Relative Atomic Mass Relative Atomic Mass and the Moleand the Mole

Chapter 4 of Hienemann Textbook

Relative Isotopic MassRelative Isotopic Mass

Knowing the mass of an individual atom is not very useful because we usually work with large quantities of atoms.

The International Union of Physics and Chemistry decided that the relative atomic weights of elements would be calculated relative to the most common isotope of carbon: 12C.

Element Isotopes Relative Isotopic Mass

Abundance (%)

Hydrogen

1H 1.008 99.9862H 2.014 0.0143H 3.016 0.0001

Carbon

12C 12 EXACTLY 98.88813C 13.003 1.11214C 14.003 Approx. 10-10

Relative Atomic MassRelative Atomic Mass

A naturally occurring sample of an element contains the same isotopes in the same proportions, regardless of the source.

Therefore we use an average of the relative isotopic masses of the isotopes that make up an element the relative atomic mass.

Relative atomic mass has the symbol Ar

ExampleExampleImagine taking 100 atoms from a sample of

chlorine.There will be:• 75.80 atoms of 35Cl• 24.20 atoms of 37Cl

Average relative mass of one chlorine atom:= 34.969 x 75.8 + 36.966 x 24.20 100= 35.452

The relative atomic mass of chlorine is 35.45 Ar (Cl) = 35.45

Relative Molecular MassRelative Molecular MassThe relative molecular mass (Mr) of a compound is the

mass of one molecule of that substance relative to the mass of a 12C atom.

e.g. Oxygen

Mr(O2) = 2 x Ar (O)

= 2 x 16.0

= 32.0

Have a go!

Find the relative molecular mass of CO2

Mr(CO2) = Ar (C) + 2 x Ar (0) = 12.0 + 2 x 16.0 = 44.0

What is a mole?What is a mole?Since atoms are so small it is impossible to

measure out how many individual atoms of a particular element is needed in reactions.

Therefore, a unit called the mole was established which allows us to measure out an exact number of atoms.

One mole contains:

6.02 x 106.02 x 1023 23 entities entities (entities can be atoms, molecules etc.)

• One mole of sodium ions contains 6.02 x 1023

sodium ions• One mole of water contains 6.02 x 1023 water

molecules• One mole of doughnuts contains 6.02 x 1023

doughnuts

The weight of a mole depends on what substance is being measured.

e.g. 6.02 x 1023 peas weighs less than 6.02 x 1023

watermelons

The weight of 1 mole of atoms of an element is defined as the relative atomic mass of that element in grams.

e.g. What is the weight of 1 mole of Magnesium? M(Mg) = 24g mol-1

Atomic mass

M means molar mass

(mass of 1 mole)

mol-1 means per mole

Give it a go!Give it a go!

How much will 1 mole of Helium weigh?

M(He) = 4g mol-1

Molar MassMolar Mass

One mole of any substance (an element or a compound) will have a mass in grams equal to the sum of the relative atomic masses of all the atoms in the formula.

This is called the molar mass (M).

e.g. one mole of chlorine gas (Cl2) weighs:

M(Cl2) = 2 x Ar(Cl) = 2 x 35.5 = 71.0g

Give it a go!Give it a go!

Calculate the Molar mass of hydrogen chloride (HCl).

M(HCl) = Ar (H) + Ar (Cl) = 1.00 + 35.5 = 36.5g

Solving Problems with the MoleSolving Problems with the Mole

The number of moles of a substance =

Mass of substance

Molar mass of the substance

Using symbols this can be written as……

n = m

Mn is the symbol for number of moles

m is the symbol for mass (of the sample

M is the symbol for molar mass

An easy way to remember this equation…..An easy way to remember this equation…..

n M

m Cover up the corner of the triangle that symbolises the value you are looking for.

e.g. if you need to calculate the mass of a sample and you know the number of moles and the molar mass of the sample

Cover the m

equation: m = n x M

Give it a go! What is the equation if you’re looking for Molar mass?

M = m/n

Give it a go!Give it a go!

How much does 0.024 mole of Chlorine gas (Cl2) weigh?

1. Work out what you’re calculating: mass

2. Equation to use: m = n x M

3. Substitute in the values that you have been given:

m = 0.024 x (2 x Ar (Cl))

m = 0.024 x (2 x 35)

m = 0.024 x 70

m = 1.68

4. Remember the units: 1.68g