For on-line help with
this topic, see the chemcal module "Stoichiometry"
which deals with moles; balancing equations; stoichiometric calculations;
molarity and solution stoichiometry.
THE MOLE CONCEPT (Advanced Questions 2)
Your feedback on these
self-help problems is appreciated. Click here
to send an e-mail.
Shortcut to Questions
Q: 1 2 3
6 7 8 9
volume of 0.100 M sulfuric acid would be needed to react completely
with a mixture of 0.500 g of sodium hydroxide and 0.800 g of potassium
Calcium carbonate (15.0 g) is quantitatively decomposed by strong
heat to calcium oxide and carbon dioxide gas. The solid oxide residue
reacts completely with a certain amount of hydrochloric acid. What
mass of sodium hydroxide would also react exactly with this amount
of hydrochloric acid?
Petrol is a mixture of many hydrocarbon compounds but can be considered
to be equivalent to about 25 mole of octane, C8H18.
In 4.55 litres of petrol,
How many mole of oxygen must be used to burn this petrol, assuming
the only products to be carbon dioxide and water?
How many mole of carbon dioxide are formed?
What mass (kg) of carbon dioxide is formed ?
What volume of carbon dioxide at 273 K and 1.00 atmosphere is released
into the atmosphere when a car consumes 45.5 litre of petrol?
A compound is composed of the elements X and Y combined so that
every two atoms of X require three atoms of Y. Element X has an
atomic weight of 75. If 0.0333 mole of X are combined with Y (1.60
The atomic weight of Y and,
The molecular weight of the compound.
A water solution of silver nitrate (50.0 cm3) was treated
with a slight excess of a water solution of sodium chloride. The
precipitate when filtered, washed, and dried had a mass of 0.497
g. What was the molarity of the silver nitrate solution?
Fluorine gas was passed over tin(II) sulfide
at 773 K and the products were gaseous sulfur hexafluoride, and
a solid. The solid contained by weight 61.0 per cent tin and 39.0
per cent fluorine. A molar weight determination gave the value 198.
What is the molecular formula of the solid? Write the equation for
the reaction between fluorine and tin(II) sulfide.
A sample (0.210 g) of a gaseous compound containing only hydrogen
and carbon was burnt. Carbon dioxide (0.660 g) was recovered.
is the empirical formula of the compound?
A determination of the density of this hydrocarbon gave a value of
1.87 gram litre-1 at 273 K and 101 kPa. What is the molecular
formula of the substance?
A sample (1.37 g) of an organic compound containing
only carbon, hydrogen and oxygen was burnt in an excess of oxygen
to yield water (1.64 g) and carbon dioxide
(1.53 litre), measured at 273 K and 1.00 atm. What is the empirical
formula of the compound?
A certain carbohydrate of molar weight 120 contains by weight 40.0%
carbon; 6.7% hydrogen and 53.3% oxygen.
is its molecular formula?
What weight of the carbohydrate will, after complete combustion, produce
dry carbon dioxide (1.12 litre) at 273 K and 1.00 atmosphere?
When solid lead(IV) oxide (PbO2)
is heated, it forms solid lead(II) oxide (PbO) and oxygen gas. Heating
solid barium peroxide (BaO2) yields solid barium oxide
(BaO) and oxygen gas. A mixture of lead(IV) oxide and barium peroxide
was heated until both decompositions were complete.
If the initial mass of the mixture were 15.00 g and the final mass
were 13.80 g, what mass of lead(IV) oxide was present in the original
MOLE CONCEPT 2 (advanced answers)
An acid reacts with a
hydroxide to give a salt and water. This type of reaction is sometimes
called "neutralisation". The balanced equations for the
neutralisation reactions here are:
H2SO4 + 2NaOH →
2H2O + Na2SO4
+ 2KOH → 2H2O
In each reaction, one
mole of sulfuric acid reacts with two moles of the relevant hydroxide,
moles of sulfuric acid
required = (moles of NaOH + moles of KOH).
Moles of NaOH = (mass
NaOH / molar mass NaOH )
= (0.500 g / 40.00 g
= 0.0125 mol.
Moles of KOH = (mass
KOH / molar mass KOH)
= (0.800 g / 56.11 g
= 0.0143 mol.
Total moles (NaOH + KOH) = (0.0125 mol + 0.0143 mol)
= 0.0268 mol.
From the equations, 1.00
mol H2SO4 reacts with 2.00 mol of either hydroxide.
Therefore moles H2SO4
required = 0.500 x total moles hyroxides
= 0.500 x 0.0268 mol
= 0.0134 mol.
