Transcript Average atomic mass/average mass/atomic mass

Isotopes
 Atoms with the same number of protons,
but different numbers of neutrons.
 Atoms of the same element (same atomic
number) with different mass numbers
Isotopes of chlorine
35Cl
37Cl
17
17
chlorine - 35
chlorine - 37
Natural abundances of
isotopes
Natural chlorine contains :
75 %
35Cl
17
and 25 %
37Cl
.
17
• These percentages are known as the
natural abundances of the isotopes and
determined by “mass spectrometry.”
Average atomic mass/average
mass/atomic mass/ atomic
weight
• Is the weighted mean.
(75x 35)  ( 25x 37)
 35.5amu
100
Exercise 1
• The atomic mass of iridium is 192.2 g / mol.
What are the naturally occurring
percentages of the two isotopes of Ir-191
and Ir-193?
solution
191( x )  193(100  x )
 192.2
100
x  40
Iridium is a mixture of 40% 191Ir and
60 % 193Ir.
Isotopes of Hydrogen element
3
1
H
Tritium
2
1
H
Deuterium
1
1
H
has the biggest abundance in nature.
Mass spectrometry
• A mass spectrometer is an instrument
which separates particles according to
their masses , records the relative
proportions of these, and determine
natural abundances of the isotopes of an
element. Therefore, it also allows us to
calculate the atomic mass of an element.
• The most accurate way for determining
atomic and molecular weights is provided
by mass spectrometer.
Mass spectrometry
• mass spectrometer, invented by the English
physicist Francis William Aston (1877-1945)
when he was working in Cambridge with J. J.
Thomson. It was in his use of this instrument
that the existence of isotopes of elements was
discovered.
• Aston eventually discovered many of the
naturally occurring isotopes of non-radioactive
elements.
• He was awarded the Nobel Prize for Chemistry
in 1922.
Mass spectrometry
accelerating
C
A
B
F
D
E
A: a gaseous sample is very slowly
introduced to the mass spectrometer.
B: atoms/molecules are bombarded by a
stream of high energy electrons to produce
positive ions, mostly w/ a 1+ charge. These
electrons collide w/ electrons in the particle
knocking them out and leaving a positive
ion.
C: positively charged ions are accelerated
high enough to make the particles pass
through the slits and magnetic field by high
electrical voltage on the negatively charged
grid. With the slits, the ions were made a
beam of ions.
D: Fast moving ions enter a magnetic field
produced by an electromagnet. Ions are
deflected by a magnetic field into a curved
path. The deflection of the ions depends on
“charge to mass ratio(q/m). ”The more
massive the ion, the less the deflection. The
ions w/ equal mass and charge will deflect
the same.
E: By changing the strength of the magnetic
field or the accelerating voltage on the
negatively charged grid, ions of varying
masses can be made to enter the detector at
the end of the instrument.
• On the detector, ions are collected on a
metal plate and the current flows
through the metal plate to neutralise the
ions and this current is recorded.
• In this way, the relative abundances of
ions of different masses in the sample
can be determined and put into a graph
called “mass spectrum.”
F: The mass spectrometer must be at a
high vacuum for its correct operation
and its correct operation depends on
particles being able to pass through it
w/o colliding with any other particles.
• A: vapourised sample introduced
• B: ionization by electron bombardment
• C: Positive ions accelerated by electrical
field
• D: ions deflected by a magnetic field
• E: detector records ions of a particular
mass
• F: vacuum prevents molecules colliding
Atomic weight measurements
How was the atomic weight measured?
• By mass spectrometry
– This also measures
% natural abundance
for a given isotope
- The graph is called as
“mass spectrum.”
Atomic weight calculation
There are three naturally occuring isotopes
of neon (Ne):
20Ne
21Ne
22Ne
isotopic mass = 19.99244018 amu
isotopic mass = 20.9938467 amu
isotopic mass = 21.9913855 amu
the atomic weight is reported in text as:
20.1797 amu
Masses of Atoms
 A scale designed for atoms gives their small
atomic masses in atomic mass units (amu)
 An atom of 12C was assigned an exact mass of
12.00 amu
 Relative atomic masses of all other atoms was
determined by comparing each to the mass of
12C
 An atom twice as heavy has a mass of 24.00
amu (Mg=24.00amu). An atom 12 times lighter
than 1 C-12 atom is 1.00 amu(H=1.00amu).
