# Atomic Masses

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

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