1
1.1
1.2
1.3
1.4
1.5
Relative Masses of Atoms and Molecules
The Mole Concept
Isotopes and Mass Spectrometry
Empirical and Molecular Formulae
Reacting Masses and Volumes of Solutions and Gases
1.1
Definitions of Relative Masses
Relative Mass
Definition
Relative Isotopic Mass
The relative isotopic mass of an
isotope is defined as the ratio of the
mass of one atom of the isotope to
1
12
Formula Definition
the mass of an atom of 12𝐶
𝑚𝑎𝑠𝑠 𝑜𝑓 𝑜𝑛𝑒 𝑎𝑡𝑜𝑚 𝑜𝑓 𝑎 𝑐𝑒𝑟𝑡𝑎𝑖𝑛 𝑖𝑠𝑜𝑡𝑜𝑝𝑒
1
x 𝑚𝑎𝑠𝑠 𝑜𝑓 𝑜𝑛𝑒 𝑎𝑡𝑜𝑚 𝑜𝑓 12𝐶 𝑖𝑠𝑜𝑡𝑜𝑝𝑒
12
isotope.
Relative Atomic Mass
(𝑨𝒓 )
The relative atomic mass, 𝐴𝑟 , of an
element is defined as the ratio of the
average mass of one atom of the
1
element to 12 the mass of an atom
𝑚𝑎𝑠𝑠 𝑜𝑓 𝑜𝑛𝑒 𝑎𝑡𝑜𝑚 𝑜𝑓 𝑎𝑛 𝑒𝑙𝑒𝑚𝑒𝑛𝑡
1
x 𝑚𝑎𝑠𝑠 𝑜𝑓 𝑜𝑛𝑒 𝑎𝑡𝑜𝑚 𝑜𝑓 12𝐶 𝑖𝑠𝑜𝑡𝑜𝑝𝑒
12
of 12𝐶 isotope.
Relative Molecular
Mass (𝑴𝒓 )
The relative molecular mass, 𝑀𝑟 , of a
substance is defined as the ratio of
the average mass of one molecule of
1
the substance to 12 the mass of an
𝑚𝑎𝑠𝑠 𝑜𝑓 𝑜𝑛𝑒 𝑚𝑜𝑙𝑒𝑐𝑢𝑙𝑒 𝑜𝑓 𝑎 𝑠𝑢𝑏𝑠𝑡𝑎𝑛𝑐𝑒
1
x 𝑚𝑎𝑠𝑠 𝑜𝑓 𝑜𝑛𝑒 𝑎𝑡𝑜𝑚 𝑜𝑓 12𝐶 𝑖𝑠𝑜𝑡𝑜𝑝𝑒
12
atom of 12𝐶 isotope.

The 𝐴𝑟 of an element is the average mass of all the isotopes of that element, and is often not close to
a whole number. Table 1.1 shows the common isotopic masses of some elements and the respective
relative atomic mass:
Common isotopic masses
Relative atomic mass
𝑴𝒈
24, 25, 26
24.3
𝑪𝒍
35, 37
35.5
𝑩𝒓
𝑩𝒂
79, 81
134, 135, 136, 137, 138
79.9
137.3
Table 1.1 Isotopic masses of some elements
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1.2

A mole of a substance is the amount of that substance which contains the same number of elementary
particles as there are carbon atoms in 12.0 grams of carbon-12. “Elementary particles’ can be atoms,
protons, electrons, ions, molecules, etc.

The number of particles in one mole of a substance
is 6.02 x 1023 . This is known as the Avogadro's number, L.

Molar mass is the mass of one mole of a substance and has
units of 𝑔 𝑚𝑜𝑙 −1 .
It
must
be
distinguished
from
relative
atomic/molecular/formula mass, which is a ratio and hence
has no units, although both have the same numerical value.

For compounds and molecules, number of moles,
mass
n=
.
𝑴𝒓


 1 mole of carbon-12 has a mass
of 12.0g.
 1 mole of hydrogen atoms has a
mass of 1.0g
 1 mole of hydrogen molecules
has a mass of 2.0g.
 1 mole of Na𝐶𝑙 has a mass of
58.5g (𝑁𝑎 = 23, 𝐶𝑙 = 35.5).
For elements such as 𝐶 and 𝐹𝑒, number of moles,
mass
n=
.
Ar
1.3


The Mole Concept
Isotopes and Mass Spectrometry
Isotopes are atoms of the same element with the same atomic number but different mass numbers.
A mass spectrometer is an instrument used for measuring the masses of atoms and molecules. It can
also be used to:
i) measure the relative abundance of different isotopes, and
ii) predict the structure of more complex molecules.
The relative atomic mass of the element can be calculated from its mass spectrum.
An example of a simple mass spectrum is shown for magnesium:
 The peak at 24 is due to the 24𝑀𝑔+ 𝑖𝑜𝑛,
and the peak at 25 is due to the 25𝑀𝑔+
ion.
 All the fragments detected by a mass
spectrometer would have been ionized to
(+) charge so that they can be attracted
to the detector plate which has a large
negative charge.
 Relative abundance is plotted against
m/e (mass to charge) value (also called
m/z).
Fig.1.1 The mass spectrum of magnesium
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

It is also possible to put molecules into the mass spectrometer. Because the conditions inside a mass
spectrometer are very extreme, the molecules often break up into smaller pieces. This is known as
fragmentation.
The mass spectrum for naturally-occurring chlorine is shown:


The spectrum for naturally
occurring 𝐶𝑙 shows 2 atomic peaks
(m/e 35 and m/e 37) and 3
molecular ion peaks (m/e 70, 72 and
74).
𝐴𝑟 of 𝐶𝑙 can be obtained:
𝑨𝒓 (𝑪𝒍) =

