Taking It Further With Math: Mole and Mass Relationships
The mole numerical value of a mole, 6.02 x 10 23, is based upon the definition of a mole:
the number of carbon atoms in exactly 12 grams of carbon. Experimentally, it was
determined that the number of atoms in that mass of carbon is 6.02 x 10 23.
This mass relationship is the basis for molar mass, the weight in grams of exactly 6.02 x
10 23 atoms of an element. The molar mass of any element can be found on the periodic
table: it is the same number as the atomic mass, but expressed in grams. For example, the
mass of 1 mole of hydrogen atoms is 1.01 grams while the mass of 1 mole of sodium
atoms is 22.99 grams. The mass of 1 mole of a compound is found by adding the
individual molar masses of its constituent atoms.
For example, 1 mole of water, H2O, contains 2 moles of hydrogen and 1 mole of oxygen.
The mass of 1 mole of water can be determined as follows:
2 moles of H x 1.01 g H/ 1 mole H = 2.02 grams of H
1 mole of O x 16.00 g O/ 1 mole O = 16.00 grams of O
1 mole of water = 18.02 grams
Problems
1. Find the mass of 1 mole of the following compounds:
a) sodium chloride, NaCl
b) glucose, C6H12O6
c) iron oxide, Fe2O3
d) ethanol, C2H5OH
Answers to Problems
1. a) 58.44 grams b) 180.06 grams c) 159.70 grams d) 46.02 grams
The definition of molar mass can be used as a conversion factor to move between mole
measurements and mass measurements.
For example, two conversion factors for moles of water and mass of water are:
18.02 grams H2O 1 mole H2O
1 mole H2O 18.02 grams H2O
You can use these to determine the mass of a sample of water if you know the number of
moles of water in it or the number of moles in a sample of water if you know its mass.
Example:
How many moles are in 45.00 grams of H2O?
45.00 grams H2O x 1 mole H2O = 2.497 moles H2O
18.02 grams H2O
0.75 moles H2O x 18.02 grams H2O = 13.51 grams H2O
1 mole H2O
Problems:
1. Use the molar mass of sodium chloride to calculate:
a) the number of moles in 100.00 grams of sodium chloride, NaCl
b) the mass of 1.25 moles of NaCl
2. Use the molar mass of glucose to calculate:
a) the number of moles in 150.00 grams of glucose, C6H12O6
b) the mass of 0.35 moles of glucose
Answers to Problems
1. a) 2.566 moles NaCl b) 73.05 grams NaCl
2. a) 0.83305 moles glucose b) 63.021 grams glucose
Mole-Mass Relationships and Chemical Reactions
The balanced equation that describes a chemical reaction can also be used to describe the
quantitative relationships between reactants and products. The coefficients in a balanced
chemical equation describe the ratios of both molecules and moles of products and
reactants. For example, the reaction that forms of water from its elements can be
described by the balanced chemical equation:
2 H2 + O2  2 H2O
The coefficients describe different reactant-product relationships: [all of a sudden you
switch from mole to mol without comment. Why don’t we just stay with full word?]
2 H2 + O2  2 H2O
2 mol H2 react with 1 mol O2
2 mol of H2O are produced for every 2 mol of H2 that react
2 mol H2O are produced for every 1 mol of O2 that reacts
Each of these relationships can be turned into conversion factors that relate the amount of
any two substances in the reaction:
2 mol H2 2 mol H2 1 mol O2
1 mol O2 2 mol H2O 2 mol H2O
These conversion factors can be used to calculate amounts of reactants or products
relative to known amounts of reactants or products.
Example:
We can calculate the number of moles of water produced by 3 moles of H2 by using the
relationship:
2 mol H2O
2 mol H2
3 mol H2 x 2 mol H2O = 3 mol H2O
2 mol H2
So, 3 mol of H2 produce 3 mol of H2O.
How many mol of O2 would be required to react with the 3 mol of H2? From the balanced
equation,
2 mol H2
1 mol O2
3 mol H2 x 1 mol O2 = 1.5 mol O2
2 mol H2
Now that we know that 3 mol of H2 react with 1.5 mol of O2 to produce 3 mol of H2O,
we can calculate the mass of each of these by going back to the molar mass relationship.
3 mol H2 x 2.02 gram H2 = 6.06 grams H2
1 mol H2
1.5 mol O2 x 32.00 gram O2 = 48.00 grams O2
1 mol O2
3 mol H2O x 18.02 gram H2O = 54.06 grams H2O
1 mol H2O
To summarize:
a) the coefficients of a balanced chemical equation provide the mole
relationships between reactants and products
b) moles can be converted to grams or grams can be converted to moles by
using the molar mass of the substance.
Problems
1. Use the balanced chemical equation describing the reaction between carbon, C, and
oxygen that produces carbon monoxide, CO to produce conversion factors for reactants
and products:
2 C + O2  2 CO
2. Use the conversion factors to calculate:
a) the number of mol of CO produced by 1 mol of C
b) the mass of carbon required to produced 28 grams of CO
c) the number of mol of O2 required to produce 5 mol of CO
d) the mass of oxygen required to react with 26 grams of C
Answers to Problems
1. 2 mol C 2 mol C 1 mol O2
1 mol O2 2 mol CO 2 mol CO
2. a) 1 mol CO b) 12 grams C c) 2.5 mol O2 d) 39 grams O2