Converting between Individual Particles and Moles
Avogadro's Number provides the conversion
factor for moving from number of particles to moles. There are
6.02×10^{23} formula units of particles in every mole of substance, with
formula unit describing the substance we are looking at, whether it is a
compound, molecule, atom, or ion. A formula unit is the smallest unit of a
substance that still retains that substance's properties and is the simplest way
to write the formula of the substance without coefficients. Some representative
formula units are listed below.
 Compounds: Cu_{2}S, NaCl
 Molecules: N_{2}, H_{2}
 Atoms: Fe, Na
 Ions: Na^{+}(aq), Cl^{}(aq)
Since
1 mole = 6.02×10^{23} formula units, the conversion from
formula units to moles is simple:
Moles = 

Converting between Solutions and Moles
Solutions are discussed in much greater detail in the series of Solutions
SparkNotes. But it is possible, and fairly easy to
convert between the measures of solution
(molarity and
molality) and moles.
Molarity is defined as the number of moles of solute divided by the number of
liters of solvent. Rearranging the equation to solve for moles yields:
Moles = molarity × liters of solution
MolaLity is defined as the number of moles of solute divided by the number of
kilograms of solvent. Rearranging the equation to solve for moles yields:
Moles = molality × kilograms of solution
Using the Mole Ratio to Calulate Yield
Before demonstrating how to calculate how much yield a reaction will produce, we
must first explain what the mole ratio is.
The Mole Ratio
Let's look once again at our balanced demonstration reaction:
The coefficients in front of iron, oxygen, and iron (III) oxide are ratios that
govern the reaction; in other words, these numbers do not demand that the
reaction can only take place with the presence of exactly 4 moles of iron and 3
moles of oxygen, producing 2 moles of iron (III) oxide. Instead, these numbers
state the ratio of the reaction: the amount of iron and oxygen reaction together
will follow a ratio of 4 to 3. The mole ratio describes exactly what its name
suggests, the molar ratio at which a reaction will proceed. For example, 2
moles of Fe will react with 1.5 moles of O_{2} to yield 1 mole of
Fe_{2}O_{3}. Alternatively, 20 moles of Fe will react with 15
moles of O_{2} to yield 10 moles of Fe_{2}O_{3}. Each
of these examples of the reaction follow the 4:3:2 ratio described by the
coefficients.
Now, with a balanced equation, the given units converted to moles, and our
understanding of the mole ration, which will allow us to see the ratio of
reactants to each other and to their product, we can calculate the yield of a
reaction in moles. Step 4 demands that we be able to convert from moles to back
to the units requested in a specific problem, but that only involves turning
backwards the specific converstion
factors
described above.
Sample Problems
Problem: Given the following equation at STP:
N_{2}(g) + H_{2}(g)→NH_{3}(g) 

Determine what volume of H
_{2}(g) is needed to produce 224 L of
NH
_{3}(g).
Solution:
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Step 1: Balance the equation.
N_{2}(g) + 3H_{2}(g)→2NH_{3}(g) 

Step 2: Convert the given quantity to moles. Note in this step, 22.4 L is on
the denominator of the conversion factors since we want to convert from liters
to moles. Remember your conversion factors must always be arranged so that the
units cancel.
= 10 moles of NH_{3}(g) 

Step 3: mole ratio.
= 15 moles H_{2}(g) 

Step 4, convert to desired units:
= 336 L H_{2}(g) 

Now for a more challenging problem:
Given the following reaction:
2H_{2}S(g) + O_{2}(g)→SO_{2}(g) + 2H_{2}O(s) 

How many atoms of oxygen do I need in order to get 18 g of ice?
Solution
Step 1. The equation is partially balanced already, but let's finish the job.
2H_{2}S(g) +3O_{2}(g)→2SO_{2}(g) + 2H_{2}O(s) 

Step 2, convert to moles:
1 formula unit of H_{2}O has 2 atoms of H and 1 atom of O
The atomic mass of H is 1 gram/mole
Atomic mass of O = 16 grams/mole
GFM of H_{2}O(s) = + = 18 grams / mole 

×1 mole = 1 mole of H_{2}O(s) 

Step 3, mole ratio:
×3 moles O_{2}(g) = 1.5 moles O_{2}(g) 

Step 4, convert to desired units:
= 9.03×10^{23} molecules O_{2}(g) 

Is this the answer? No. The question asks for ATOMS of oxygen. There are two
atoms of oxygen in each molecule of O_{2}(g).
×2 atoms O = 1.806×10^{24} atoms O 

Now we're done. Note how important it was to write out not only your units, but
what substance you're currently working with throughout the problem. Only a
brief check was needed to ascertain if we were really answering the given
question. Always check to make sure you have answered the correct question.