Chapter 9.
Chemical Calculations I
Chemical Formulas
The Law of Definite Proportions states
that in a pure compound, the elements
are always present in the same definite
proportion by mass.
This is consistent with Atomic Theory.
It allows us to make useful calculations.
Chemical Formulas
Two samples of NH3 from different sources:
#
Mass of
Sample
Mass of N
Mass of H
A
B
1.840 g
2.000 g
1.513 g
1.644 g
0.327 g
0.356 g
A % N = 1.513 g x 100% = 82.23 %
1.840 g
B % N = 1.644 g x 100% = 82.20 %
2.000 g
Chemical Formulas
Two samples of N2H4 from different sources:
#
Mass of
Sample
Mass of N
Mass of H
A
B
3.245 g
2.950 g
2.836 g
2.578 g
0.409 g
0.372 g
A % N = 2.836 g x 100% = 87.40 %
3.245 g
B % N = 2.758 g x 100% = 87.39 %
2.950 g
Chemical Formulas
A property of NH3 (ammonia) is that it
always has 82.2% nitrogen, regardless of the source or amount of the
sample.
Hydrazine (N2H4), a different compound
than ammonia, always has 87.4%
nitrogen, regardless of the source or
amount of the sample.
Percent composition is a property of a
compound.
Chemical Formulas
If you try to make a compound by combining
its elements, you must combine them in the
correct mass ratios, or you'll have some of
one element left over:
Make CaS (calcium sulfide)
Mass
of Ca
Mass
of S
Mass
of CaS
Excess
S
Mass Ratio
Ca/S
55.6 g
55.6 g
44.4 g
50.0 g
100.0 g
100.0 g
0.0 g
5.6 g
1.25/1.00
1.25/1.00
Chemical Formulas
What's going on? At the atomic level:
4 atoms
of Ca
4 atoms
of S
4 units
of CaS
4 atoms
of Ca
6 atoms
of S
4 units
of CaS
2 units of S
left over
Chemical Formulas
And no matter what happens, the mass ratio
of Ca to S in the compound is 1.25 to 1.00.
Therefore, the individual atoms of Ca must
be 1.25 times the mass of the S atoms.
Experiments with relative masses of elements
in compounds were used to determine
atomic masses for the Periodic Table.
Chemical Quantities
How many atoms does it take to get measurable quantities of an element?
A WHOLE LOT!!!
Chemical Quantities
Since we can't see or work with individual
atoms, we work with them en mass, so
to speak. Just like we do with lots of
common things:
flour, sugar, produce, other staples
We also count things in groups:
pairs, dozens, scores, gross, reams
Moles
We count atoms in groups called moles.
1.000 mole = 6.022 x 1023 atoms
(atoms, or anything else)
Moles
Moles
1 mole = 6.022 x 1023 atoms (or anything else)
This is huge!
602,200,000,000,000,000,000,000




volume of Earth's oceans in liters
age of earth in seconds
population of earth, individuals
cost of a car, US dollars
Molar Masses
Molar Masses
The molar mass of an element is the mass of
6.022 x 1023 atoms of that element.
1.008 g is mass of 6.022 x 1023 hydrogen atoms
12.01 g is mass of 6.022 x 1023 carbon atoms
238.0 g is mass of 6.022 x 1023 uranium atoms
The atomic mass of an element is the mass
of 1 atom of that element.
1.008 amu is mass of one hydrogen atom, etc.
Molar Masses
Relationship between grams and
amu's (atomic mass units):
1.000 gram = 6.022 x 1023 amu
1.000 amu = 1.661 x 10-22 gram
Molar Masses
6.022 x 1023 is also called Avogadro's number
for Amedeo Avogadro, who first deduced a
relationship between the number of molecules of a gas and its volume.
Avogadro's number can be used as a conversion factor, like "dozen" or "score".
It allows us to "count" atoms by determining the
mass of a group of them.
Molar Masses
The molar mass is a conversion factor
between moles of a substance and its
mass.
