Relative Mass: Atomic, Molecular, and Formula (HSC SSCE Chemistry): Revision Notes

Relative Mass: Atomic, Molecular, and Formula

Introduction

In chemistry, we need to compare the masses of different atoms and molecules. Since atoms are extremely small (about 1-2 billion atoms fit along a 30 cm ruler edge), measuring their actual masses is very difficult.

Instead, chemists developed a system of relative masses - comparing the mass of one atom to a standard reference atom.

This system allows us to perform important calculations, such as:

• Determining how much of each reactant to use in a chemical reaction
• Calculating how much product a reaction will make
• Working out the composition of compounds

Relative atomic mass

Understanding the concept

Relative atomic mass (also called atomic weight) compares the mass of an atom to the mass of a carbon-12 atom, which is taken as exactly 12. This doesn't mean carbon-12 has a mass of 12 grams or 12 of any unit - it's simply assigned the number 12 as our reference point.

To understand this better, imagine comparing the masses of different atoms to carbon:

• A titanium atom is four times as heavy as a carbon atom, so titanium's relative atomic mass is $4 \times 12 = 48$
• Three helium atoms together equal one carbon atom in mass, so helium's relative atomic mass is $12 \div 3 = 4$

This visual representation shows how we compare atomic masses using carbon-12 as our standard.

Table of common atomic masses

Here are the relative atomic masses of some commonly encountered elements:

Element	Symbol	Atomic Mass	Element	Symbol	Atomic Mass
Aluminium	Al	26.98	Lead	Pb	207.2
Argon	Ar	39.95	Magnesium	Mg	24.31
Calcium	Ca	40.08	Mercury	Hg	200.6
Carbon	C	12.01	Nitrogen	N	14.01
Chlorine	Cl	35.45	Oxygen	O	16.00
Copper	Cu	63.55	Phosphorus	P	31.97
Fluorine	F	19.00	Potassium	K	39.10
Gold	Au	197.0	Silver	Ag	107.9
Helium	He	4.003	Sodium	Na	23.99
Hydrogen	H	1.008	Sulphur	S	32.07
Iodine	I	126.9	Uranium	U	238.0
Iron	Fe	55.85	Zinc	Zn	65.38

The isotope complication

Many elements exist as isotopes - atoms with the same number of protons but different numbers of neutrons. This means atoms of the same element can have different masses. For example, chlorine has two main isotopes: chlorine-35 and chlorine-37.

Because of isotopes, we need to refine our definition:

The relative atomic mass of an element is the average mass of the atoms present in the naturally occurring element, relative to the mass of a carbon-12 atom taken as exactly 12.

To calculate this average, we use the relative abundance (percentage) of each isotope. The formula is:

$\text{Average atomic mass} = \frac{(\text{abundance}_1 \times \text{mass}_1) + (\text{abundance}_2 \times \text{mass}_2) + ...}{100}$

Worked example: Chlorine isotopes

Relative molecular mass

Definition and calculation

For compounds made of molecules (covalent compounds), we use relative molecular mass (also called molecular weight). This is the mass of one molecule of the compound compared to a carbon-12 atom.

The calculation rule is simple:

The relative molecular mass equals the sum of the relative atomic masses of all atoms in the molecular formula.

Mathematically: $M = \sum(\text{number of atoms} \times A_{\text{element}})$

where $M$ represents relative molecular mass and $A$ represents relative atomic mass.

Simple examples

Let's calculate the relative molecular mass of some common compounds:

Water ($H_2O$):

• 2 hydrogen atoms: $2 \times 1.008 = 2.016$
• 1 oxygen atom: $1 \times 16.00 = 16.00$
• Total: 18.02

Nitrogen dioxide ($NO_2$):

• 1 nitrogen atom: $1 \times 14.01 = 14.01$
• 2 oxygen atoms: $2 \times 16.00 = 32.00$
• Total: 46.01

Sulphuric acid ($H_2SO_4$):

• 2 hydrogen atoms: $2 \times 1.008 = 2.016$
• 1 sulphur atom: $1 \times 32.07 = 32.07$
• 4 oxygen atoms: $4 \times 16.00 = 64.00$
• Total: 98.09

Worked example: Sucrose

Relative formula mass

When to use formula mass

Many compounds, especially ionic compounds, don't exist as separate molecules. Instead, they form crystal lattices - orderly arrangements of ions bound together.

For example, sodium chloride ($NaCl$) doesn't have individual $NaCl$ molecules.

For these compounds, we use relative formula mass instead of molecular mass.

Examples of formula mass

Sodium chloride ($NaCl$):

• 1 sodium atom: $22.99$
• 1 chlorine atom: $35.45$
• Total: 58.44

Calcium fluoride ($CaF_2$):

• 1 calcium atom: $40.08$
• 2 fluorine atoms: $2 \times 19.00 = 38.00$
• Total: 78.08

Worked example: Calcium phosphate

Remember!