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Relationship between mass and moles
The number of moles (amount of a substance), molar mass (the mass of one mole) and the mass
can be calculated from the formula:
Mass, m (g)
Moles, n (mol)
(amount of the substance)
=
Molar mass, M (g mol-1)
The molar mass is equal to the relative molecular mass of a molecule or the relative atomic mass of
an atom. Remember that the relative atomic mass of an element, Ar, is defined as the weighed
mean mass of all the naturally occurring isotopes of an element relative a carbon-12 atom. The
relative molecular mass, Mr is the sum of the relative atomic masses of the elements in a
compound
Questions
Points are awarded for your process so all problems need to show the step by step reasoning you
used to solve the problem:
Steps:
1. If an equation is given check that it is balanced. Otherwise write a balanced equation if
required.
2. Identify the variables provided in the problem and their units.
3. Identify the unknown – what you are solving for and its units.
4. Write the relevant formula with the subject. e.g n(NaCl), m(I2).
5. Substitute the known variables into the formula, including units.
6. Calculate the answer.
7. Make sure the answer has the correct number of significant figures and units.
Exercises
1. Determine the Relative molecular mass of:
a)
HI
b)
NaClO3
c)
Cr2O3
d)
(NH4)2HPO4
e)
Fe2SO4
2. Calculate the mass of 0.70 moles of Li2SO4 if its molar mass is 110 gmol-1
3. 0.20 moles of a substance has a mass of 2.7g. Calculate the molar mass.
4. One drop of water weighs 0.040g. How many molecules are there in one drop, if the molar
mass of water is 18.00 gmol-1?
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5. Calculate the mass of:
a)
3.0 moles of ammonia
b)
0.25 moles of lithium oxide
c)
0.050 mole of aluminum nitrate
d)
3.01 x 1023 molecules of phosphorus trichloride
e)
2.6 x 1022 molecules of dinitrogen monoxide
6. Calculate how many moles are there in:
a)
31g of phosphorus
b)
303g of potassium nitrate
c)
4.0g of nickel (II) sulphate
d)
87.3g of methane, CH4
7. Vitamin C, ascorbic acid has the formula, C6H8O6
a) The recommended daily dose of Vitamin C is 0.60 grams. Calculate how many moles
of Vitamin C are you consuming if you ingest 0.60 grams of the vitamin?
b) A typical tablet contains 1.0 g of vitamin C. Determine how many oxygen atoms are
you eating?
8. Chlorofluorocarbons are molecules used as the propellant in hair sprays and other aerosol
cans. They have been banned from use because they deplete the ozone layer. If there is
255.0 g of chloroflorocarbon, CCl2F2 in a can calculate:
a) How many molecules of CCl2F2 are released to the air when the can is empty?
b) How many chlorine atoms are released to the air when the can is empty?
9. Determine:
a)
Molar mass of the hydrate salt copper sulphate pentahydrate, CuSO 4 . 5H2O
b)
Moles of water in 1 mol of CuSO4 . 5H2O
c)
Mass water in 1 mol of CuSO4 . 5H2O
d)
% water in CuSO4 . 5H2O
10. In the following reaction:
2NaN3 (s)
a)
b)
 2Na (s)
+
3N2 (g)
If 500.0 grams of NaN3 decomposes to form 323.2 grams of nitrogen gas, N2
determine how many grams of sodium is produced.
What law does this represent?
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Mass relationships in chemical reactions
Once we understand the principle of the law of conservations of mass and understand the
principles of the mole rations we can ask questions like: How much is reacting or how much do we
need? To do this we need to be able to read equations in terms of the moles of a substance.
Consider the following problem:
When 50.0 g of calcium carbonate is heated it decomposes.
a)
Calculate mass of calcium oxide is formed?
CaCO3 → CaO + CO2
1.
2.
3.
4.
5.
6.
7.
b)
Calculate the mass of carbon dioxide gas formed in the reaction?
c)
What do you notice about the masses of the products and reactants? What is this law
called?
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Notice the steps used to solve this problem:
1.
Write a balanced equation (if one is given check that is balanced).
2.
List all the data given, including units. Identify what you are asked to find.
3.
Under the balanced equation write down the ratio of moles of each compound.
4.
Calculate the molar mass of each substance. Remember molar mass is the
mass of one mole of a substance.
5.
Calculate the actual number of moles of the substance with the known mass and molar
mass using the equation:
n=m÷M
6.
Use the mole ratio in the equation and the actual number of moles found in step five to
calculate the number of moles of the unknown compound.
7.
Using the new mole ratio found in step six, calculate the mass of the unknown using the
equation: m = n x M
Now try another problem
Limewater is a dilute solution of calcium hydroxide and is used to test for the presence of carbon
dioxide gas. Some calcium hydroxide is prepared by reacting 28.05g of calcium oxide with water
according to the equation:
CaO (s) + H2O(l) → Ca(OH)2 (aq)
a)
b)
c)
d)
Calculate the mass of calcium hydroxide is formed
Calculate the mass of water is needed to complete this reaction?
Calculate the mass of calcium hydroxide produced if 84.15kg of calcium oxide were used?
What are the symbols (s), (l) and (aq) used to represent?
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Exercises
1. Camels store the fat tristearin, C57H110O6 in their humps. The fat
reacts with the oxygen from respiration to produce water which
the camel stores in its hump for later use. Calculate the mass of
water produced from 1000. g of fat?
2 C57H110O6
+
163 O2
→
114 CO2
+
110 H2O
2. Lithium oxide is used on board a space shuttle to remove water from the atmosphere
according to the equation:
Li2O
+
H2O → LiOH
Calculate the mass of lithium oxide that is needed on a shuttle to remove
80100g of water?
3. Consider the following equation for the process of rusting:
Fe
+
O2
+
H2 O
→
Fe2O3.H2O
a) If a piece of iron of mass 25.0 g rusts away to form iron (III) oxide monohydrate,
calculate the mass of rust would be formed?
b) What does the . refer to in Fe2O3.H2O and what is type of compound called?
4. Soda lime glass is used for containers.
The glass is prepared by melting sodium carbonate, Na2CO3 and
sand, SiO2. The composition of glass varies, but the accepted
general formula is Na2O.CaO.6SiO2.
Using the equation below find the mass of sand in grams and
kilograms that would be required to produce 4.00 x 102g of glass?
Na2CO3
Na2O.CaO.6SiO2 + 2 CO2
(Soda-lime glass)
5. The reaction involved in baking powder (a mixture of potassium hydrogen tartrate and
sodium hydrogen carbonate) is:
KHC4H4O6
+
+
NaHCO3
CaCO3
→
+
6 SiO2
KNaC4H4O6
→
+
H2O
+ CO2
A recipe for banana bread calls for two level teaspoons (8.0g) of potassium hydrogen
tartrate. Determine the mass of sodium hydrogen carbonate that must be added for both
materials to react completely?
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6. In 1938, the British Interplanetary Society suggested the use of
sodium hydroxide, to remove carbon dioxide produced by the
astronauts in their exhaled air from the cabin atmosphere during a
expedition to the moon. The average human body discharges approximately
938g of carbon dioxide per day. Determine the mass of sodium hydroxide that
must be carried on board to absorb all this carbon dioxide for a ten day voyage by
one astronaut?
NaOH (s) + CO2 (g) → NaHCO3 (s)
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