𝟑𝟓(𝟕𝟓)+ 𝟑𝟕(𝟐𝟓)
𝟕𝟓+𝟐𝟓
= 𝟑𝟓. 𝟓
NB: Only atomic peaks are used to
obtain 𝐴𝑟 , not molecular peaks.
Fig.1.2 The mass spectrum of chlorine
Worked Examples: Calculations Involving Percentage Abundance
Question 1: Calculate the relative atomic mass of sulphur from the following isotopic percentage compositions:
𝟑𝟐
𝑺 = 𝟗𝟓%; 𝟑𝟑𝑺 = 𝟏%; 𝟑𝟒𝑺 = 𝟒%.
Question 2: Bromine has isotopes with mass number 79 and 81. If the relative atomic mass of bromine is 79.908,
calculate the percentage of each of the two isotopes present.
Solution 1
𝐴𝑟 (𝑆) =
32(95)+ 33(1)+ 34(4)
95+4+1
= 𝟑𝟐. 𝟏
Solution 2
Let the % composition of 79𝐵𝑟 be 𝑥. Then 81𝐵𝑟 has % composition (100 – 𝑥). Therefore,
79(𝑥)+ 81(100−𝑥)
𝐴𝑟 (𝐵𝑟) =
= 79.908
100
79𝑥 + 8 100 – 81𝑥 = 7990.8
⇒ 𝑥 = 𝟓𝟒. 𝟔
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1.4
Empirical and Molecular Formula

The empirical formula of a compound shows the simplest whole-number ratio of the atoms in
compound. It can be calculated if the composition by mass of the compound is known.

The molecular formula shows the total number of atoms of each element in the substance. It can be
deduced if the empirical formula and molar mass of the compound are known.

The molecular formula is always a simple whole number multiple of the empirical formula. For
example, butane has the empirical formula 𝑪𝟐 𝑯𝟓 and molecular formula 𝑪𝟒 𝑯𝟏𝟎 .
Question: If a substance contains 85.8% carbon and 14.2% hydrogen, what is its empirical formula? Given that its
relative molecular mass is 56, what is its molecular formula?
Solution
Element
Write out percentage by mass
Divide by relative atomic mass, 𝑨𝒓
𝑪
85.8
𝑯
14.2
Empirical formula = 𝐶𝐻2
85.8
12
14.2
1
Empirical Mass of 𝐶𝐻2 = 14
7.15
14.2
Molecular formula = 𝑪𝟒 𝑯𝟖 .
1
2
This gives the molar ratio
Relative Molecular Mass = 56
∴ 14𝑥 = 56 ⟹ 𝑥 = 4
Question: Calculate the empirical formula of a compound containing C (39.13g), O (52.17g), and H (8.70g).
Solution
Element
Write out the mass
𝑪
39.13
𝑯
8.70
𝑶
52.17
NB. Values such as 0.33 and 0.66
39.13
12
8.70
1
52.17
16
multiplying by 3. Multiply by 4 for
Divide by relative atomic mass, 𝑨𝒓
3.26
8.70
3.26
Do not round 1.5 to 2 or 1.33 to 1.
1
2.66
1
Find a suitable multiplier to get a
3
8
3
Dividing by smallest value (3.26)
does not give whole numbers.
Multiply by 3 to scale up to a whole
number
are scaled up to whole numbers by
values like 1.25, etc.
whole number.
Empirical formula is 𝑪𝟑 𝑯𝟖 𝑶𝟑 .

It is possible to calculate the percentage composition by mass of a substance, if the empirical or
molecular formula is known. The following example illustrates this.
Question: What is the percentage composition by mass of ethanoic acid, 𝐶2 𝐻4 𝑂2 ? (𝑴𝒓 = 60).
Solution
%C=
12 x 2
60
x 100 = 40.0%
%H=
1x4
60
x 100 = 6.67%
%O =
16 x 2
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60
x 100 = 53.3%
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1.5
Reacting Masses and Volumes
Chemical Equations

a)
A chemical equation indicates the species involved in the reaction and shows the way in which they
react. Every chemical equation must contain three pieces of information:
The identities of all the reactants and products
The chemical formulae of all the species involved in the reaction should be shown.
Reactants must be written on the left of the arrow and products on the right.
The total number of atoms of each type must be the same on each side of the equation.
b)
The reaction coefficients
The ratio in which the species react and in which products are formed are shown in the reaction
coefficients. These are the numbers which precede the chemical formula of each species in the
equation. If no coefficient is shown it is assumed to be 1.
When balancing chemical equations, always balance compounds first and elements next.
c)
The state symbols
The state symbol shows the physical state of each reacting species and must be included in every
chemical equation. There are four state symbols required for A-level Chemistry:
(s) for solid; (l) for liquid/molten; (g) for gas, and (aq) for aqueous, or dissolved in water.

The relationship
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑚𝑜𝑙𝑒𝑠, n =
mass
Mr
can be used to deduce the masses of reactants and products that react or form in most reactions.



The total combined mass of the reactants must be the same as the total combined mass of the
products. This is known as the law of conservation of mass.
The ratio in which species react corresponds to the number of moles, and not their mass. Masses must
therefore all be converted into moles, then compared to each other, and converted back.
Some reactions, however, particularly organic reactions, do not go to completion. It is possible to
calculate the percentage yield of product by using the following equation:
% 𝑦𝑖𝑒𝑙𝑑 =
amount of product formed
𝑥 100%
maximum amount of product possible
Reacting Volumes


The volume occupied by a gas depends on a number of factors:
1. the temperature: the hotter the gas, the faster the particles are moving and the more space they
will occupy;
2. the pressure: the higher the pressure, the more compressed the gas will be and the less space it
will occupy;
3. the amount of gas: the more gas particles there are, the more space they will occupy.
The volume occupied by a gas does not depend on what gas it is, i.e. one mole of any gas, at the
same temperature and pressure, will have the same volume as one mole of any other gas.
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
1 mol of any gas occupies 22.4dm3 at s.t.p, and 24dm3 at r.t.p (For ZIMSEC syllabus, molar volume =
28dm3 at r.t.p).
Volumes and Concentrations of Solutions


