1.
Explaining and how to calculate the relative atomic mass RAM or Ar of
an element
(a)
Introduction - defining relative atomic mass - carbon-12 scale
- Every atom has its own unique relative atomic
mass (RAM) 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
(amu = relative atomic mass unit).
- The relative atomic mass of an element takes into
account the different masses of the isotopes of that element and the
abundance of the isotopes in the naturally occurring element (meaning the
percentage of each isotope present).
- Relative atomic mass is defined and explained below,
and examples of how to calculate it from data.
-
The relative atomic
mass scale is now based on an isotope of carbon, namely, carbon-12,
nuclide symbol
,
which is given the arbitrary value of 12.0000 amu by international agreement.
- The unit 'amu' is now being replaced by a
lower case u, where u is the symbol for the unified atomic mass
unit.
- Therefore one atom of carbon, isotopic mass
12, equals 12 u, or,
- 1 u = 1/12th the
mass of one atom of the carbon-12 isotope.
- Note that for the standard nuclide notation,
, the top
left number is the mass number (12) and the bottom left number is the
atomic/proton number (6).
- Since the relative atomic mass of an element is now
based on the carbon-12 isotope
it can now be defined as ...
- ...
relative atomic mass equals the average mass of all the atoms in an element
compared to 1/12th the mass of a carbon-12 atom
(carbon-12 isotope).
- Examples are shown in the Periodic Table
diagram above.
- Note
- (i) Because of the presence of
neutrons in the nucleus, the relative atomic mass is usually at least double
the atomic/proton number because there are usually more neutrons than
protons in the nucleus (mass proton = 1, neutron = 1). Just scan the
periodic table above and examine the pairs of numbers.
- You should also notice that generally
speaking the numerical difference between the atomic/proton number and the
relative atomic mass tends to increase with increasing atomic number.
- This
has consequences for
nuclear
stability.
- (ii) For many calculation
purposes, relative atomic masses are usually quoted and used at this
academic level (GCSE/IGCSE/O level) to zero or one decimal place eg.
- hydrogen H = 1.008 or ~1; calcium
Ca = 40.08 or
~40.0; chlorine Cl = 35.45 ~35.5, copper Cu =
63.55 or ~63.5/64, silver Ag = 107.9 or ~108
etc.
- At Advanced level, values of relative
atomic masses may be quoted to one or two decimal places.
- Many atomic masses are known to an accuracy
of four decimal places, but for some elements, isotopic composition varies
depending on the mineralogical source, so four decimal places isn't
necessarily more accurate!
- Note that in the case of carbon, there are three
isotopes carbon-12 12C the most abundant and small amounts
of carbon-13 13C and carbon-14 14C. The average
calculated mass of the atoms compared to carbon 12 is 12.01, but for
most purposes at pre-university level, 12.0 is sufficient accuracy.
- In using the symbol Ar 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 relative atomic mass scale
is based on a specific isotope of carbon, carbon-12, 12C = 12.0000
units exactly, for most purposes C = 12 is used for simplicity.
- For
example
hydrogen-1,
hydrogen-2, and
hydrogen-3, are
the nuclide notation for 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!
-
See
also GCSE/IGCSE/AS Atomic Structure Notes
- Therefore, a stricter definition of
relative atomic mass (Ar) is that it equals the average mass of all the
isotopic atoms present in the element compared to 1/12th
the mass of a carbon-12 atom.
- AND, the relative isotopic mass of carbon-12 is
assigned a numerical value of 12.0000.
- So,
in calculating relative atomic mass you
must take 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.
- For approximate calculations of relative
atomic mass you can just use the mass numbers of the isotopes, which are
obviously all integers ('whole numbers'!) e.g. in the two calculations
below.
- To the nearest whole number, isotopic
mass = mass number for a specific isotope.
- If an element only has one isotope, relative
atomic mass = relative mass of this isotope.
- A good example is fluorine.
- All fluorine
atoms have a mass of 19 (19F), therefore its
relative atomic mass is 19 and no calculation is needed.
Above is typical periodic table used in GCSE science-chemistry specifications
and I've 'usually' used these values in my exemplar calculations to cover most
syllabuses
TOP OF PAGE
and sub-index
(b) Examples of relative atomic mass calculations
for GCSE 9-1/IGCSE/AS/A level chemistry students
How do I calculate relative atomic mass?