The volume of 0.100 M
= moles H2SO4
/ molarity of H2SO4 solution
= 0.0134 mol / 0.100
M L-1 = 0.134 L.
Balanced equation for
the thermal decomposition of CaCO3 to give calcium oxide
and carbon dioxide:
CaCO3 → CaO
Moles CaCO3 = mass CaCO3 / molar mass
= 15.0 g / 100.19 g mol-1
= 0.150 mol.
From above equation,
0.150 mol CaCO3 will produce 0.150 mol CaO.
Oxides of metals react
with acids to form a salt and water.
Reaction of CaO with
CaO + 2HCl → CaCl2
From this equation moles
HCl required = 2 x moles CaO
= 2 x 0.150 mol = 0.300
Acids also react with
hydroxides of metals to form a salt and water.
Balanced equation for
the reaction between HCl hydrochloric acid and sodium hydroxide::
HCl + NaOH → NaCl
From this equation, 1.00 mol NaOH reacts with 1.00 molHCl
Therefore moles NaOH
= moles HCl = 0.300
Mass NaOH = mol NaOH
x molar mass NaOH
= 0.300 mol x 40.00 g
mol-1 = 12.0 g.
Balanced equation for
combustion of octane:
2C8H18 + 25O2 →
16CO2 + 18H2O
(1.) From the equation, 1 mol C8H18
requires 12.5 mol O2 for combustion. Therefore moles
O2 required to burn 25 moles C8H18
= 25 x 12.5 mol
= 3.1 x 102
From the equation, 1 mole C8H18 produces 8
CO2 produced from 25 mol C8H18
= 25 x 8 mol
= 2.0 x 102
Mass CO2 = moles CO2 x molar mass CO2
= 2 x 102
mol x 44.01 g mol-1 = 8.8 kg.
Using the ideal gas approximation:
Volume CO2 (273 K, 1.00 atm) = moles CO2 x
= 200 mol x 22.4 L mol-1
= 4.5 x 104 L
The empirical formula
of the compund is X2Y3.
If 0.0333 mol X are combined
with Y, then mol Y present
= 3/2 x 0.0333 mol =
The weight of Y is 1.60
g, therefore molar mass of Y
= mass Y / moles Y =
1.60 g / 0.0500 mol = 32.0 g mol-1and the atomic weight
of Y = 32.0
Molecular weight of X2Y3
= (2 x atomic weight
of X) + (3 x atomic weight of Y)
= 2 x 75 + 3 x 32.0 =
AgNO3 + NaCl →
AgCl + NaCl
Moles AgCl = mass AgCl / molar mass AgCl
= 0.497 g / 143.35 g
mol-1 = 0.00347 mol.
From the balanced equation, moles AgNO3 = moles AgCl
= 0.00347 mol.
Since this amount of
AgNO3 was contained in the original 50.0 cm3
of silver nitrate solution, the molarity of the AgNO3
= moles AgNO3
x (1000 cm3 / 50.0 cm3)
= 0.00347 x 20.0 = 0.0694
In 100.0 g of compound,
moles Sn = mass Sn / molar mass of Sn atoms
= 61.0 g / 118.7 g mol-1
= 0.514 mol.
and moles F = mass F
/ molar mass of F atoms
= 39.0 g / 19.00 g mol-1
= 2.05 mol.
Thus the ratio of Sn
atoms to F atoms = 0.514 : 2.05
Dividing through by 0.514:
Molar ratio Sn:F = 1:3.99
Allowing for errors, the empirical formula is SnF4.
The formula weight of SnF4 is 195, which is very close
to the molar mass determination of 198, therefore the molecular
formula is SnF4. This allows the balanced equation to
SnS + 5F2 → SnF4
Moles CO2 = mass CO2 / molar mass CO2
= 0.660 g / 44.01 g mol-1 = 0.0150
Since all the C present in the CO2
must have been produced from C in the compound, there must have
been 0.0150 mol C in the original sample. Mass C in sample = moles
C x molar mass C atoms
= 0.0150 x 12.01 = 0.180 g.
Therefore mass of H in original sample (since
it only contains C and H)
= mass of sample - mass C in sample
= 0.210 g - 0.180 g = 0.030 g.
Moles H in sample = mass of H in sample / molar
mass H atoms
= 0.030 g / 1.008 g mol-1 = 0.030
Mole ratio of C : H = 0.0150 : 0.030
Dividing through by 0.0150 gives the empirical formula CH2.
As the substance is a gas, the ideal gas approximation can be used:
1 mole of any gas at 273K, 1 atm will occupy
Mass of 1 mole gas = density of gas x volume
of 1 mole
= 1.87 g L-1 x 22.4 L = 41.9 g.