The amount of solute present in a fixed quantity of solvent or solution is called the concentration of
the solution.
number of moles = concentration x volume
Remember it is moles which react in the ratio shown in equations, so all quantities must be converted
to moles before the comparison can be made.
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Examination Practice 1
1. Nitroglycerine, 𝐶3𝐻5𝑁3𝑂9, is an explosive which, on detonation, decomposes rapidly to form a large
number of gaseous molecules. The equation for this decomposition is given below.
𝟒𝑪𝟑𝑯𝟓𝑵𝟑𝑶𝟗(𝒍)
𝟏𝟐𝑪𝑶𝟐(𝒈) + 𝟏𝟎𝑯𝟐𝑶(𝒈) + 𝟔𝑵𝟐(𝒈) + 𝑶𝟐(𝒈)
A sample of nitroglycerine was detonated and produced 0.350 g of oxygen gas.
(i) State what is meant by the term one mole of molecules.
(ii) Calculate the number of moles of oxygen gas produced in this reaction, and hence deduce the
total number of moles of gas formed.
(iii) Calculate the number of moles, and the mass, of nitroglycerine detonated.
(7)
(Total 7 marks)
2. Sodium chlorate (V), 𝑁𝑎𝐶𝑙𝑂3, contains 21.6% by mass of sodium, 33.3% by mass of chlorine and 45.1%
by mass of oxygen.
(a) Use the above data to show that the empirical formula of sodium chlorate (V) is 𝑁𝑎𝐶𝑙𝑂3.
(b) Sodium chlorate (V) may be prepared by passing chlorine into hot aqueous sodium hydroxide.
Balance the equation for this reaction below.
… 𝑪𝒍𝟐 + … 𝑵𝒂𝑶𝑯
… 𝑵𝒂𝑪𝒍 + 𝑵𝒂𝑪𝒍𝑶𝟑 + 𝟑𝑯𝟐𝑶
(3)
(Total 3 marks)
3. The equation for the reaction between magnesium hydroxide and hydrochloric acid is shown below.
𝑴𝒈(𝑶𝑯)𝟐(𝒔) + 𝟐𝑯𝑪𝒍(𝒂𝒒)
𝑴𝒈𝑪𝒍𝟐(𝒂𝒒) + 𝟐𝑯𝟐𝑶(𝒍)
3
–3
Calculate the volume, in cm , of 1.00 moldm hydrochloric acid required to react completely with
1.00g of magnesium hydroxide.
(4)
(Total 4 marks)
4. When aluminium is added to an aqueous solution of copper (II) chloride, 𝐶𝑢𝐶𝑙2, copper metal and
aluminium chloride, 𝐴𝑙𝐶𝑙3, are formed. Write an equation to represent this reaction.
(1)
(Total 1 mark)
5. (a) Ammonia, 𝑁𝐻3, reacts with sodium to form sodium amide, 𝑁𝑎𝑁𝐻2, and hydrogen. Write an equation
for the reaction between ammonia and sodium.
(1)
(b) A salt, 𝑿, contains 16.2% by mass of magnesium, 18.9% by mass of nitrogen and 64.9% by mass of
oxygen.
(i) State what is meant by the term empirical formula.
(ii) Determine the empirical formula of 𝑿.
(3)
(Total 4 marks)
6. Ammonium sulphate reacts with aqueous sodium hydroxide as shown by the equation below.
(𝑵𝑯𝟒)𝟐𝑺𝑶𝟒 + 𝟐𝑵𝒂𝑶𝑯
𝟐𝑵𝑯𝟑 + 𝑵𝒂𝟐𝑺𝑶𝟒 + 𝟐𝑯𝟐𝑶
3
–3
A sample of ammonium sulphate was heated with 100 cm of 0.500 moldm
aqueous sodium
hydroxide. To ensure that all the ammonium sulphate reacted, an excess of sodium hydroxide was used.
Heating was continued until all of the ammonia had been driven off as a gas.
3
The unreacted sodium hydroxide remaining in the solution required 27.3 cm
of
–3
0.600 moldm hydrochloric acid for neutralisation.
3
–3
(i) Calculate the original number of moles of 𝑁𝑎𝑂𝐻 in 100 cm of 0.500 moldm aqueous sodium
hydroxide.
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3
–3
(ii) Calculate the number of moles of 𝐻𝐶𝑙 in 27.3 cm of 0.600 moldm hydrochloric acid.
(iii) Deduce the number of moles of the unreacted 𝑁𝑎𝑂𝐻 neutralised by the hydrochloric acid.
(iv) Use your answers from parts (a) (i) and (a) (iii) to calculate the number of moles of 𝑁𝑎𝑂𝐻 which
reacted with the ammonium sulphate.
(v) Use your answer in part (a) (iv) to calculate the number of moles and the mass of ammonium
sulphate in the sample.
(7)
(Total 7 marks)
7. A hydrocarbon, 𝑾, contains 92.3% carbon by mass. The relative molecular mass of 𝑾 is 78.0.
(a) Calculate the empirical formula of 𝑾.
(b) Calculate the molecular formula of 𝑾.
(4)
(Total 4 marks)
8. One isotope of sodium has a relative mass of 23. Calculate the mass, in grams, of a single atom of this
isotope of sodium.
(2)
(Total 2 marks)
9. (a) State what is meant by the term empirical formula.
(b) A chromium compound contains 28.4% of sodium and 32.1% of chromium by mass, the remainder
being oxygen. Calculate the empirical formula of this compound.
(4)
(Total 4 marks)
10. (a) Titanium(IV) chloride reacted with water as shown in the following equation.
𝑻𝒊𝑪𝒍𝟒(𝒍) + 𝟐𝑯𝟐𝑶(𝒍)
𝟒𝑯𝑪𝒍(𝒂𝒒) + 𝑻𝒊𝑶𝟐(𝒔)