Molar mass has units
12.01 g C
mol C
grams
mole
1 mol C
12.01 g C
g
mol
Molar Masses
Example:
In 27.43 grams of iron,
(a)
How many moles of iron are there?
(b)
How many atoms of iron are there?
Competency I-2
Note:
When working with molar mass, always use
enough significant figures in the molar mass
to match or exceed the significant figures in
other terms. Don't limit the accuracy of your
work with molar mass!
Molar Masses
Conversion between molar mass, moles,
and atoms (or molecules).
Molar
Mass
Grams
Avogadro's
Number
Moles
Atoms
Use the correct conversion, and don't use
one you don't need!
Molar Masses
Examples:
(a) What is the mass of 2.500 mol of carbon?
(b) How many atoms of carbon are present?
Molar Masses
Examples:
In 1.00 x 1022 atoms of gold,
(a) What mass of gold is present?
(b) How many moles of atoms are present?
Molar Masses of Compounds
At the atomic level, the formula of a compound
gives the number of each type of atom that
makes up a formula unit or molecule of the
compound.
At the macroscopic level, the formula of a compound gives the number of moles of each
type of atom that makes up a mole of formula units or molecules of the compound.
Molar Masses of Compounds
One molecule of H2O contains
2 hydrogen atoms
1 oxygen atom
One mole of H2O contains
2 moles of hydrogen atoms
1 mole of oxygen atoms
1 mole of water molecules
Molar Masses of Compounds
What is the mass of one mole of water?
2 mol H x
1.01 g H =
mol H
2.02 g H
1 mol O x 16.00 g O = 16.00 g O
mol O
18.02 g H2O
Molar Masses of Compounds
What is the mass of one mole of water?
18.02 g H2O
mol H2O
There are 6.022 x 1023 molecules in
there, and you can swallow it in
one gulp!
Molar Masses of Compounds
Examples:
Find the molar masses of
(a)
(b)
(c)
(d)
N2
NaCl
CaCO3
Mg(NO3)2
Percent Composition
The percent composition of a compound
is the percent of its mass contributed by
each element in its formula.
Percent composition can be calculated and
checked against an experimental value
to confirm the identity of a compound.
Percent Composition
Steps:
(a) calculate molar mass of compound,
writing out mass contributions of
the elements
(b) divide mass contribution of each
element by molar mass, express
result as a percentage.
Percent Composition
Examples:
Calculate the percent composition of
the following compounds.
(a) H2O
(b) Mg(NO3)2
Empirical Formulas
Empirical formulas show the smallest
whole-number ratio of the elements
found in a compound.
One can obtain a percent composition by
experiment, and use it to calculate the
empirical formula of a compound.
The calculation is essentially the reverse
of determining a percent composition.
Empirical Formulas
Steps:
(a) assume 100.00 g of compound, so
mass percent of each element can
be expressed in grams
(b) calculate number of moles of each
element present in that mass
(c) determine mole ratios of elements
(d) write empirical formula
Empirical Formulas
Example:
The empirical formula for Freon-12,
a refrigerant, is given below. Determine its empirical formula.
9.933 % C
58.63 % Cl
31.44 % F
Competency I-3
Molecular Formulas
Molecular formulas show the number of atoms
present in a molecule of a compound. A molecular formula is a whole number multiple of
an empirical formula.
Empirical Formula Molecular Formula
NH2
N 2H 4
CH2
C2H4, C4H8, C6H12
CH2O
C5H10O5, C6H12O6
Molecular Formulas
To determine a molecular formula, one needs:
(a) The empirical formula of the compound.
(b) The molar mass of the compound.
Steps:
(a) Use empirical formula to determine
formula mass of compound.
(b) Divide molar mass by formula mass.
(c) Multiply empirical formula by result from (b)
Molecular Formulas
Example:
Uracil, a component of ribonucleic acid (RNA),
has the empirical formula C2H2NO. Its
molar mass is 112.09 g/mol. What is
its molecular formula?
Competency I-4