DK SMITHSONIAN SUPERSIMPLE CHEMISTRY

Nanoscience and Smart Materials 101

Properties of Key Facts

Nanoparticles ✓ A nanoparticulate material

Nanoparticles have very different properties compared to may have very different
the same substance “in bulk” (powders, lumps, and sheets). properties compared to the
In a bulk material, only a small proportion of its atoms are same material in bulk.
on the surface. A nanoparticle is much smaller, so many
more of its atoms are on the surface. As a result, materials ✓ Nanoparticles have a very high
containing nanoparticles can be much more reactive.
surface area to volume ratio,
making them more likely to get
involved in chemical reactions.

Surface area to volume ratio 10 nm 10 nm
Nanoparticles have an
extremely large surface area 10 nm The sides of the small
for their volume. This is 1 nm cube are ten times
because as a particle shorter than those of
reduces in size, its surface the large cube.
area increases in comparison
to its volume. Figure this out 1 nm 1 nm
by comparing the surface
area to volume ratios of two
cube-shaped nanoparticles
of different sizes.

Figuring it out Large cube Small cube
Calculate the surface area
The surface area of each side is The surface area of each side is
10 nm × 10 nm = 100 nm2 1 nm × 1 nm = 1 nm2

The cube has 6 sides, so the The cube has 6 sides, so the
surface area of the cube is surface area of the cube is
100 nm2 × 6 = 600 nm2 1 nm2 × 6 = 6 nm2

Calculate the volume 10 nm × 10 nm × 10 nm = 1000 nm3 1 nm × 1 nm × 1 nm = 1 nm3

Calculate the surface area Ratio = surface area Ratio = surface area
to volume ratio. volume volume

= 600 nm2 = 0.6 : 1 = 6 nm2 =6:1
1000 nm3 1 nm3

The surface area to volume ratio
of the small cube is ten times
bigger than that of the large cube.

102 Nanoscience and Smart Materials Key Facts

Uses and Risks ✓ Nanoparticles have many useful
of Nanoparticles
properties because of their
Because nanoparticles have an extremely large surface tiny size and large surface area
area to volume ratio, materials made up of nanoparticles to volume ratio.
are needed in smaller quantities to make an effective
catalyst (see page 184). Useful materials that may be too ✓ Nanoparticles can be breathed in,
expensive to use in bulk can be used in nanoparticles.
However, not all the effects of nanoparticles are known, or even absorbed through skin.
and scientists are concerned about their safety.
✓ Some nanoparticles could be
Nanomedicine
Nanoparticles are so tiny that they can be harmful to our health and the
absorbed by the body and cross cell environment.
membranes. This means they can be used to
deliver drugs to specific cells—nanovaccines The vaccine-loaded immune
have been developed to fight some cancers. cells are injected back into the
blood stream to search out and
destroy cancerous cells.

Porous silicon discs
loaded with nanovaccine

are mixed with cells of
the immune system.

How Nanoparticles
Are Used

Nanoparticles have some very Tiny electronics Sunscreen Synthetic skin
important practical uses,
including in medicine and Graphene is just one atom Sunscreens containing Nanoparticles of gold have
electronics. However, as they thick, super-strong, and a nanoparticles of titanium enabled scientists to create
appear more in everyday brilliant conductor of oxide and zinc oxide are touch-sensitive synthetic
products, scientists have electricity. Nanoparticles can more effective at protecting skin, capable of picking up
become concerned about the be used to make microchips against harmful UV rays than heat, cold, and moisture.
impact they could have on the for tiny electronic devices. traditional sunscreens.
environment and our bodies.

Nanoscience and Smart Materials 103

Thermochromic Key Facts
and Photochromic
Pigments ✓ A pigment is a substance

Smart materials react to their surroundings and that gives something else a
have properties that allow them to return to their particular color.
original form. Thermochromic pigments change
color with temperature, while photochromic ✓ Thermochromic pigments change
pigments change color when exposed to light.
color with temperature.

✓ Photochromic pigments change color

when exposed to light.

Changing colors

Thermochromic film changes color at different temperatures.

It starts out black at room temperature, changes color when
heated above about 80.6°F (27°C), and reverts to black as it cools.

The hottest areas
turn blue–violet.

The cooler areas
are red–orange.

How Photochromic Pigments Work

Photochromic materials change The lenses darken and In shade, the lenses
color when they’re exposed to act as sunglasses when return to their
light. Typically, they’re made from exposed to light. original color.
compounds that change their
form as they absorb light. One Sunglasses in sunlight Sunglasses in shade
common use is to make lenses
for sunglasses that turn dark
when exposed to bright light.

104 Nanoscience and smart materials Key Facts

Shape Memory ✓ Shape (or smart) memory polymers
Materials
and alloys return to their original
Shape memory (or “smart memory”) materials shape when heated or when
can be manipulated into different shapes and pressure is released.
return to their original shape when warmed or
when pressure is released. They can be ✓ Smart materials can “remember”
used to make surgical stitches, car
bumpers, and glasses. their original shape.

