Unit 4 Stoichiometry Moles 1
Mole Theory
Definition: The mole is defined as the atomic or molecular weight of a substance
expressed in grams. It is a metric unit for amount of substance and has the abbreviation
mol.
History
Atomic weights were originally determined by weighting equal volumes of gases which
according to Avogadro's Hypothesis contain the same number of particles. Since they
contain the same number of particles, the mass of the equal volumes also represented the
mass of the particles that comprised the gas. Guy Lussac's work on the combining
volumes of gases helped chemists determine the number of atoms in each molecule of the
gases, and therefore allowed chemists to determine the relative weights of the atoms that
made up the gases.
In order to make this information useful chemists then picked a standard of atomic
weight that they compared all values to.
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Originally the standard was the oxygen molecule since so many of the
known elements combined with oxygen. It's value was set at 32 g.
This value was chosen because it made the value of a hydrogen molecule
2 grams and the value of a hydrogen atom 1 gram.
Today the standard is the isotope carbon - 12 .
Atomic weights today are determined using a mass spectrometer. This
instrument measures the atomic weight very precisely and can be used for
all elements, whether in a gas form or not.
Atomic weights are listed for each element in the periodic table.
A twist in logic allows chemists to apply their knowledge of atomic weights to develop a
new measure for the amount of substance in a sample. As long as the relative weights are
the same a sample of elements or compounds contains the same number of particles.
Since Atomic weights were measured using equal number of particles, chemists simply
express the relative weights (atomic weight) in grams in order to always have the same
number of particles.
One mole of a substance then is the atomic weight of the element expressed in
grams.
The number of particles in this amount is termed Avogadro's Number and has been
estimated at 6.023* 10 23 particles. Whenever we have Avogadro's number of particles in
a sample we have one mole. This number is almost unimaginable. To give you a sense of
it's size, imagine that each particle in a mole was a piece of paper. If we were to stack this
paper one sheet on top of another, a mole of paper would stretch from the surface of the
earth to the planet Pluto.
Task 1: Gram molecular weight (Molar Mass)
To calculate the gram molecular weight of a substance made up of more than one element
(compound), we add up the atomic weights of the elements that comprised the
compound. Atomic weight are listed in most periodic tables.
Example Ca(NO3)2
Element
Number of Atoms
Atomic Weight
Total weight
Ca
1
40.08
40.08
N
2
14.01
28.02
O
6
16.00
96.00
Gram Molecular weight ( Molar Mass ) ; 1 mole =
166.10 g
If the compound is a hydrate (containing water) then the mass of the water
molecules is added to the weight of the other atoms.
Assignment #1: Calculations of Molar Mass
Calculate the gram molecular weight (molar mass) of the following compounds. Use the
atomic weights listed in the following periodic table
Formula
Molar Mass
K3PO4
(NH4)2SO4
CuCO3
P4O6
Na3PO4 *10 H2O
CO2
Pb(CH3COO)2
MnO2
Al(OH)3
TiCl4
After completing this assignment, please switch over to the notes on solutions.
Task 2: Percentage Composition
Now that we can determine the molar mass of a substance, we need to learn how to
determine the percentage composition of the elements. This is done to compare results,
but also to determine or verify the purity of a substance. In general, we use the formula:
(Atoms of an element) (Atomic Weight)
Percent of an element = -------------------------------------------------- x 100
Formula Weight
Example: Calculate the percentage composition of (NH4)3PO4.
Step 1: Find the formula weight:
(3 x N) + (12 x H) + (1 x P) + (4 x 0)
(3 x 14.01) + (12 x 1.01) + (1 x 30.97) + (4 x 16.00)
149.12g/mol
Step 2: Use the formula
3(14.01g/mol)
% N = ----------------------- x100 = 28.2%
149.12 g/mol
12(1.01 g/mol)
% H = ----------------------- x 100 = 8.1%
149.12 g/mol
1 (30.97g/mol)
% P=------------------------- x 100 = 20.8%
149.12 g/mol
4(16.00 g/mol)
% O = ----------------------- x 100 = 42.9
149.12 g/mol
Assignment 2 Percentage Compositions
1. Find the percentage composition of AlPO4, Na2SO4, Cu(OH)2, Al2(SO4)3, and
NH4NO3.