You
can calculate relative atomic mass from isotopic abundances
- For accurate chemical calculations relative atomic
mass must be used and not an individual mass number.
- Therefore relative atomic mass takes into account all
the different 'stable' isotopes of an element which are naturally present.
- The relative atomic mass is the average mass and is
quite easily calculated from the percentage composition (% abundance).
- The presence of isotopes accounts for why some
relative atomic masses are not even close to a whole number.
- Some relative atomic masses are nearly whole numbers
due to coincidence of % isotopes, others because one isotope might dominate
the composition with only tiny amounts of lighter or heavier isotopes.
-
Example 1.1 Calculating the relative atomic mass of bromine
and

- bromine consists of
two isotopes, 50% 79Br and 50% 81Br, calculate the Ar of bromine
from the mass numbers (top left numbers).
- Think of the calculation in terms of '100 atoms'
- Ar = [ (50 x 79) + (50
x 81) ] /100 = 80
- So the relative atomic mass of
bromine is 80 or RAM or Ar(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
bromine-79 and bromine-81.
- The element bromine is the only case I know where averaging
the isotopic masses actually works! so beware!
- -
-
Example 1.2 Calculating the relative atomic mass of chlorine
based on the
and
isotopes
- Chlorine consists of
two isotopes, 75% chlorine-35 and 25% chlorine-37, so using
these two mass numbers ...
- ... again 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 Ar(Cl) =
35.5
- Note: 35Cl and 37Cl 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: Calculating the relative atomic
mass of copper from its isotopic composition (isotope abundance)
- Naturally occurring copper consists of 69.2% copper-63
(63Cu) and 30.8% copper-65 (65Cu)
- Still think in terms of 100 atoms and don't be put
off by decimal fractions, it still works out correctly because 69.2 + 30.8 =
100!
- average mass = relative atomic mass of copper
= {(63 x 69.2) + (65 x 30.8)} / 100 =
63.6
- -
- Example 1.4: Silver atoms consist of 51.4% of
the isotope 107Ag and 48.6% of the isotope 109Ag
- Calculate the relative atomic mass of silver.
-
|
|
(51.4 x 107) +
(48.6 x 109) |
5499.8 + 5297.4 |
|
Ar(Ag)
|
= |
-------------------------------------- |
=
--------------------------- |
= 108.0 |
|
|
100 |
100 |
|
- The relative atomic mass of silver is 108.0 (to 1
decimal place)
- -
- Example 1.5: Europium atoms consist of 47.8%
Eu-151 and 52.2% of Eu-153
- Calculate the relative atomic mass of europium.
-
|
|
(47.8 x 151) +
(52.2 x 153) |
7217.8 + 7986.6 |
|
Ar(Eu)
|
= |
-------------------------------------- |
=
--------------------------- |
= 152.0 |
|
|
100 |
100 |
|
- The relative atomic mass of europium is 152.0 (to 1
decimal place)
- -
- Example 1.6: Atoms of the element silicon
consist of 92.2% silicon-28, 4.7% silicon-29 and 3.1% of silicon-30.
- Calculate the relative atomic mass of silicon.
-
|
|
(92.2 x 28) + (4.7
x 29) + (3.1 x 30) |
2581.6 + 136.3 + 93.0 |
|
Ar(Si)
|
= |
-------------------------------------------------- |
=
-------------------------------- |
= 28.1 |
|
|
100 |
100 |
|
- The relative atomic mass of silicon is 28.1 (to 1
decimal place or 3 significant figures)
- -
- See below and
mass Spectrometer and isotope analysis
on the GCSE-Advanced A Level (basic) Atomic Structure Notes, with further
relative atomic mass calculations.
(c) Examples for Advanced A Level Chemistry students only
How to calculate relative atomic mass with accurate relative
isotopic masses
Using data from modern very accurate mass spectrometers
(1)
Very accurate calculation of relative atomic mass
(need to know and define what relative isotopic mass is)
Relative
isotopic mass
is defined as the accurate mass of a single isotope of
an element compared to 1/12th the mass of a
carbon-12 atom e.g. the accurate relative isotopic mass of the cobalt-5
is 58.9332
This definition of relative isotopic mass is
a completely different from the definition of relative atomic mass, except
both are based on the same international standard of atomic mass i.e. 1 unit
(1 u)
= 1/12th the mass of a carbon-12 isotope (12C).