3
–3
The reaction produced 200 cm of a 1.20 moldm
solution of hydrochloric acid.
Calculate the number of moles of 𝐻𝐶𝑙 in the solution and use your answer to
find the original mass of 𝑇𝑖𝐶𝑙4.
(4)
–3
(b) Calculate the volume of 1.10 moldm sodium hydroxide solution which would be required to
3
–3
neutralise a 100 cm portion of the 1.20 moldm solution of hydrochloric acid.
(3)
3
–3
(c) An excess of magnesium metal was added to a 100 cm portion of the 1.20 moldm solution of
hydrochloric acid. Calculate the volume of hydrogen gas produced at 98 kPa and 20°C.
𝑴𝒈(𝒔) + 𝟐𝑯𝑪𝒍(𝒂𝒒)
𝟒 𝑴𝒈𝑪𝒍𝟐(𝒂𝒒) + 𝑯𝟐(𝒈)
(4)
(Total 11 marks)
–3
11. (a) Calculate the concentration, in moldm , of the solution formed when 19.6 g of hydrogen chloride,
3
𝐻𝐶𝑙, are dissolved in water and the volume made up to 250 cm .
(3)
(b) The carbonate of metal 𝑴 has the formula 𝑀2𝐶𝑂3. The equation for the reaction of this carbonate
with hydrochloric acid is given below.
𝑴𝟐𝑪𝑶𝟑 + 𝟐𝑯𝑪𝒍
𝟐𝑴𝑪𝒍 + 𝑪𝑶𝟐 + 𝑯𝟐𝑶
3
–3
A sample of 𝑀2𝐶𝑂3, of mass 0.394 g, required the addition of 21.7 cm of a 0.263 moldm solution
of hydrochloric acid for complete reaction.
(i) Calculate the number of moles of hydrochloric acid used.
(ii) Calculate the number of moles of 𝑀2𝐶𝑂3 in 0.394g.
(iii) Calculate the relative molecular mass of 𝑀2𝐶𝑂3.
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(iv) Deduce the relative atomic mass of 𝑴 and hence suggest its identity.
(6)
(Total 9 marks)
12. (a) The mass of one mole of 1H atoms is 1.0078g and that of one 1H atom is
–24
1.6734 × 10
g. Use these data to calculate a value for the Avogadro constant accurate to five
significant figures. Show your working.
(2)
(b) How does the number of atoms in one mole of argon compare with the number of molecules in
one mole of ammonia?
(1)
3
(c) A solution containing 0.732 mol of ammonia was made up to 250 cm in a volumetric flask by
adding water. Calculate the concentration of ammonia in this final solution and state the
appropriate units.
(2)
(d) A different solution of ammonia was reacted with sulphuric acid as shown in the equation below.
𝟐𝑵𝑯𝟑(𝒂𝒒) + 𝑯𝟐𝑺𝑶𝟒(𝒂𝒒)
(𝑵𝑯𝟒)𝟐𝑺𝑶𝟒(𝒂𝒒)
3
–3
In a titration, 25.0 cm of a 1.24 moldm solution of sulphuric acid required 30.8 cm3 of this
ammonia solution for complete reaction.
(i) Calculate the concentration of ammonia in this solution.
(ii) Calculate the mass of ammonium sulphate in the solution at the end of this titration.
(6)
(e) The reaction of magnesium nitride, 𝑀𝑔3𝑁2, with water produces ammonia and magnesium
hydroxide. Write an equation for this reaction.
(2)
(Total 16 marks)
18. (a) Define the term relative molecular mass.
(2)
(b) Give the meaning of the term empirical formula.
(1)
(c) Compound 𝑿 contains 32.9% by mass of carbon and 1.40% by mass of hydrogen; the remainder is
oxygen.
(i) Calculate the empirical formula of 𝑿.
(ii) The relative molecular mass of 𝑿 is 146. Deduce its molecular formula.
(4)
(d) A 1.0 kg sample of methane was burned in air. It reacted as follows:
𝑪𝑯𝟒 (𝒈) + 𝟐𝑶𝟐 (𝒈)
𝑪𝑶𝟐 (𝒈) + 𝟐𝑯𝟐𝑶(𝒈)
(i) Calculate the number of moles in 1.0 kg of methane.
(ii) Calculate the volume of oxygen gas, measured at 298 K and 100 kPa, which would be required
for the complete combustion of 1.0 kg of methane.
(6)
(Total 13 marks)
19. Give the meaning of the term mole as used in the phrase 'one mole of molecules'.
(1)
(Total 1 mark)
12
–23
20. The mass of one atom of
C is 1.99 × 10
g. Use this information to calculate a value for the
Avogadro constant. Show your working.
(2)
(Total 2 marks)
21. (a) What experimental data are required in order to calculate the empirical formula of a compound?
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(1)
(b) Give the meaning of the term molecular formula.
(1)
(c) When barium nitrate is heated it decomposes as follows:
𝑩𝒂(𝑵𝑶𝟑)𝟐(𝒔)
𝑩𝒂𝑶(𝒔) + 𝟐𝑵𝑶𝟐(𝒈) + ½ 𝑶𝟐(𝒈)
(i) Calculate the total volume, measured at 298 K and 100 kPa, of gas which is produced by
decomposing 5.00 g of barium nitrate.
–3
(ii) Calculate the volume of 1.20 moldm hydrochloric acid which is required to neutralise exactly
the barium oxide formed by decomposition of 5.00 g of barium nitrate. Barium oxide reacts