2. Find the percentage of Nitrogen in Ca(NO3)2.
Task 3: Empirical Formula
A formula that gives the simplest whole-number ratio of atoms in a compound.
Steps for Determining an Empirical
Formula
1. Start with the number of grams of each element, given in the problem.
o If percentages are given, assume that the total mass is 100 grams so that
the mass of each element = the percent given.
2. Convert the mass of each element to moles using the molar mass from the
periodic table.
3. Divide each mole value by the smallest number of moles calculated.
4. Round to the nearest whole number. This is the mole ratio of the elements and is
represented by subscripts in the empirical formula.
o If the number is too far to round (x.1 ~ x.9), then multiply each solution by
the same
factor to get the lowest whole number multiple.
 e.g. If one solution is 1.5, then multiply each solution in the
problem by 2 to get 3.
 e.g. If one solution is 1.25, then multiply each solution in the
problem by 4 to get 5.
Once the empirical formula is found, the molecular formula for a
compound can be determined if the molar mass of the compound is
known. Simply calculate the mass of the empirical formula and
divide the molar mass of the compound by the mass of the
empirical formula to find the ratio between the molecular formula
and the empirical formula. Multiply all the atoms (subscripts) by
this ratio to find the molecular formula. (See Example #2)
Example Problem #1
A compound was analyzed and found to contain 13.5 g Ca, 10.8 g O, and 0.675 g H.
What is the empirical formula of the compound?
Start with the number of grams of each element, given in the problem.
Convert the mass of each element to moles using the molar mass from the periodic table.
Divide each mole value by the smallest number of moles calculated. Round to the
nearest whole number.
This is the mole ratio of the elements and is represented by subscripts in the empirical
formula.
Example Problem #2
NutraSweet is 57.14% C, 6.16% H, 9.52% N, and 27.18% O. Calculate the
empirical formula of NutraSweet and find the molecular formula. (The molar mass
of NutraSweet is 294.30 g/mol)
Start with the number of grams of each element, given in the problem.
 If percentages are given, assume that the total mass is 100 grams so that
the mass of each element = the percent given.
Convert the mass of each element to moles using the molar mass from the periodic table.
Divide each mole value by the smallest number of moles calculated. Round to the
nearest whole number.
This is the mole ratio of the elements and is represented by subscripts in the empirical
formula.
 If the number is too far to round (x.1 ~ x.9), then multiply each solution by the same
factor to get the lowest whole number multiple.
Now, we can find the molecular formula by finding the mass of the empirical formula
and setting up a ratio:
Please complete assignment 3 Empirical Formula Worksheet
Task 4: Rules Utilized With MOLES
There are 4 general rules associated with the MOLE concept. These rules allow
us to compare mass with volume, mass with number of particles, and balance
chemical equations.
I. The chemical formula represents a mole of that substance.
II. The formula mass, expressed in grams, represents the mass of one mole of
that substance.
III. One mole of any substance contains 6.02 x 10-23 particles.
IV. One mole of any gas, at STP conditions, occupies 22.4 liters of volume.
Now let me expand on each of these and include some examples.
Rule: The chemical formula represents a mole of that substance.
Remember that any number placed to the left of a chemical symbol or formula is
called the COEFFICIENT. This number (integer, decimal, or in scientific notation)
tells us the number of moles of that substance.
Examples: Pb --> 1 mole of lead atoms (understood 1)
3 Pb --> 3 moles of lead atoms
4.5 Cl --> 4.5 moles of chloride ions
2 CaCl --> 2 moles of calcium chloride
3.5 x 10-2 NaOH --> 3.5 10-2 moles of sodium hydroxide
Rule: The formula mass, in grams, represents the mass of that substance.
The formula mass of an element is its atomic mass (found on Periodic Table.)
The formula mass of a compound is found by multiplying the number of `moles'
of that element (see its subscript in the formula) by that atom's atomic mass.
Then add masses of all elements and record in grams.
The following example is given to demonstrate how to find formula mass.