If we were to redo the calculation of the
relative atomic mass of chlorine (example
1.1 above), which is quite adequate for GCSE purposes (and maybe A level too),
but more accurately at A
level, we might do ....
chlorine is 75.77% 35Cl of
isotopic mass 34.9689 and 24.23% 37Cl of isotopic mass 36.9658
so Ar(Cl) = [(75.77 x
34.9689) + (24.23 x 36.9658)] / 100
=
35.4527
(but 35.5 is usually ok in calculations pre-university!)
See also
Mass Spectrometer and isotope analysis
on the GCSE/A level Atomic Structure Notes, with further RAM calculations.
(2)
Calculations of % composition of isotopes
It is possible to do the reverse
of a relative atomic mass calculation if you know the Ar and
which isotopes are present.
It involves a little bit of
arithmetical algebra.
The Ar of boron is
10.81 and consists of only two isotopes, boron-10 and boron-11
The relative atomic mass of
boron was obtained accurately in the past from chemical analysis of reacting
masses but now
mass spectrometers can sort
out all of the isotopes present and their relative abundance.
If you let X = % of boron
10, then 100-X is equal to % of boron-11
Therefore Ar(B) = (X
x 10) + [(100-X) 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% 10B and
81% 11B
(the
data books actually quote 18.7 and 81.3, but we didn't use the very accurate
relative isotopic masses mentioned above!)
TOP OF PAGE
and sub-index
On other pages
on
Atomic structure and
Relative Formula
Mass
Self-assessment Quizzes on relative atomic mass
type in answer
QUIZ or
multiple choice
QUIZ
APPENDIX 1. A typical periodic table used in pre-university examinations
Above is typical periodic table used in GCSE science-chemistry specifications in
doing chemical calculations,
and I've 'usually' used these values in my exemplar calculations to cover most
syllabuses
TOP OF PAGE
and sub-index
(d)
APPENDIX 2. Table of relative atomic masses for elements 1 to 92
Notes on
the relative atomic mass data:
(i) The list of relative atomic mass are in
alphabetical order by element name, together with chemical symbol and
proton/atomic number from 1 to 92.
(ii) The relative atomic masses are quoted to two decimal
places, though it is essential to be aware that values in pre-university
examinations might be rounded to the nearest integer or one decimal place.
(iii) Trans-uranium elements have been eliminated because
their isotopic composition varies depending on the source e.g. cyclotron,
nuclear reactor etc. AND all their isotopes are highly radioactive and most are
very unstable (so your relative atomic mass changes all the time!)
(iv) * radioactive, mass number of most stable isotope
quoted
Chemical Symbol
|
Element name
|
Atomic No. Z
|
Relative atomic mass |
Ac |
Actinium |
89 |
227.03 |
Al |
Aluminium |
13 |
26.98 |
Sb |
Antimony |
51 |
121.75 |
Ar |
Argon |
18 |
39.95 |
As |
Arsenic |
33 |
74.92 |
At |
Astatine |
85 |
210
* |
Ba |
Barium |
56 |
137.33 |
Be |
Beryllium |
4 |
9.01 |
Bi |
Bismuth |
83 |
208.98 |
B |
Boron |
5 |
10.81 |
Br |
Bromine |
35 |
79.90 |
Cd |
Cadmium |
48 |
112.41 |
Cs |
Caesium |
55 |
132.91 |
Ca |
Calcium |
20 |
40.08 |
C |
Carbon |
6 |
12.01 |
Ce |
Cerium |
58 |
140.12 |
Cl |
Chlorine |
17 |
35.45 |
Cr |
Chromium |
24 |
52.00 |
Co |
Cobalt |
27 |
58.93 |
Cu |
Copper |
29 |
63.55 |
Dy |
Dysprosium |
66 |
162.50 |
Er |
Erbium |
68 |
167.26 |
Eu |
Europium |
63 |
151.97 |
F |
Fluorine |
9 |
19.00 |
Fr |
Francium |
87 |
223
* |
Gd |
Gadolinium |
64 |
157.25 |
Ga |
Gallium |
31 |
69.72 |
Ge |
Germanium |
32 |
72.60 |
Au |
Gold |
79 |
196.97 |
Hf |
Hafnium |
72 |
178.49 |
He |
Helium |
2 |
4.00 |
Ho |
Holmium |
67 |
164.93 |
H |
Hydrogen |
1 |
1.01 |
In |
Indium |
49 |
114.82 |
I |
Iodine |
53 |
126.90 |
Ir |
Iridium |
77 |
192.22 |
Fe |
Iron |
26 |
55.85 |
Kr |
Krypton |
36 |
83.80 |
La |
Lanthanum |
57 |
138.91 |
Pb |
Lead |
82 |
207.20 |
Li |
Lithium |
3 |
6.94 |
Lu |
Lutetium |
71 |
174.97 |
Mg |
Magnesium |
12 |
24.31 |
Mn |
Manganese |
25 |
54.94 |
Hg |
Mercury |
80 |
200.59 |
|
|
|
|
|
Chemical Symbol
|
Element name
|
Atomic No.