Atomic mass unit(amu or u or
Da)
• 1/12th of the mass of one C-12 atom.
Average atomic mass(atomic
weight/average mass/atomic
mass)
• “atomic weight or mass” = average
mass of an atom calculated from the
masses and natural abundances of all
isotopes
Atomic Mass
Na
22.99
 Average atomic mass is based on all the
isotopes and their abundance %
Atomic mass is not a whole
number!!!!
Calculating Atomic Weight or
Mass
 Percent(%) abundance of isotopes
 Mass of each isotope of that element
 Weighted average =
mass isotope1(%) + mass isotope2(%) + …
100
100
• Naturally occurring C is composed of 98.93
% 12C and 1.07 % 13C. The masses of these
nuclides are 12 amu (exactly) and 13.00335
amu, respectively.
(98.93x12amu )  (1.07 x13.00335amu )
 12.01amu
100
Average atomic
mass(atomic mass) or
atomic weight
Atomic Mass of Magnesium
Isotopes
Mass of Isotope
Abundance
24Mg
=
24.0 amu
78.70%
25Mg
=
25.0 amu
10.13%
26Mg
=
26.0 amu
11.17%
Atomic mass (average mass) Mg = 24.3 amu
Mg
24.3
Atomic mass calculation
How was the atomic mass calculated?
• multiply each isotopic mass by the
reported natural abundance for the
isotope, then:
• add these individual contributions for
each isotope to get the average atomic
mass for the element
Atomic mass calculation
There are three naturally occuring isotopes of
neon (Ne):
20Ne mass # = 19.99244018 amu (90.51%)
21Ne mass # = 20.9938467 amu
(0.27%)
22Ne mass # = 21.9913855 amu
(9.22%)
the atomic mass is reported in text as:
20.1797 amu
18.10 + 0.057 + 2.03 = 20.19 amu
Learning Check 5
Gallium is a metallic element found in
small lasers used in compact disc players.
In a sample of gallium, there is 60.2% of
gallium-69 (68.9 amu) atoms and 39.8% of
gallium-71 (70.9 amu) atoms. What is the
atomic mass of gallium?
Solution
Ga-69
68.9 amu x
60.2
=
41.5 amu for
69Ga
28.2 amu for
71Ga
100
Ga-71 (%/100)
70.9 amu x 39.8
=
100
Atomic mass Ga =
69.7 amu
Finding An Isotopic Mass
A sample of boron consists of 10B (mass
10.0 amu) and 11B (mass 11.0 amu). If
the average atomic mass of B is 10.8
amu, what is the % abundance of each
boron isotope?
Assign X and Y values:
X = % 10B
Y = % 11B
Determine Y in terms of X
X
+
Y
= 100
Y = 100 - X
Solve for X:
X (10.0) + (100 - X )(11.0)
100
100
= 10.8
Multiply through by 100
10.0 X + 1100 - 11.0X = 1080
Collect X terms
10.0 X - 11.0 X
=
1080 - 1100
- 1.0 X = -20
X
=
-20
- 1.0
=
Y = 100 - X
% 11B = 100 - 20% =
20 %
10B
80% 11B
Learning Check 6
Copper has two isotopes 63Cu (62.9 amu)
and 65Cu (64.9 amu). What is the %
abundance of each isotope? (Hint: Check
Zumdahl or any other chemistry text for
atomic mass)
1) 30%
2) 70%
3) 100%
Solution
2) 70%
Solution
62.9X + 6490 = 64.9X = 6350
-2.0 X = -140
X = 70%
Atomic Masses
13C
12C
13.00335 amu (1.11%)
12.0000 amu (98.89%)
atomic weight of C = 12.01115 amu WHY?
Calculating masses of
atoms relative to 12C
(mass of 12C atom) * 1.58320 = mass of F
atom
= 18.99840
reported atomic weight of F = 18.9984