with hydrochloric acid as follows
𝑩𝒂𝑶(𝒔) + 𝟐𝑯𝑪𝒍(𝒂𝒒)
𝑩𝒂𝑪𝒍𝟐(𝒂𝒒) + 𝑯𝟐𝑶(𝒍)
(7)
(Total 9 marks)
25. The mass spectrum of a compound has a molecular ion peak at m/e = 168. Elemental analysis shows it
to contain 42.9% carbon, 2.4% hydrogen and 16.7% nitrogen by mass. The remainder is oxygen.
Calculate the empirical and molecular formulae of this compound.
(4)
(Total 4 marks)
26. Compound 𝑿 contains only boron and hydrogen. The percentage by mass of boron in 𝑿 is 81.2%. In
the mass spectrum of 𝑿 the peak at the largest value of m/e occurs at 54.
(a) Use the percentage by mass data to calculate the empirical formula of 𝑿.
(b) Deduce the molecular formula of 𝑿.
(4)
(Total 4 marks)
27. (a) Define the term relative molecular mass.
(2)
12
–23
(b) The mass of one atom of
C is 1.993 × 10
g. Use this mass to calculate a value
for the Avogadro constant (𝐿) showing your working.
(1)
(Total 3 marks)
28. When iodine reacts directly with fluorine, a compound containing 57.2% by mass of iodine is formed.
(a) Determine the empirical formula of this compound.
(b) The empirical formula of this compound is the same as the molecular formula. Write a balanced
equation for the formation of this compound.
(4)
(Total 4 marks)
29. Compound 𝑨 (𝑀𝑟 = 215.8) contains 22.24% carbon, 3.71% hydrogen and 74.05% bromine by mass.
Show that the molecular formula of 𝑨 is 𝐶4𝐻8𝐵𝑟2.
(3)
(Total 3 marks)
30. (a) Define the term relative atomic mass.
(2)
(b) How would you calculate the mass of one mole of atoms from the mass of a single atom?
(1)
(c) Sodium hydride reacts with water according to the following equation.
𝑵𝒂𝑯(𝒔) + 𝑯𝟐 𝑶 (𝒍)
𝑵𝒂𝑶𝑯 (𝒂𝒒) + 𝑯𝟐 (𝒈)
A 1.00 g sample of sodium hydride was added to water and the resulting solution was diluted to a
volume of exactly 250 cm3
–3
(i) Calculate the concentration in moldm , of sodium hydroxide solution formed.
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(ii) Calculate the volume of hydrogen gas evolved, measured at 293 K and 100 kPa.
–3
(iii) Calculate the volume of 0.112 moldm hydrochloric acid which would react exactly with a 25.0
cm3 sample of sodium hydroxide solution.
(8)
(Total 11 marks)
31. (a) Sodium carbonate forms a number of hydrates of general formula 𝑵𝒂𝟐𝑪𝑶𝟑. 𝒙𝑯𝟐𝑶. A 3.01 g sample
3
of one of these hydrates was dissolved in water and the solution made up to 250 cm .
3
3
–3
In a titration, a 25.0 cm portion of this solution required 24.3 cm of 0.200 moldm hydrochloric
acid for complete reaction.
The equation for this reaction is shown below.
𝑵𝒂𝟐𝑪𝑶𝟑 + 𝟐𝑯𝑪𝒍
𝟐𝑵𝒂𝑪𝒍 + 𝑯𝟐𝑶 + 𝑪𝑶𝟐
3
–3
(i) Calculate the number of moles of 𝐻𝐶𝑙 in 24.3 cm of 0.200 moldm hydrochloric acid.
3
(ii) Deduce the number of moles of 𝑁𝑎2𝐶𝑂3 in 25.0 cm of the 𝑁𝑎2𝐶𝑂3 solution.
3
(iii) Hence deduce the number of moles of 𝑁𝑎2𝐶𝑂3 in the original 250 cm of solution.
(iv) Calculate the 𝑀𝑟 of the hydrated sodium carbonate.
(5)
(b) In an experiment, the 𝑀𝑟 of a different hydrated sodium carbonate was found to be 250.
Use this value to calculate the number of molecules of water of crystallisation, 𝒙, in this hydrated
sodium carbonate, 𝑵𝒂𝟐𝑪𝑶𝟑. 𝒙𝑯𝟐𝑶.
(3)
(Total 8 marks)
33. (a) The equation for the reaction between magnesium carbonate and hydrochloric acid is given below.
𝑴𝒈𝑪𝑶𝟑 + 𝟐𝑯𝑪𝒍
𝑴𝒈𝑪𝒍𝟐 + 𝑯𝟐𝑶 + 𝑪𝑶𝟐
3
–3
When 75.0 cm of 0.500 moldm hydrochloric acid were added to 1.25 g of impure 𝑀𝑔𝐶𝑂3 some
3
acid
was
left
unreacted.
This
unreacted
acid
required
21.6
cm
of
a
–3
0.500 moldm solution of sodium hydroxide for complete reaction.
3
–3
(i) Calculate the number of moles of 𝐻𝐶𝑙 in 75.0 cm of 0.500 moldm hydrochloric acid.
(ii) Calculate the number of moles of 𝑁𝑎𝑂𝐻 used to neutralise the unreacted 𝐻𝐶𝑙.
(iii) Show that the number of moles of 𝐻𝐶𝑙 which reacted with the 𝑀𝑔𝐶𝑂3 in the sample was
0.0267.
(iv) Calculate the number of moles and the mass of 𝑀𝑔𝐶𝑂3 in the sample, and hence deduce the
percentage by mass of 𝑀𝑔𝐶𝑂3 in the sample.
(8)
(b) A compound contains 36.5% of sodium and 25.5% of sulphur by mass, the rest being oxygen.
(i) Use this information to show that the empirical formula of the compound is 𝑁𝑎2𝑆𝑂3.
