CHEMISTRY NOTES – Chapter 7
Chemical Quantities
Goals : To gain an understanding of :
1. Problem solving in chemistry.
2. The use of dimensional analysis to solve problems.
3. The concept of the mole.
4. The relationship between masses of substances and moles of substances.
5. The relationship between moles and the volumes and densities of gases.
6. The calculation of empirical and molecular formulas.
Notes
1. The five steps to problem solving are:
•
•
•
•
•
Identify the unknown.
Identify what is known or given.
Plan a solution.
Do the calculations.
Check your work.
A mole is the metric unit of amount. It is analogous to a dozen. One mole equals 6.02 x 1023 representative particles of a
substance. Therefore one mole of pencils would be 6.02 x 1023 pencils, just as one dozen pencils equals 12 pencils.
A representative particle is the type of particle that a substance is usually composed of. The representative particle of an
element is an atom. Therefore one mole of copper contains 6.02 x 1023 copper atoms. The representative particle of an ionic
compound is the formula unit. Therefore one mole of sodium chloride contains 6.02 x 1023 formula units of NaCl. The
representative particle of a molecular compound is the molecule. Therefore one mole of water contains 6.02 x 1023
molecules.
A formula unit is the smallest whole number ratio of the ions which make up an ionic compound. For example, NaCl is the
formula unit of sodium chloride, it is the smallest whole number ratio for this compound (actual ratio is Na17Cl17).
Avogadro's number is 6.02 x 1023. It is the number of representative particles in a mole. Amedeo Avogardro (1776-1856)
was an Italian scientist and lawyer who's work made the calculation of this number possible.
If we know the equivalent of one mole = 6.02 x 1023 representative particles we can easily convert from moles and
numbers of representative particles. Here are some example problems and their solutions.
•
How many atoms (rep. particle of elements) are there in 2.06 moles of carbon?
•
How many molecules are there in 3.33 moles of water?
•
How many formula units are there in 8.90 moles of calcium chloride?
We can also convert from number of representative particles to moles using the same equivalent (only turned upside down
so the appropriate units cancel out) :
•
How many moles are there in 6.50 x 1029 molecules of carbon dioxide?
The atomic mass unit (amu) is the mass unit used in the atomic mass of the elements as given on the periodic table. The C12 (carbon with an amu of 12) isotope is the isotope which is used as a standard to which the masses of all other isotopes
are determined. An amu is exactly 1/12 the mass of a C-12 atom. An amu has been experimentally shown to be 1/6.02 x
1023 grams. So if we take the mass of one atom of C-12 in amu we can determine the mass of one mole of C-12 atoms by
multiplying it by Avogadro's number :
It turns out that we can convert the atomic masses of the elements in amu directly into grams to get the mass of one mole.
This is called the gram atomic mass (gam) of the element. Since the mass of a compound is the sum of the masses of the
elements which comprise it, the mass of one mole of a molecular compound is the sum of the masses of its elements
expressed in grams and is called the gram molecular mass (gmm). The same is true of an ionic compound, only the mass of
one mole is called the gram formula mass (gfm). To summarize :
•
•
•
•
The gram atomic mass (gam) of an element is the mass in grams of one mole of that element and equals the
atomic mass (as given on the periodic table) in grams. (e.g. The atomic mass of one copper atom equals 63.55
amu ; one mole of copper equals 63.55 grams).
The gram molecular mass (gmm) of a molecular compound is the mass of one mole that compound. It equals the
sum of its elements in amu expressed in grams. (e.g. A water molecule has a mass of 18.02 amu ( 2x the mass of a
hydrogen atom plus the mass of one oxygen atom ; one mole of water has a mass of 18.02 g).
The gram formula mass (gfm) of an ionic compound is the mass of one mole of that ionic compound and equals
the sum of the mass of its ions in amu expressed in grams. (e.g. The mass of one formula unit sodium chloride
(NaCl) is 58.44 amu (the mass of one sodium ion plus the mass of one chloride ion ; the mass of one mole of
formula units is 58.44 grams).
The term "molar mass" is a general term referring to the mass of one mole of a substance, regardless of its type of
representative particle. We will use this term
The molar mass of some compounds can be a little tricky to calculate. For example in the compound ammonium phosphite,
(NH4)3PO3, there are 3 nitrogen atoms, 12 hydrogen atoms, one phosphorus atom and three oxygen atoms. The molar mass
is then calculated as follows:
If we know the relationship between mass and moles for a substance we can easily convert between the two. For example
we know that the mass of one mole of NaCl is 58.44 g (equivalent then is one mole = 58.44g). We can now determine the
number of moles in 100.0 g by the following calculations.
Or if we have 5.06 moles and we want to know the mass :
If you wish to practice these (and I highly recommend it) go to : http://proton.csudh.edu/homework/hwmassmoles.html
THE MOLE MAP
Grams of a
substance
M olar mass
M ole
from
periodic
table
Avogadro's
number
# of atoms,
molecules
6.022 x
1023
The volume of any gas at STP (standard temperature and pressure) is 22.4 L (equivalent is one mole = 22.4 L). We can use
this relationship to convert between moles of a gas at STP and volume of a gas. The problem below shows how you would
convert 5.50 moles of a gas at STP into volume.
Here's how you would convert volume into moles:
Standard temperature is 0 ºC and standard pressure is 1 atm.
We saw how moles were calculated from volume data. If we carry this one step further by multiplying by the mass/mole
ratio equivalent we can determine the mass of a given volume of a gas. Let's say we wanted to know the mass of 122.0 L of
oxygen (O2) gas. The equivalents need to convert are 1 mole = 22.4 L and 1 mole of O2 = 32.00 grams (from periodic table
info.). The problem is then set up and solved as follows.
Percent composition is the percent by mass of each element in a compound. If we look at the compound NaCl, the sodium
ion has a mass of 22.99 g/mole, the choride ion has a mass of 35.45 g/mole making the total mass 58.44 g. Percent
composition is calculated below. Note the sum of the percents adds up to 100%.
For a more complex compound you need only do a little more work. For example to calculate the percent composition of
sodium phosphite (see data from #9 above) :
The empirical formula of a compound is its formula expressed as the smallest whole number ratio. Ionic compounds are
usually expressed as the smallest whole number ratio, but the empirical formula of a molecular compounds may also be
useful when determining the composition of a molecular compound experimentally. There are three steps to determine the
empirical formula of a compound from given data:
a. Determine the mass of each compound given. This may be given by the problem, or the problem may present the data as
percent composition. If the data is given as percent composition assume you have 100.00 g of the substance and convert
directly to grams.
b. Convert mass to moles.
c. Determine the lowest whole number ratio of the moles determined.
Molecular formulas are the actual ratio of the atoms of elements in a compound and are whole number multiples of their
empirical fomulas. For example if the molecular formula of a compound was N2O4, the empirical formula would be NO2.
In this case the molecular formula is 2 times the empirical formula ( NO2 x 2 = N2O4 ). The mass of the molecular formula
is necessarily also 2 times that of the mass of the empirical formula. This relationship can then be used to determine the
molecular formula of a compound if the empirical formula and molecular mass of the compound are known. Here is a
sample problem.