The gram formula mass of the empirical CH2
unit is 14.03 g mol-1, and the molar mass of the gas
is 41.9 g mol-1, so the number of empirical formula units
in each molecule = 41.9 g mol-1 / 14.03 g mol-1
= 3, providing a molecular formula of C3H6.
CO2 (273 K, 1.00 atm) = volume CO2 (1.53 L)
/ 22.4 L mol-1
= 0.0683 mol.
All C atoms present in
the CO2 produced must be from C atoms in the sample,
therefore there are 0.0683 mol C in the sample.
Mass C = moles C x molar
mass C atoms
= 0.0683 mol x 12.01g
mol-1 = 0.820 g.
H2O = mass H2O / molar mass H2O
= 1.64 g / 18.02 g mol-1
= 0.0910 mol.
All H atoms present in
the H2O produced must be from H atoms in the sample,
each mol H2O molecules containing 2 mol H atoms.
moles H atoms in sample = 2 x moles H2O
= 2 x 0.0910 mol = 0.182
Mass H = moles H x molar
mass H atoms
= 0.182 mol x 1.008 g
mol-1 = 0.183 g.
The mass of O in the
sample = total sample mass - mass C - mass H
= 1.37 g - 0.820 g -
= 0.37 g.
O in sample = mass O / molar mass O atoms
= 0.37 g / 16.00 g mol-1
= 0.023 mol.
Molar ratios: C : H :
O = 0.0683 : 0.182 : 0.023
Dividing through by 0.023:
Molar ratios: C : H :
O = 3.0 : 7.9 : 1.0
Allowing for errors, this gives the empirical formula C3H8O
In 100.0 g of sample,
moles C atoms = mass C / molar mass C atoms
= 40.0 g / 12.01 g mol-1 = 3.33 mol
moles H atoms = mass H / molar mass H atoms
= 6.7 g / 1.008 g mol-1 = 6.6 mol
moles O atoms = mass O / molar mass O atoms
= 53.3 g / 16.00 g mol-1 = 3.33 mol
Molar ratios: C : H : O = 3.33 : 1.98 : 3.33
Dividing through by 3.33:
C : H : O = 1.00 : 1.98 : 1.00
Allowing for errors an empirical formula of
CH2O can be assigned. (Note that all carbohydrates have
the same empirical formula - hence the name "carbohydrate".)
The empirical formula unit CH2O has
a formula weight = 30.0.
No. empirical units per molecule
= molar mass molecule / molar mass of empirical
= 120 / 30.0= 4.00.
This allows assignment of the molecular formula
Moles CO2 = volume CO2 (1.12 L) / 22.4 L mol-1=
C4H8O4 + 4O2 →
4CO2 + 4H2O
From the equation, 1 mole of C4H8O4
produces 4 moles of CO2
Therefore 0.0125 mole C4H8O4
is required to produce 0.0500 mole CO2.
= moles C4H8O4 x molar mass C4H8O4
= 0.0125 x 120 = 1.50 g.
2PbO2 → 2PbO
2BaO + O2
The initial mass =15.00 g is composed of
x molar mass PbO2) + (moles BaO2 x molar mass
As the oxygen gas has
escaped, the final mass = 13.80 g is composed of
(moles PbO x molar mass
PbO) + (moles BaO x molar mass BaO).
Note that the moles of PbO2 before reaction equals the
moles of PbO after reaction and moles of BaO2 before
reaction = moles of BaO after reaction (see reaction equations).
These two relationships
can be used to form a pair of simultaneous equations:
Molar mass BaO2 = 169.3 g mol-1
Molar mass BaO = 153.3 g mol-1
Molar mass PbO2 = 239.2 g mol-1
Molar mass PbO = 223.3 g mol-1
Let P = moles PbO2
= moles PbO
Let B = moles BaO2 = moles BaO
Excluding units for the sake of clarity, the two equations are now:
(Eqn 1) 15 = 239.2 P + 169.3 B
(Eqn 2) 13.8 = 223.2 P + 153.3 B
From Eqn 2:
153.3 B = 13.80 - 223.2 P
B = (13.80 - 223.2 P) / 153.3
Substituting this into Eqn 1:
15.00 = 239.2 P + (169.3 / 153.3)(13.80 - 223.2 P)
15.00 = 239.2 P + (169.3 / 153.3)(13.80) - (169.3 / 153.3)(223.2
15.00 = 239.2 P + 15.24 - 246.5 P
-0.24 = -7.3 P
P = 0.033,
moles PbO2 = 0.033 mol.
= moles PbO2 x molar mass PbO2
= 0.033 mol x 239.2 g
mol-1 = 7.9 g.