Atomic Masses

Atomic Masses
Chemist in the 1800's realized that
it would be impossible to ever
measure the mass of an atom, so
they decided to assign Carbon
atom the mass of 12 units. All
other elements were assigned
mass relative to it.
Carbon-12 = 12 amu

Average Atomic Mass
• weighted average of all isotopes
• on the Periodic Table
• round to two decimal places
Avg.
Atomic
Mass
=
(mass)(%) + (mass)(%)
(% in decimal form)

q Average Atomic Mass (AAM)
This is the weighted average mass of all atoms of
an element, measured in a.m.u.
For an element with
isotopes A, B, etc.:
AAM = Mass A (% A) + Mass B (% B) + …
% abundance
(use the decimal form of the %;
e.g., use 0.253 for 25.3%)

Lithium has two isotopes.
Li-6 atoms have mass 6.015 amu;
Li-7 atoms have mass 7.016 amu.
Li-6 makes up 7.5% of all Li atoms.
Find AAM of Li.
Li batteries
AAM = Mass A (% A) + Mass B (% B)
AAM = 6.015 amu (0.075) + 7.016 amu
(0.925)
AAM = 0.451 amu + 6.490 amu
AAM = 6.94 amu
** Decimal number on Table refers to…
AAM (in amu).
1 average atom

Average Atomic Mass
• EX: Calculate the avg. atomic mass of oxygen if its
abundance in nature is 99.76% Oxygen-16, 0.04%
Oxygen-17, and 0.20% Oxygen-18.
AAM = Mass A (% A) + Mass B (% B) + Mass C (%C)
Avg.
Atomic
Mass
=
(15.995)(.9976) + (16.999)(.00038) + (17.999)(.0020)
= 16.00 amu

100
90
Mass spectrum of chlorine. Elemental chlorine (Cl 2 ) contains
only two isotopes: 34.97 amu (75.53%) and 36.97 (24.47%)
17
Cl
35.4594
Abundance
80
70
60
50
40
30
20
10
Cl-35
AAM = (34.97 amu)(0.7553) + (36.97 amu)(0.2447)
AAM = (26.412841 amu) + (9.046559 amu)
AAM = 35.4594 amu
Cl-37
0
34 35 36 37
Mass

Mass Spectrophotometer
magnetic field
heaviest
ions
stream
of ions of
different
masses
lightest
ions
electron
beam
gas
Dorin, Demmin, Gabel, Chemistry The Study of Matter 3rd Edition, page 138

Mass Spectrometry
Photographic plate
198 200 202
196 199 201
- +
Mass spectrum of mercury vapor
Stream of positive ions
Hill, Petrucci, General Chemistry An Integrated Approach 1999, page 320

Mass Spectrum for Mercury
(The photographic record has been converted to a scale of relative number of atoms)
The percent natural abundances
for mercury isotopes are:
198 200 202
Relative number of atoms
30
25
20
15
10
Hg-196 0.146%
Hg-198 10.02%
Hg-199 16.84%
Hg-200 23.13%
Hg-201 13.22%
Hg-202 29.80%
Hg-204 6.85%
196 199 201 204
Mass spectrum of mercury vapor
5
196 197 198 199 200 201 202 203 204
Mass number

The percent natural abundances
for mercury isotopes are:
A
B
C
D
E
F
G
Hg-196 0.146%
Hg-198 10.02%
Hg-199 16.84%
Hg-200 23.13%
Hg-201 13.22%
Hg-202 29.80%
Hg-204 6.85%
Hg
200.59
80
AAM = (massA)(%A) +(massB)(%B) + (massC)(%C) + (massD)(%D) + (massE)(%E) +
(mass F) (% F)+ (mass G)(% G)
AAM = (196)(0.00146) + (198)(0.1002) + (199)(0.1684) + (200)(0.2313) + (201)(0.1322) + (202) (0.2980) + (204)(0.0685)
AAM = 0.28616 + 19.8396 + 33.5116 + 46.2600 + 26.5722 + 60.1960 + 13.974
AAM = 200.63956 amu

Isotope
U-234
U-235
U-238
Mass
%
abundance
234.04 amu 0.005%
235.04 amu 0.720%
238.05 amu
99.275%
AAM = M A (% A) + M B (% B) + M C (% C)
AAM = 234.04 (0.00005) + 235.04 (0.00720) + 238.05 (.99275)
AAM = 0.011702 + 1.692288 + 236.32491
AAM = 238.0289 amu

Isotope
Si-28
Si-29
Si-30
Mass
%
abundance
27.98 amu 92.23%
28.98 amu 4.67%
3.10%
AAM = M A (% A) + M B (% B) + M C (% C)
28.086 = 27.98 (0.9223) + 28.98 (0.0467) + X (0.031)
28.086 = 25.806 + 1.353 + 0.031X
28.086 = 27.159 + 0.031X
0.927 = 0.031X
0.031
X = M Si-30 = 29.90 amu
0.031

Hyphen Notation
• Put the mass number after the name of
the element
• Carbon- 12
• Uranium- 235
• Chlorine- 35
• Hydrogen- 2

Atomic Mass
Calculate the atomic mass of copper if copper has two isotopes.
69.1% has a mass of 62.93 amu and the rest has a mass of
64.93 amu.
Isotope
Percent
Abundance
Mass
Cu-63 69.1 62.93
Cu-65 30.9 64.93
AAM = Mass A (%A) + Mass B (%B)
AAM = 43.48463 + 20.06337
AAM = 63.548 amu
43.48463
20.06337
63.548
Cu 29
63.548