CaCO3 (calcium carbonate)
Ca 1 x 40.1 = 40.1 C 1 x 12.0 = 12.0 O 3 x 16.0 = 48.0 ---- 100.1 grams = 100. g
(3 sig figs)
Now for some examples involving this rule:
2 Cu --> 2 moles of copper atoms --> 2 x 63.5 = 127 g
5.00 NaCl --> 5 moles sodium chloride --> 5.00 x 58.4 = 292 g
2.5 H2SO4 2.5 moles of sulfuric acid --> 2.5 x 98.1 = 245 g
Rule: One mole of any substance contains 6.02 x 1023 particles.
Particles here might mean atoms, molecules, ions, electrons, or just about
anything you might need to work with. Remember: just as there are 12 items in a
dozen; 6.02 x 1023 particles in a mole.
Examples:
HNO3 --> 1 mole of nitric acid, 1.00 x 63.0 = 63.0 grams, 6.02 x 1023 molecules of
nitric acid
3.00 K --> 3.00 moles of potassium atoms , 3.00 x 39.1 = 117 grams, 3.00 x 6.02
x 1023 =1.81 x 1024 potassium atoms
Rule: One mole of any gas, at STP conditions, occupies 22.4 L of volume.
STP is a shorthand way of requiring the temperature to be at 0 degrees C and a
standard pressure of 1 atm (101.3 kPa).
This rule is most commonly used when studying gas laws.
Suppose you have 4 grams of helium gas. This represents 1 mole of helium (see
2nd rule). These 6.02 x 1023 atoms of helium would take up 22.4 liters of volume.
This large volume would be fully occupied if the temperature was 0 degrees
Celsius and the pressure 1 atmosphere. A change in the temperature/pressure
would, of course, change the volume occupied by the gas.
No problems are given for this rule at this time.
To summarize these rules in an easier format, we often use the Mole Triangle figure to
help work through these types of problems. All we need to do is to follow the arrows and
do whatever it is we are asked to do to solve the problems we are given.
Mole Triangle
Mass (grams)
By Gram/Molecular
Weight(g/mol)
Divide
Multiply
Mole (n)
By 22.4
L/mol
Divide
Volume (L)
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Multiply
Divide
By
6.023 x1023
particles
Molecules (Particles)
To use the device students need only identify what information they are starting
with and what they are asked to calculate. Students then follow the arrows and
perform the operations indicated.
Examples and Assignments
Examples
1. Calculate the mass in grams of 35 moles of CaCO3.
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Given information is 35 moles of CaCO3.
Asked to calculate the mass in grams.
The mole triangle indicates that you should multiply the 35 moles by the molar
mass of CaCO3.
Step 1; Calculation of molar
mass
1 * 40.08 g = 40.08 g
1 * 12.01 g = 12.01 g
3 * 16.00 g = 48.00 g
Step 2; Calculation of Answer
35 moles * 100.09 g/mol = 3503.15 g
3500 g rounded to 2 significant figures
1 mole = 100.09 g
2. Calculate the # of molecules in 820 L of SO2 (g) given off by a chemical plant at STP.
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The given information is 820 L of SO2 (g)at STP.
Information you are asked to find is the # of particles.
The mole triangle indicates that you should divide 820 L by the molar volume to
calculate moles and then multiply the moles by 6.023 * 10 23 p/mol.
Step 1;Calculation of moles
Step 2; Calculation of Answer
820 L / 25.4 L/mol. = 32.28 mol.
32.28 mol. * 6.023 *10 23 p/mol. = 1.9 *10 24 particles
Assignment # 4: Mole Calculations using a periodic table
1.
2.
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4.
5.
Calculate the mass of 65 L of carbon dioxide ( CO2 ).
Calculate the volume of 78 g of tetraphosphorus hexaoxide ( P4O6 ).
Calculate the volume of 47 moles of nitrogen dioxide ( NO2 ) gas at STP.
Calculate the number of particles in 120 grams of sodium nitrate.
Calculate the # of molecules in 89 L of CO gas at STP.
6. Calculate the mass of 1.35 * 10 24 molecules of sulfur trioxide gas at STP.
7. Calculate the volume of 63 moles of dinitrogen tetraoxide.