert the masses into moles of atoms.3. Determine the ratio of moles of atoms.4. Express the moles ratio as the smallest possible

ratio of integers.5. Write the empirical formula, using the number in the

integer ratio as the subscript in the formula.

Find Empirical Formula

What is the empirical formula of a compound that has 85.6% carbon, 14.4 % hydrogen?

Solution:It is usually helpful to organize the calculations in a

table with the following headings:

Mole FormulaEmpirical

Element Grams Moles Ratio Ratio Formula

Find Empirical Formula Mole Formula

EmpiricalElement Grams Moles Ratio Ratio Formula

C 85.6 1

7.13 1

H 14.4 2 CH2

14.3 2.01

C g/mol 12.01

C g 85.6 7.137.13

H g/mol 1.008H g 14.4 7.13

14.3

Find Empirical Formula

What is the empirical formula of a compound that analyzes as 20.0% carbon, 2.2% hydrogen, and 77.80% chlorine?

Mole FormulaEmpirical

Element Grams Moles Ratio Ratio Formula

C 20.0 1.67 1 3

H 2.2 2.2 1.3 4

Cl 77.8 2.19 1.31 4C3H4Cl4

Molecular Formula

The molecular formula of a compound can befound by determination of the number ofempirical formula units in the molecule.

How to Find the Molecular Formula

1. Determine the empirical formula of the compound.

2. Calculate the molar mass of the empirical formula unit.

3. Divide the molar mass of the compound by the molar mass of the empirical formula unit to get n, the number of empirical formula units per molecule.

Molecular Formula

What is the molecular formula of a compound with the empirical formula C2H5and a molar mass of 58.12 g/mol?

The molar mass of the empirical formula unit is2(12.01 g/mol C) + 5(1.008 g/mol H) =29.06 g/molThe number of empirical formula units per molecule is

(C2H5)2 = C4H10

2 = g/mol 29.06

g/mol 58.12

Find Molecular Formula

• An unknown compound is found to be 40.0% of carbon, 6.71% of hydrogen and the remainder is oxygen. The molar mass of the compound is 180.16 g/mol. Find the empirical and molecular formulas of the compound.

First Find Empirical Formula

Mole FormulaEmpirical

Element Grams Moles Ratio Ratio Formula

C 40.0 3.33 1 1

H 6.71 6.66 2 2

O 53.3 3.33 1 1 CH2O

Calculate Molar Mass/Empirical Formula Mass

The molar mass of the empirical formula unit is(12.01 g/mol C) + 1(1.008 g/mol H) + (16.00 g/mol O) =

30.03 g/molThe number of empirical formula units per

molecule is

(CH2O) 6 = C6H12O6

6 = g/mol 30.03

g/mol 180.16

Molecular Formula

Another way to find molecular formula is to consider one mole of the compound (180.16 g of compound). The numbers of moles are also numbers of atoms in the molecule.

The masses of carbon, hydrogen and oxygen are :40.0% x 180.16 g = 72.06 g of C6.71% x 180.16 g = 12.09 g of H53.3% x 180.16 g = 96.03 g of O

Molecular Formula

Element Grams Moles Molecular Formula

C 72.06 6

H 12.09 12

O 96.03 6 C6H12O6

Homework

7, 15, 21, 23, 43, 57, 61, 63, 65, 68, 74.