Chapter 3: Chemical Formulae and Equations

3.1 Relative Atomic Mass and

Relative Molecular Mass

Mass of Nitrogen

Relative atomic mass, Ar

The mass of an atom is too small to measure.

We can only measure the mass of an atom by comparing its mass to the mass of another atom.

Relative atomic mass, Ar

Relative atomic mass, Ar

Relative atomic mass, Ar

What is relative atomic mass???

The mass of an atom when compared to a standard atom is known as its relative atomic mass (Ar). It has no unit.

Relative atomic mass, Ar

Since hydrogen atom is the lightest atom, chemists first started comparing masses of other atoms with the mass of one hydrogen atom.

We can consider the relative atomic mass of hydrogen to be 1.

We can compare the mass of other atom to the mass of the hydrogen atom.

An atom of carbon-12 is 12 times heavier than one atom of hydrogen.

The relative atomic mass, Ar of one carbon-12 atom is 12.

Relative atomic mass, Ar

Relative atomic mass, Ar

This method, however is not always convenient. Do you know why?

Hydrogen is a gas. Therefore it is difficult to measure its mass.

It has a number of isotopes with different masses. Thus it is difficult to measure exactly.

Oxygen was then used as a standard to compare the masses of atoms, however, this also posed some problems.

Relative atomic mass, Ar

Relative atomic mass, Ar

At present carbon-12 is used as the standard of comparison because

It is solid and can be easily handled, Its mass can be more easily measured with

a mass spectrometer. Carbon-12 is easily found as its compounds

are abundant. Carbon-12 isotopes is assigned a mass of

exactly 12 units.

Relative atomic mass, Ar

The relative atomic mass of an element is the average mass of one atom of the element when compared with of the mass of a carbon -12.

12

1

Relative atomic mass, Ar

Examples

An atom of oxygen is 16 times heavier than of the mass of an atom of carbon-12. Its relative atomic mass is 16.

An atom of sodium is 23 times heavier than of the mass of an atom of carbon-12. Its relative atomic mass is 23.

12

1

12

1

Relative atomic mass, Ar

Since relative atomic mass compares the masses of atoms , it does not have any units.

The relative atomic mass is also related to the number of protons and neutrons in the atom.

The symbols, relative mass and the charge of subatomic particles

Subatomic particle

Symbol Relative mass

Charge

Proton p 1 +1

Electron e -1

Neutron n 1 0

1840

1

Relative atomic mass, Ar

If more than one isotope of element is present, the atomic mass is calculated by taking the average of the relative atomic masses of different isotopes.

Examples of isotopes of some elementsElement Proton

numberNucleon number

Number of protons

Number of neutrons

Percentage abundance

Hydrogen,

Deuterium,

Tritium,

1

1

1

1

2

3

1

1

1

0

1

2

99.985%

0.015%

Man-made isotope

Carbon-12,

Carbon-13,

Carbon-14,

6

6

6

12

13

14

6

6

6

6

7

8

98.1%

1.1%

0.8 %

Chlorine-35,

Chlorine-37,

17

17

35

37

17

17

18

20

75.5%

24.5%

Oxygen-16,

Oxygen-17,

Oxygen-18,

8

8

8

16

17

18

8

8

8

8

9

10

99.757%

0.038%

0.205%

H11

H21

H31

C126

C136

C146

Cl3517

Cl3717

O168

O178

O188

Example How many times heavier is a krypton

atom compared to a helium atom?

Solution:

mass of a krypton atom = Ar of krypton

mass of a helium atom Ar of helium

= 84

4

= 21 times

Example Calculate how many times heavier are 3

calcium atoms compared to 5 carbon atoms.

Solution:

mass of 3 calcium atoms = 3 x Ar of calcium

mass of 5 carbon atoms 5 x Ar of carbon

= 3 x 40

5 x 12

= 21 times

Relative Molecular Mass, Mr

The idea of relative atomic mass can be extended to molecules.

The Relative molecular mass of a molecule is the average mass of the molecule when compared with of the mass of one atom carbon-12.

Example: Relative Molecular Mass of CO2

is 44. This means that the molecule of carbon

dioxide is 44 times heavier than of one atom of carbon-12

12

1

12

1

Relative Molecular Mass, Mr

Relative Molecular Mass, Mr

Since a molecule is made up of atoms, the relative molecular mass of a molecule can be calculated by adding up the relative atomic masses of all the atom present in the molecule.

Calculation of Relative Molecular Mass Step 1: Determine the molecular formula. Step 2: Find the relative atomic mass of each element in the molecule. Step 3: Add up all the relative atomic masses of the element or elements.

Relative Molecular Mass, Mr

Molecule Molecular formula

Relative molecular mass

Chlorine Cl2 2 x 35.5 = 72

Nitrogen N2 2 x 14 = 28

Ammonia NH3 14 + (3 x 1) = 17

Ethanol C2H5OH (2 x 12) + (5 x 1) + 16 + 1 = 46

Carbon dioxide

CO2 12 + (2 x 16) = 44

Relative formula masses

Some substances consists of ions and not molecules.

For these ionic substances, the relative formula masses are used in place of relative molecular masses.

Relative formula masses

Ionic substance

Ionic formula

Relative formula mass

Sodium chloride

NaCl 23 + 35.5 = 58.5

Hydrated magnesium sulphate

MgSO4.7H2O

24 + 32 + (4x 16) + 7(2 + 16) = 246

Calcium oxide

CaO 40 + 16 = 56

Example The relative formula mass of a compound with the

formula Y2SO4 is 142. Calculate the relative atomic mass of element Y.

[ Relative atomic mass: O, 16; S,32] Solution: Let the relative atomic mass of element Y=y. Given

that the relative formula mass of Y2SO4 =142 Therefore, 2y + 32 + 4(16) = 142

2y + 96 = 142

2y = 142 – 96

2y = 46

y = 23

So, the relative atomic mass of element Y is 23.