(ii) When 𝑁𝑎2𝑆𝑂3 is treated with an excess of hydrochloric acid, aqueous sodium chloride is
formed and sulphur dioxide gas is evolved. Write an equation to represent this reaction.
(4)
(Total 12 marks)
34. (a) Give the meaning of the term empirical formula.
(1)
(b) Analysis of 3.150 g of compound 𝑿 showed that it contained 0.769 g of calcium and 0.539 g of
nitrogen; the remainder was oxygen. Calculate the empirical formula of 𝑿.
(3)
(c) What additional information is required in order to deduce the molecular formula of 𝑿.
(1)
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(d) A sample of 𝑿 when heated in alkaline solution with an aluminium-zinc alloy produced ammonia
gas. After cooling to 293 K, the ammonia occupied a volume of 1.53 x 10 -3 m3 at a pressure of 95.0
kPa. The ammonia was dissolved in water and made up to 250 cm3 of aqueous solution. A 25.0 cm3
–3
sample of this was then titrated with a 0.150 moldm hydrochloric acid.
(i) Calculate the number of moles of ammonia gas in 1.53 x 10-3 m3, at a pressure of 95.0 kPa and
a temperature of 293K.
(ii) Calculate the concentration in moldm-3 of ammonia in aqueous solution.
–3
(iii) Calculate the volume of 0.150 moldm hydrochloric acid required to neutralise the 25.0 cm3
sample of ammonia solution.
(6)
(Total 11 marks)
35. In the sixteenth century, a large deposit of graphite was discovered in the Lake District. People at the
time thought that the graphite was a form of lead. Nowadays, graphite is used in pencils but it is still
referred to as ‘pencil lead’.
A student decided to investigate the number of carbon atoms in a ‘pencil lead’. He found that the mass
of the ‘pencil lead’ was 0.321 𝑔.
(i) Calculate the amount, in mol, of carbon atoms in the student’s pencil lead.
Assume that the ‘pencil lead’ is pure graphite.
(ii) Using the Avogadro constant, 𝑁𝐴, calculate the number of carbon atoms in the student’s ‘pencil
lead’.
(1 + 1)
(Total 2 marks)
3
36. A student reacted 0.438 g of strontium with 200 cm of water.
𝑺𝒓(𝒔) + 𝟐𝑯𝟐𝑶(𝒍)
𝑺𝒓(𝑶𝑯)𝟐(𝒂𝒒) + 𝑯𝟐(𝒈)
(i) Calculate how many moles of 𝑆𝑟 were reacted.
3
(ii) Calculate the volume, in dm , of H2(g) produced.
–3
(iii) Calculate the concentration, in moldm , of the 𝑆𝑟(𝑂𝐻)2 produced.
(Total 3 marks)
37. Calcium oxide neutralises acids such as nitric acid. A student neutralised 1.50 g of 𝐶𝑎𝑂 with 2.50 mol
–3
dm nitric acid, 𝐻𝑁𝑂3. The equation for this reaction is shown below.
𝑪𝒂𝑶(𝒔) + 𝟐𝑯𝑵𝑶𝟑(𝒂𝒒)
𝑪𝒂(𝑵𝑶𝟑)𝟐(𝒂𝒒) + 𝑯𝟐𝑶(𝒍)
(i) How many moles of 𝐶𝑎𝑂 were reacted?
–3
(ii) Calculate the volume of 2.50 moldm
𝐻𝑁𝑂3 needed to exactly neutralise
1.50 g of 𝐶𝑎𝑂.
(Total 4 marks)
38. The element strontium forms a nitrate, 𝑆𝑟(𝑁𝑂3)2, which decomposes on heating as shown below.
𝟐𝑺𝒓(𝑵𝑶𝟑)𝟐(𝒔)
𝟐𝑺𝒓𝑶(𝒔) + 𝟒𝑵𝑶𝟐(𝒈) + 𝑶𝟐(𝒈)
A student heats 5.29 g of 𝑆𝑟(𝑁𝑂3)2 and collects the gas at room temperature and pressure.
3
Calculate the volume of gas, in dm , obtained by the student at room temperature and pressure.
(Total 3 marks)
39. Chlorine can be prepared by reacting concentrated hydrochloric acid with manganese (IV) oxide.
𝟒𝑯𝑪𝒍(𝒂𝒒) + 𝑴𝒏𝑶𝟐(𝒔)
𝑪𝒍𝟐(𝒈) + 𝑴𝒏𝑪𝒍𝟐(𝒂𝒒) + 𝟐𝑯𝟐𝑶(𝒍)
3
–3
A student reacted 50.0 cm of 12.0 moldm hydrochloric acid with an excess of manganese (IV) oxide.
(i) Calculate how many moles of 𝐻𝐶𝑙 were reacted.
3
(ii) Calculate the volume of 𝐶𝑙2(𝑔) produced, in dm .
(1 + 2)
(Total 3 marks)
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40. Antimony is found naturally in a number of minerals including stibnite. Stibnite typically contains 5% of
𝑆𝑏2𝑆3. Antimony can be obtained by reducing S𝑏2𝑆3 with scrap iron.
𝑺𝒃𝟐𝑺𝟑 + 𝟑𝑭𝒆
𝟐𝑺𝒃 + 𝟑𝑭𝒆𝑺
(i) How many moles of 𝑆𝑏2𝑆3 are in 500 kg of a typical sample of stibnite containing 5% by mass of
𝑆𝑏2𝑆3?
–1
(Molar mass of 𝑆𝑏2𝑆3 = 340 gmol ; relative atomic mass of 𝑆𝑏 = 122).
(ii) Calculate the mass of antimony that could be obtained by processing 500 kg of stibnite.
[2 + 2]
(Total 4 marks)
41. (a) A student carries out a titration to find the concentration of some sulphuric acid. The student finds
3
–3
3
that 25.00 cm of 0.0880 moldm aqueous sodium hydroxide, 𝑁𝑎𝑂𝐻, is neutralised by 17.60 cm
of dilute sulphuric acid, 𝐻2𝑆𝑂4.
𝑯𝟐𝑺𝑶𝟒(𝒂𝒒) + 𝟐𝑵𝒂𝑶𝑯(𝒂𝒒)
𝑵𝒂𝟐𝑺𝑶𝟒(𝒂𝒒) + 𝟐𝑯𝟐𝑶(𝒍)
