Transcript Calculating Atomic Mass

Quantitative Chemistry
Atomic Number
Tells the number of
protons and electrons
the element contains
Atomic Mass
The average of all the
mass numbers of all the
isotopes of that
element. The unit is
amu, stands for atomic
mass units
Mass Number
The number of protons
plus the number of
neutrons found in that
element
Isotope
Atoms of the same
element with different
numbers of neutrons
Calculating Atomic Mass
 Percent(%) abundance of isotopes
 Mass of each isotope of that element
 Weighted average =
mass isotope1(%) + mass isotope2(%) + …
100
100
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Atomic Mass of Magnesium
Isotopes
24Mg
=
Mass of Isotope Abundance
24.0 amu
78.70%
25Mg
=
25.0 amu
10.13%
=
26.0 amu
11.17%
26Mg
Atomic mass (average mass) Mg = 24.3 amu
Mg
24.3
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Learning Check AT7
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?
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Solution AT7
Ga-69
68.9 amu x 60.2 = 41.5 amu for
69Ga
100
Ga-71 (%/100)
70.9 amu x 39.8
=
28.2 amu for
=
69.7 amu
71Ga
100
Atomic mass Ga
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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?
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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) = 10.8
100
100
Multiply through by 100
10.0 X + 1100 - 11.0X = 1080
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Collect X terms
10.0 X - 11.0 X = 1080 - 1100
- 1.0 X = -20
X
= -20
- 1.0
= 20 %
10B
Y = 100 - X
% 11B = 100 - 20% = 80% 11B
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Learning Check AT8
Copper has two isotopes 63Cu (62.9 amu) and
65Cu (64.9 amu). What is the % abundance of
each isotope? (Hint: Check periodic table for
atomic mass)
1) 30%
2) 70%
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3) 100%
14
Solution AT8
2) 70%
Solution
62.9X + 6490 - 64.9X = 6350
-2.0 X = -140
X = 70%
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Ratio
Is the mathematical
relationship between
two quantities in the
form of a fraction or
percentage
Ratio Analysis
is essentially concerned with
the calculation of relationships
Law of Conservation of
Mass
States that in
any reaction, the
same amount of
mass must be
found on both
sides of the
equation.
Significant Figures
When making
measurements, it is
the size of the
measurement needed
to be precise.
Sig. Fig. Rule
1) Non-zero numbers are always
significant
2) Zeros between non-zero numbers
are always significant.
3) All final zeros to the right of the
decimal place are significant.
Sig. Fig. Rule
4) Zeros that act as placeholders are
not significant.
5) All numbers in calculations should
have same sig. fig. go with the
smallest sig. fig. number
6) Counting numbers and defined
constants do not change.
What’s the Sig. Fig.
• 857
• 3 •0.00243
• 950
• 2 •505
• 1800
• 2 •0.0012300
5
• 45.2
• 3 •3.22X10
• 45.0
• 3 •1200.0060
• 92000.0 • 6 •0023
•3
•3
•5
•3
•8
•2
Scientific Notation
Expresses numbers as a
multiple of two factors-a
number between 1 and 10,
and 10 raised to a power or
exponent; makes it easier to
write a really big number or
really small number.
Round to 3 sig. fig.
• 15624
• 17853
• 19278
• 17750
• 17650
• 24503
• 276453
• 15600
• 17900
• 19300
• 17800
• 17600
• 24500
• 276000
Rounding Rules
• If digit after sig # is above 5, then
round up
• If digit after sig # is below 5 then
leave as is
• If digit after sig # is 5 and # after 5 is
not zero, then round up
• If digit after sig # is 5 and # after 5 is
zero; if sig # is odd round up and if
even then leave as is.
•
15
• 10
• 1012
• 109
• 106
• 103
2
• 10
1
• 10
18
10
exa E
peta P
tera T
giga G
mega M
kilo k
hecto h
deka da
•
deci d
-2
• 10 centi c
• 10-3 milli m
• 10-6 micro µ
• 10-9 nano n
• 10-12 pico p
-15
• 10 femto f
-18
• 10 atto a
-1
10
Dimensional Analysis
A problem
solving method
that focuses on
the units that
are used to
describe matter.
System International Units
(SI Units)
Units are a name tag that lets
you know what measurement
the number is for. The SI
Units are the standard units
use throughout the world.
SI Units
•
Temperature=
• Time= second
Kelvin (K)
(s)
• Volume= liter (L)
• Length=
or cubic
meter (m)
centimeter (cm3)
• Mass=
• Density= g/cm3
kilogram (kg)