Z
|
Relative atomic mass |
Mo |
Molybdenum |
42 |
95.94 |
Nd |
Neodymium |
60 |
144.24 |
Ne |
Neon |
10 |
20.18 |
Ni |
Nickel |
28 |
58.69 |
Nb |
Niobium |
41 |
92.91 |
N |
Nitrogen |
7 |
14.01 |
Os |
Osmium |
76 |
190.20 |
O |
Oxygen |
8 |
16.00 |
Pd |
Palladium |
46 |
106.42 |
P |
Phosphorus |
15 |
30.97 |
Pt |
Platinum |
78 |
195.08 |
Po |
Polonium |
84 |
209
* |
K |
Potassium |
19 |
39.10 |
Pr |
Praseodymium |
59 |
140.91 |
Pm |
Promethium |
61 |
145
* |
Pa |
Protactinium |
91 |
231.04 |
Ra |
Radium |
88 |
226.03 |
Rn |
Radon |
86 |
222
* |
Re |
Rhenium |
75 |
186.21 |
Rh |
Rhodium |
45 |
102.91 |
Rb |
Rubidium |
37 |
85.47 |
Ru |
Ruthenium |
44 |
101.07 |
Sm |
Samarium |
62 |
150.36 |
Sc |
Scandium |
21 |
44.96 |
Se |
Selenium |
34 |
78.96 |
Si |
Silicon |
14 |
28.09 |
Ag |
Silver |
47 |
107.87 |
Na |
Sodium |
11 |
23.00 |
Sr |
Strontium |
38 |
87.62 |
S |
Sulfur |
16 |
32.07 |
Ta |
Tantalum |
73 |
180.95 |
Tc |
Technetium |
43 |
98.91 |
Te |
Tellurium |
52 |
127.60 |
Tb |
Terbium |
65 |
158.93 |
Tl |
Thallium |
81 |
204.38 |
Th |
Thorium |
90 |
232.04 |
Tm |
Thulium |
69 |
168.93 |
Sn |
Tin |
50 |
118.71 |
Ti |
Titanium |
22 |
47.88 |
W |
Tungsten |
74 |
183.85 |
U |
Uranium |
92 |
238.03 |
V |
Vanadium |
23 |
50.94 |
Xe |
Xenon |
54 |
131.29 |
Yb |
Ytterbium |
70 |
173.04 |
Y |
Yttrium |
39 |
88.91 |
Zn |
Zinc |
30 |
65.39 |
Zr |
Zirconium |
40 |
91.22 |
|
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 Gay-Lussac's Law (ratio of gaseous
reactants-products)
-
Molarity, volumes and solution
concentrations (and diagrams of apparatus)
-
How to do acid-alkali
titration calculations, diagrams of apparatus, details of procedures
-
Electrolysis products calculations (negative cathode and positive anode products)
-
Other calculations
e.g. % purity, % percentage & theoretical yield, 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 & half-life calculations including
dating materials
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are unofficial. |
Alphabetical order of the
elements of the periodic table symbol name atomic number: relative atomic
mass of Ac Actinium 89, relative atomic mass of Al Aluminium 13, relative
atomic mass of Sb Antimony 51, relative atomic mass of Ar Argon 18, relative
atomic mass of As Arsenic 33, relative atomic mass of At Astatine 85,
relative atomic mass of Ba Barium 56, relative atomic mass of Be Beryllium 4,
relative atomic mass of Bi Bismuth 83, relative atomic mass of B Boron 5,
relative atomic mass of Br Bromine 35, relative atomic mass of Cd Cadmium 48,
relative atomic mass of Cs Caesium 55, relative atomic mass of Ca Calcium 20,
relative atomic mass of C Carbon 6, relative atomic mass of Ce Cerium |
58, relative atomic mass of Cl Chlorine 17, relative atomic mass of Cr Chromium 24,
relative atomic mass of Co Cobalt 27, relative atomic mass of Cu Copper 29,