(i) Calculate the amount, in moles, of 𝑁𝑎𝑂𝐻 used.
(ii) Determine the amount, in moles, of 𝐻2𝑆𝑂4 used.
–3
(iii) Calculate the concentration, in moldm , of the sulfuric acid.
[1 + 1 + 1]
(b) After carrying out the titration in (a), the student left the resulting solution to crystallise. White
–1
crystals were formed, with a formula of 𝑵𝒂𝟐𝑺𝑶𝟒 • 𝒙 𝑯𝟐𝑶 and a molar mass of 322.1 gmol .
(i) What term is given to the ‘ • 𝒙 𝑯𝟐𝑶’ part of the formula?
(ii) Using the molar mass of the crystals, calculate the value of 𝒙.
[1 + 2]
(Total 6 marks)
42. Epsom salts can be used as bath salts to help relieve aches and pains. Epsom salts are crystals of
hydrated magnesium sulfate, 𝑴𝒈𝑺𝑶𝟒 • 𝒙𝑯𝟐𝑶.
A sample of Epsom salts was heated to remove the water. 1.57 g of water was removed leaving behind
1.51 g of anhydrous 𝑀𝑔𝑆𝑂4.
(i) Calculate the amount, in mol, of anhydrous 𝑀𝑔𝑆𝑂4 formed.
(ii) Calculate the amount, in mol, of 𝐻2𝑂 removed.
(iii) Calculate the value of 𝒙 in 𝑴𝒈𝑺𝑶𝟒 • 𝒙𝑯𝟐𝑶.
[2 + 1 + 1]
(Total 4 marks)
43. Rubidium forms an ionic compound with silver and iodine. This compound has a potential use in
miniaturised batteries because of its high electrical conductivity.
The empirical formula of this ionic compound can be calculated from its percentage composition by
mass: 𝑅𝑏, 7.42%; 𝐴𝑔, 37.48%; 𝐼, 55.10%.
(i) Define the term empirical formula.
(ii) Calculate the empirical formula of the compound.
[1 + 2]
(Total 3 marks)
44. A student reacted 1.44 g of titanium with chlorine to form 5.70 g of a chloride 𝑿.
(i) How many moles of 𝑇𝑖 atoms were reacted?
(ii) How many moles of 𝐶𝑙 atoms were reacted?
(iii) Determine the empirical formula of 𝑿.
(iv) Construct a balanced equation for the reaction between titanium and chlorine.
[1 + 2 + 1 + 1]
(Total 5 marks)
45. Both calcium carbonate, 𝐶𝑎𝐶𝑂3, and calcium oxide, 𝐶𝑎𝑂, are white solids. Dilute hydrochloric acid, 𝐻𝐶𝑙,
can be used to identify whether a sample of white solid is 𝐶𝑎𝐶𝑂3 or 𝐶𝑎𝑂.
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(i) Write equations, including state symbols, for the reaction of 𝐻𝐶𝑙 with 𝐶𝑎𝐶𝑂3 and the reaction of
𝐻𝐶𝑙 with 𝐶𝑎𝑂.
(ii) How would observation of the reactions with hydrochloric acid allow the identification of the white
solid?
[1 + 3]
(Total 4 marks)
46. A student carries out experiments using acids, bases and salts. Calcium nitrate, 𝐶𝑎(𝑁𝑂3)2, is an example
of a salt.
The student prepares a solution of calcium nitrate by reacting dilute nitric acid, 𝐻𝑁𝑂3, with the base
calcium hydroxide, 𝐶𝑎(𝑂𝐻)2.
(i) Why is calcium nitrate an example of a salt?
(ii) Write the equation for the reaction between dilute nitric acid and calcium hydroxide. Include state
symbols.
(iii) Explain how the hydroxide ion in aqueous calcium hydroxide acts as a base when it neutralises
dilute nitric acid.
[1 + 2 + 1]
(Total 4 marks)
47. Ammonium compounds such as ammonium sulfate, (𝑵𝑯𝟒)𝟐𝑺𝑶𝟒, can be used as fertilizers.
(i) Write a balanced equation to show how ammonium sulphate could be formed by the reaction
between aqueous ammonia and sulfuric acid.
(ii) Ammonium sulphate is an example of a salt formed when an acid is neutralised by a base.
Explain what is meant by the term salt.
(iii) Why is ammonia acting as a base in this neutralisation?
(iv) What is the relative formula mass of (𝑵𝑯𝟒)𝟐𝑺𝑶𝟒,? Give your answer to one decimal place.
[1 + 1 + 1 + 1]
(Total 4 marks)
48. Zinc is an essential trace element which is necessary for the healthy growth of animals and plants. Zinc
deficiency in humans can be easily treated by using zinc salts as dietary supplements.
(a) One salt which is used as a dietary supplement is a hydrated zinc sulfate, 𝒁𝒏𝑺𝑶𝟒 • 𝒙𝑯𝟐𝑶, which is a
colourless crystalline solid.
Crystals of zinc sulfate may be prepared in a school or college laboratory by reacting dilute sulfuric
acid with a suitable compound of zinc.
Give the formulae of two simple compounds of zinc that could each react with dilute sulfuric acid
to produce zinc sulfate.
[2]
(b) A simple experiment to determine the value of 𝑥 in the formula 𝒁𝒏𝑺𝑶𝟒 • 𝒙𝑯𝟐𝑶 is to heat it carefully
to drive off the water.
𝒁𝒏𝑺𝑶𝟒 . 𝒙𝑯𝟐 𝑶(𝒔)
𝒁𝒏𝑺𝑶𝟒 (𝒔) + 𝒙𝑯𝟐 𝑶(𝒈)