✓ These materials have many uses,

such as in engineering, jewelry-
making, and medicine.

Smart alloys Nitinol glasses spring
Nitinol is an example of a shape back to their original
memory alloy (a mixture of metals). shape when pressure
It’s made from nickel and titanium, is released.
and is often used to make glasses.

Smart glasses
frames can be easily

bent or twisted.

The internal structure of shape
memory materials flips back and
forth between two different forms.

Shape Memory Shape memory At cool temperatures, When warmed, the particles
material in its the material can be gain just enough energy to
Polymers bent and shaped. move and the material
original shape.
Shape memory polymers, “remembers” its original shape.
like shape memory alloys,
can also return to their Force Heat
original shape when heated, applied applied
and are used to make many
things, including sports
equipment such as
mouth guards.

Hydrogels Nanoscience and Smart Materials 105

Hydrogels are smart materials that can absorb Key Facts
huge amounts of water. They have lots of uses,
such as in diapers, sanitary products, contact ✓ Hydrogels can absorb up to 1,000 times
lenses, artificial snow, and watering plants. Their
ability to absorb water is reversible—they can their own weight in water.
release the water and then absorb it again.
✓ They release absorbed water when

the surroundings are dry.

✓ Hydrogels are used in diapers and provide

slow-release moisture for plants.

Hydrogel granules How Hydrogels Work
Colorful hydrogel granules
can be used in place of soil Hydrogel granules can absorb a large amount of
for indoor houseplants. They water and later release it. They’re added to the soil
release water to the plant’s where water is scarce. Special hydrogels are also
roots gradually. used to release pesticides (substance that kills
pests) over a long period.

1. When water is available,

hydrogel granules in the soil

absorb it and swell up.

Plants can be kept
hydrated using hydrogels.

The multicolored beads 2. When water is in short
can absorb up to 1,000
times their own weight supply, hydrogel granules
in water.
release water slowly and

keep the soil moist.

Quantitative
Chemistry

Quantitative Chemistry 107

Relative Key Facts

Formula Mass ✓ Molecules and compounds can be

The relative atomic mass (Ar) of each element is often described by their relative formula
shown in the periodic table—it is the bigger number next mass (Mr).
to the chemical symbol. You calculate the relative formula
mass (Mr) of a substance by adding together the Ar values ✓ The Mr of a substance is the total Ar
for all the atoms in the substance’s formula.
for all the atoms in its formula.

✓ Percentage mass is calculated using

Ar and Mr values.

Copper sulfate The relative
Copper sulfate exists as blue atomic mass of
crystals or blue powder. Its oxygen is 16.
chemical formula is CuSO4.

One copper atom

63.5 32 16

CuSO4 Cu S O The relative
formula mass of
One sulfur atom Copper Sulfur Oxygen copper sulfate
is 159.5.
Four oxygen atoms

Mr = 63.5 + 32 + (4 × 16) = 159.5

Calculating Percentage Mass

You can calculate the percentage mass of an element in a compound if you know three things: the element’s
relative atomic mass, the compound’s formula, and the compound’s relative formula mass.

Percentage mass = (atoms of the element) × (Ar of the element) × 100
of an element Mr of the compound

Question

Calculate the percentage of oxygen in copper sulfate using the equation above.

Figuring it out

Percentage mass = (4 × 16) × 100 = 64 × 100 = 40.1%
of oxygen 159.5 159.5

Answer

The percentage of oxygen in copper sulfate is 40.1%.

108 Quantitative Chemistry

Using the Percentage Key Facts
Mass Formula
✓ The total mass of a compound is
The percentage mass of an element in a compound
is a measure of the mass of its atoms. due to the atoms it contains.

Question ✓ The atoms of different elements

A gardener has a fertilizer that is a mixture of 75% ammonium have different masses.
nitrate and 25% potassium sulfate. Calculate the mass of
fertilizer that is needed to supply 10.5 g of nitrogen. ✓ The percentage mass of an element

in a compound takes into account
the number and mass of its atoms.

Hydrogen Oxygen

Figuring it out Nitrogen
1. Calculate the relative formula mass (Mr) of ammonium nitrate.
Ammonium nitrate
The formula of ammonium nitrate is NH4NO3.
Relative atomic masses (Ar): H = 1, N = 14, O = 16.
Relative formula mass (Mr): 14 + (4 × 1) + 14 + (3 × 16) = 80

2. Calculate the percentage by mass of nitrogen in

ammonium nitrate.

percentage mass = (number of atoms of the element in formula) × (Ar of the element) × 100
of an element Mr of the compound

percentage mass of nitrogen in ammonium nitrate = 2 × 14 × 100 = 28 × 100 = 35%
80 80

3. Calculate the mass of ammonium nitrate needed.

mass of compound needed = required mass of the element × 100
percentage by mass

We want to supply 10.5 g of nitrogen, so mass of ammonium nitrate needed = 10.5 × 100 = 30 g
35

4. Calculate the mass of fertilizer needed.

The fertilzer is 75% ammonium nitrate and we need 30 g of ammonium nitrate, so:

mass of fertilizer needed = mass of ammonium nitrate needed × 100
mass of fertilizer needed = percentage of ammonium nitrate in the mixture

30 × 100 = 40 g
75

Answer

The mass of fertilizer needed is 40 g.

