1.
Explaining and how to calculate the relative atomic mass RAM or A_{r} of
an element
How to calculate relative atomic mass
Introduction
 Every atom has its own unique atomic
mass based on a standard comparison or relative scale
e.g. it has been based on hydrogen H = 1 amu and oxygen O = 16 amu in the past.

The relative atomic
mass scale is now based on an isotope of carbon, carbon12,
,
which is given the value of 12.0000 amu.
 In this standard nuclide notation, the top
left number is the mass number and the bottom left number is the
atomic/proton number.
 In other words the relative atomic mass
of an element is now based on the arbitrary value of the carbon12 isotope
being assigned a mass of 12.0000 by international agreement!
 Examples are shown in the Periodic Table
diagram above.
 Note that because of the presence of
neutrons in the nucleus, the relative atomic mass is usually at least double
the atomic/proton number because there usually at the number of neutrons as
protons in the nucleus (mass proton = 1, neutron = 1).
 Also note, that for many calculations
purposes, relative atomic masses are usually quoted and used at this
academic level to one decimal place eg.
 hydrogen H = 1.0 or ~1, calcium Ca= 40.0 or
~40, chlorine Cl = 35.5, copper Cu = 63.6 or ~64, silver Ag 107.9 or ~108.
 Sometimes at A level, values of relative
atomic masses to two decimal places may be quoted.
 In using the symbol A_{r} for
RAM, you should bear in mind that the letter A on its own usually means the mass number of a particular isotope
and amu is the acronym shorthand for atomic mass units.
 However there are complications due to isotopes and
so very accurate atomic masses
are never whole integer numbers.
 Isotopes are atoms of the same element with different
masses due to different numbers of neutrons. The very accurate atomic mass scale
is based on a specific isotope of carbon, carbon12, ^{12}C = 12.0000
units exactly, for most purposes C = 12 is used for simplicity.
 For
example
,
and
are
the three isotopes of hydrogen, though the vast majority of hydrogen atoms have
a mass of 1. When their accurate isotopic masses, and their % abundance are
taken into account the average accurate relative mass for hydrogen =
1.008, but for most purposes H = 1 is good enough!
 The strict definition of relative
atomic mass (A_{r}) is that it equals the average mass of all the
isotopic atoms present in the element compared to ^{1}/_{12}th
the mass of a carbon12 atom.
 So, you are taking into account the
different isotopic masses of the same elements, but also their %
abundance in the element.
 Therefore you need to know the
percentage (%) of each isotope of an element in order to accurately
calculate the element's relative atomic mass.
Examples of relative atomic mass calculations
for GCSE/IGCSE/AS level students
How do I calculate relative atomic mass?

and
 Relative Atomic Mass Calculation Example 1.1
BROMINE
 bromine consists of
50% ^{79}Br and 50% ^{81}Br, calculate the Ar of bromine.
 A_{r} = [ (50 x 79) + (50
x 81) ] /100 = 80
 So the relative atomic mass of
bromine is 80 or RAM or A_{r}(Br) = 80
 Note the full working shown. Yes, ok, you can do it in your head BUT many students ignore the %'s and
just average all the isotopic masses (mass numbers) given, in this case
bromine79 and bromine81.

and
 Relative Atomic Mass Calculation Example 1.2
CHLORINE
 chlorine consists of
75% chlorine35 and 25% chlorine37.
 Think of the data based on 100
atoms, so 75 have a mass of 35 and 25 atoms have a mass of 37.
 The average mass = [ (75 x 35) +
(25 x 37) ] / 100 = 35.5
 So the relative atomic mass of
chlorine is 35.5 or RAM or A_{r}(Cl) = 35.5
 Note: ^{35}Cl and ^{37}Cl are the most common isotopes of chlorine, but, there
are tiny percentages of other chlorine isotopes which are usually
ignored at GCSE/IGCSE and Advanced GCE AS/A2 A level.
 Example 1.3:
The mass number for any isotope
is the sum of the protons and neutrons in
the nucleus, and is always an integer i.e. a whole number.
Examples for Advanced Level Chemistry students only
How to calculate relative atomic mass with accurate relative
isotopic masses
(a)
Calculation of relative atomic mass
Relative
isotopic mass
= the accurate mass of a single isotope of
an element compared to ^{1}/_{12}th the mass of a
carbon12 atom e.g. the accurate mass of
is 58.9332 !
If we were to redo the chlorine example
1.1 above, which is quite adequate for GCSE purposes, more accurately at A
level, we would do ....
chlorine is 75.77% ^{35}Cl of
isotopic mass 34.9689 and 24.23% ^{37}Cl of isotopic mass 36.9658
so A_{r}(Cl) = [(75.77 x
34.9689) + (24.23 x 36.9658)] / 100 =
35.4527 (but 35.5 is usually ok in calculations preuniversity!)
See also
Mass Spectrometer and isotope analysis
on the GCSEAS(basic) Atomic Structure Notes, with further RAM calculations.
(b)
Calculations of % composition of isotopes
It is possible to do the reverse
of a relative atomic mass calculation if you know the A_{r} and
which isotopes are present.
It involves a little bit of
arithmetical algebra.
The A_{r} of boron is
10.81 and consists of only two isotopes, boron10 and boron11
The relative atomic mass of
boron was obtained accurately in the past and
mass spectrometers can sort
out the isotopes present.
If you let X = % of boron
10, then 100X is equal to % of boron11
Therefore A_{r}(B) = (X
x 10) + [(100X) x 11)] / 100 = 10.81
so, 10X 11X +1100
=100 x 10.81
X + 1100 = 1081, 1100 
1081 = X (change sides change sign!)
therefore X = 19
so naturally occurring boron
consists of 19% ^{10}B and 81% ^{11}B (the
data books quote 18.7 and 81.3)
Selfassessment Quizzes
[ram]
type in answer
Honly or multiple choice
Honly
OTHER CALCULATION PAGES

What is relative atomic mass?,
relative isotopic mass & calculating relative atomic mass
(this page)

Calculating relative
formula/molecular mass of a compound or element molecule

Law of Conservation of Mass and simple reacting mass calculations

Composition by percentage mass of elements
in a compound

Empirical formula and formula mass of a compound from reacting masses
(easy start, not using moles)

Reacting mass ratio calculations of reactants and products
from equations
(NOT using
moles) and brief mention of actual percent % yield and theoretical yield,
atom economy
and formula mass determination

Introducing moles: The connection between moles, mass and formula mass  the basis of reacting mole ratio calculations
(relating reacting masses and formula
mass)

Using
moles to calculate empirical formula and deduce molecular formula of a compound/molecule
(starting with reacting masses or % composition)

Moles and the molar volume of a gas, Avogadro's Law

Reacting gas volume
ratios, Avogadro's Law
and GayLussac's Law (ratio of gaseous
reactantsproducts)

Molarity, volumes and solution
concentrations (and diagrams of apparatus)

How to
do volumetric titration calculations e.g. acidalkali titrations
(and diagrams of apparatus)

Electrolysis products calculations (negative cathode and positive anode products)

Other calculations
e.g. % purity, % percentage & theoretical yield, volumetric titration
apparatus, dilution of solutions
(and diagrams of apparatus), water of crystallisation, quantity of reactants
required, atom economy

Energy transfers in physical/chemical changes,
exothermic/endothermic reactions

Gas calculations involving PVT relationships,
Boyle's and Charles Laws

Radioactivity & halflife calculations including
dating materials
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