relative atomic mass of Dy Dysprosium 66, relative atomic mass of Er Erbium 68,
relative atomic mass of Eu Europium 63, relative atomic mass of F Fluorine 9,
relative atomic mass of Fr Francium 87, relative atomic mass of Gd Gadolinium 64,
relative atomic mass of Ga Gallium 31, relative atomic mass of Ge Germanium 32,
relative atomic mass of Au Gold 79, relative atomic mass of Hf Hafnium 72,
relative atomic mass of He Helium 2, relative atomic mass of Ho Holmium 67,
relative atomic mass of H Hydrogen 1, relative atomic mass of In Indium 49,
relative atomic mass of I Iodine 53, relative atomic mass of Ir Iridium 77,
relative atomic mass of Fe Iron 26, relative atomic mass of Kr Krypton 36,
relative atomic mass of La Lanthanum 57, relative atomic mass of Pb Lead 82,
relative atomic mass of Li Lithium 3, relative atomic mass of Lu Lutetium 71,
relative atomic mass of Mg Magnesium 12, relative atomic mass of Mn Manganese 25,
relative atomic mass of Hg
Mercury 80, relative atomic mass of Mo Molybdenum 42, relative atomic
mass of Nd Neodymium 60, relative atomic mass of Ne Neon 10, relative atomic
mass of Ni Nickel 28, relative atomic mass of Nb Niobium 41, relative atomic
mass of N Nitrogen 7, relative atomic mass of Os Osmium 76, relative atomic
mass of O Oxygen 8, relative atomic mass of Pd Palladium 46, relative atomic
mass of P Phosphorus 15, relative atomic mass of Pt Platinum 78, relative
atomic mass of Po Polonium 84, relative atomic mass of K Potassium 19,
relative atomic mass of Pr Praseodymium 59, relative atomic mass of Pm Promethium 61,
relative atomic mass of Pa Protactinium 91, relative atomic mass of Ra Radium 88,
relative atomic mass of Rn Radon 86, relative atomic mass of Re Rhenium 75,
relative atomic mass of Rh Rhodium 45, relative atomic mass of Rb Rubidium 37,
relative atomic mass of Ru Ruthenium 44, relative atomic mass of Sm Samarium 62,
relative atomic mass of Sc Scandium 21, relative atomic mass of Se Selenium 34,
relative atomic mass of Si Silicon 14, relative atomic mass of Ag Silver 47,
relative atomic mass of Na Sodium 11, relative atomic mass of Sr Strontium 38,
relative atomic mass of S Sulfur 16, relative atomic mass of Ta Tantalum 73,
relative atomic mass of Tc Technetium 43, relative atomic mass of Te Tellurium 52,
relative atomic mass of Tb Terbium 65, relative atomic mass of Tl Thallium 81,
relative atomic mass of Th Thorium 90, relative atomic mass of Tm Thulium 69,
relative atomic mass of Sn Tin 50, relative atomic mass of Ti Titanium 22,
relative atomic mass of W Tungsten 74, relative atomic mass of U Uranium 92,
relative atomic mass of V Vanadium 23, relative atomic mass of Xe Xenon 54,
relative atomic mass of Yb Ytterbium 70, relative atomic mass of Y Yttrium 39,
relative atomic mass of Zn Zinc 30, relative atomic mass of Zr Zirconium 40