A student placed a sample of the hydrated zinc sulfate in a weighed boiling tube and reweighed it.
He then heated the tube for a short time, cooled it and reweighed it when cool. This process was
repeated four times. The final results are shown below.
(i)
(ii)
(iii)
(iv)
Mass of empty tube / g
Mass of tube + hydrated salt / g
74.25
77.97
Mass of tube + salt after
fourth heating / g
76.34
Why was the boiling tube heated, cooled and reweighed four times?
Calculate the amount, in moles, of the anhydrous salt produced.
Calculate the amount, in moles, of water driven off by heating.
Use your results to (ii) and (iii) to calculate the value of 𝑥 in 𝒁𝒏𝑺𝑶𝟒 • 𝒙𝑯𝟐𝑶.
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[7]
(c) For many people, an intake of approximately 15 mg per day of zinc will be sufficient to prevent
deficiencies.
Zinc ethanoate crystals, (𝑪𝑯𝟑𝑪𝑶𝟐)𝟐𝒁𝒏 • 𝟐𝑯𝟐𝑶, may be used in this way.
(i) What mass of pure crystalline zinc ethanoate (𝑀𝑟 = 219.4) will need to be taken to obtain a
dose of 15 mg of zinc?
(ii) If this dose is taken in solution as 5 cm3 of aqueous zinc ethanoate, what would be the
concentration of the solution used? Give your answer in moldm–3.
[4]
(Total 13 marks)
(© UCLES 2012 9701/21/O/N/12)
49. A 10 g sample of activated charcoal containing 𝑆𝑂2 was added to 1000 𝑐𝑚3 of 0.05 moldm–3 iodine
solution. 𝑆𝑂2 in charcoal reacts with some iodine.
A 20 𝑐𝑚3 volume of the solution were then titrated with 0.01 moldm–3 𝑁𝑎2 𝑆𝑂3 (𝑎𝑞) solution and
11.6 𝑐𝑚3 were required for complete reaction.
The equations for the reactions are:
𝑺𝑶𝟐 (𝒂𝒒) + 𝑰𝟐 (𝒂𝒒) + 𝟐𝑯𝟐 𝑶(𝒍)
𝟐𝑰− (𝒂𝒒) + 𝟒𝑯+ (𝒂𝒒) + 𝑺𝑶𝟐−
𝟒 (𝒂𝒒)
𝟐− (𝒂𝒒)
𝟐− (𝒂𝒒)
− (𝒂𝒒)
(𝒂𝒒)
𝑰𝟐
+ 𝟐𝑺𝟐 𝑶𝟑
𝟐𝑰
+ 𝑺𝟒 𝑶𝟔
Calculate
(i) The number of moles of 𝑁𝑎2 𝑆2 𝑂3 in 11.6 𝑐𝑚3 of its solution;
(ii) The number of moles of iodine which reacted with the 𝑁𝑎2 𝑆2 𝑂3 (𝑎𝑞).
(iii) The number of moles of iodine which reacted with the 𝑆𝑂2 .
Hence deduce the number of moles of 𝑆𝑂2 (𝑔) in 10 g of activated charcoal.
[4]
(Total 4 marks)
[© ZIMSEC 9189/2 J2011]
50. A sample of a hydrated double salt, 𝑪𝒖(𝑵𝑯𝟒)𝒙(𝑺𝑶𝟒)𝟐 • 𝟔𝑯𝟐𝑶, was boiled with an excess of sodium
hydroxide. Ammonia was given off.
The ammonia produced was absorbed in 40.0 cm3 of 0.400 moldm–3 hydrochloric acid. The resulting
solution required 25 cm3 of 0.12 moldm–3 sodium hydroxide to neutralise the excess acid.
(a) Write the ionic equation for the reaction between ammonium ions and hydroxide ions.
[1]
3
–3
(b) (i) Calculate the amount, in moles, of hydrochloric acid in 40.0 cm of 0.400 moldm solution.
[1]
(ii) Calculate the amount, in moles, of sodium hydroxide needed to neutralise the excess acid.
This will be equal to the amount of hydrochloric acid left in excess.
[1]
(iii) Calculate the amount, in moles, of hydrochloric acid that reacted with ammonia.
[1]
(iv) Calculate the amount, in moles, of ammonium ions in the sample of the double salt.
[1]
(v) The sample contained 0.413𝑔 of copper. Use this information and your answer to (iv) to
calculate the value of 𝑥 in 𝑪𝒖(𝑵𝑯𝟒)𝒙(𝑺𝑶𝟒)𝟐 • 𝟔𝑯𝟐𝑶.
[2]
(vi) Calculate the 𝑀𝑟 of 𝑪𝒖(𝑵𝑯𝟒)𝒙(𝑺𝑶𝟒)𝟐 • 𝟔𝑯𝟐𝑶.
[1]
(Total 8 marks)
(© UCLES 2014 9701/23/M/J/14)
51. (a) Chemists recognise that atoms are made of three types of particle.
Complete the following table with their names and properties.
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Name of particle
Relative mass
Relative charge
0
1
1836
[3]
(b) The relative atomic mass of an element can be determined using data from its mass spectrum.
The mass spectrum of element 𝑿 is shown, with the percentage abundance of each isotope labelled.
(i) Define the terms relative atomic mass and isotope.
[2]
(ii) Use the data in the mass spectrum to calculate the relative atomic mass, 𝐴𝑟 , of 𝑿.
Give your answer to two decimal places and suggest the identity of 𝑿.
(c) The element tellurium, 𝑻𝒆, reacts with chlorine to form a single solid product, with a relative formula
mass of 270. The product contains 52.6% chlorine by mass.
Calculate the molecular formula of this chloride.
[3]
(Total 8 marks)
(© UCLES 2015 9701/21/M/J/15)
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