Moles Quantitative Chemistry 109

It is useful in chemistry to know the Key Facts
number of particles in a substance. This is
the amount of substance. It is measured in ✓ The amount of a substance is the number of
moles (mol). One mole of particles
contains the Avogadro number of particles. particles it contains.
It is important to say what the particles are
(atoms, molecules, ions, or electrons). ✓ The unit for amount of substance is the mole.
✓ Its symbol is “mol.”
✓ The mass of 1 mol of a substance is its relative atomic

mass (Ar) or relative formula mass (Mr) in grams.

The Avogadro number 6.02 × 1023
The number of particles in one 602 000 000 000 000 000 000 000
mole of a substance is known
as the Avogadro number. It is
equal to 6.02 × 1023. The
particles can be atoms,
molecules, ions, or electrons.

Moles of atoms Element Symbol Relative atomic Mass of 1 mol (g)
The relative atomic mass (Ar) of Iron Fe mass (Ar) 56 g
each element is often shown in
the periodic table. The mass of Compound 56
1 mol of atoms of an element is Water
equal to its Ar in grams. Formula Relative formula Mass of 1 mol (g)
H2O mass (Mr)
Moles of molecules and
compounds 1+1+16 = 18 18 g
The relative formula mass (Mr) of
a substance is the total Ar of the
atoms it contains. The mass of
1 mol of a molecule or compound
is equal to its Mr in grams.

One mole of a selection of substances
From left to right: table sugar, nickel(II) chloride, copper(II) sulfate,
potassium manganate(VII), copper shavings, and iron filings.

110 Quantitative Chemistry Key Facts

Mole Calculations ✓ Moles, mass, and relative mass

The amount of a substance is measured in moles are all related.
(mol), and is related to its mass and its relative
mass. If you know two of these three values, you ✓ Number of moles = mass ÷ relative mass.
can calculate the unknown one. When doing mole ✓ This equation can be rearranged to find
calculations, use Ar for atoms and Mr for molecules
and compounds. mass or relative formula mass.

Calculating the Question
Number of Moles
Calculate the number of moles of water molecules in 9.0 g of water (H2O).
You can calculate the Relative atomic masses (Ar): H = 1, O = 16
amount of a substance in Relative formula mass (Mr) of H2O = (2 × 1) + 16 = 18
moles if you know the mass
of the substance and its number of moles = mass
relative mass. relative mass

Figuring it out 9.0

number of moles = = 0.5 mol
18

Answer

There are 0.5 moles of water molecules in 9.0 g of water.

Calculating the Mass Calculating the Relative Mass

You can calculate the mass of a substance if you You can calculate the Ar or Mr of a substance if you
know the amount in moles and its relative mass. know its mass and number of moles.

Question Question

Calculate the mass of 2.0 mol of water 16 g of sulfur dioxide contains 0.25 mol of sulfur
molecules (H2O). dioxide molecules (SO2). Calculate the relative
formula mass of sulfur dioxide.
mass = moles × relative mass
relative mass = mass
Figuring it out
number of moles
mass = 2.0 × 18 = 36 g
Figuring it out 16
Answer
relative formula mass = 0.25 = 64
The mass of 2.0 mol of water molecules is 36 g.
Answer

The relative formula mass of sulfur dioxide is 64.

Quantitative Chemistry 111

Conservation Key Facts
of Mass
✓ Mass is conserved in chemical
The law of conservation of mass states that the total
mass of reactants and products does not change during reactions.
a reaction, because no atoms are created or destroyed.
This is why the numbers of atoms of each element is the ✓ The total mass of reactants and
same on both sides of a balanced chemical equation.
products stays the same.

✓ No atoms are created or destroyed

during a chemical reaction.

Making precipitates Orange potassium
Silver nitrate solution reacts dichromate solution
with potassium dichromate
solution to produce Cloudy orange–
potassium nitrate and brown precipitate in
silver dichromate. the reaction mixture

Colorless
silver nitrate

solution

173.64 173.64

The total mass of the flask, measuring
cylinder, and reaction mixture stays the same.

The Law of Conservation of Mass

This equation shows how magnesium chlorine magnesium chloride
magnesium reacts with Mg Cl2 MgCl2
chlorine when it is heated
to form magnesium There is one There are two The number of atoms is
chloride. No atoms are magnesium atom at the chlorine atoms at the the same at the start and
created or destroyed in start of the reaction. start of the reaction. end of the reaction.
this reaction. They just
separate and join together
in different ways.

112 Quantitative Chemistry

Changing Mass Key Facts

The recorded mass may change in some chemical ✓ Substances can leave or enter
reactions, but the law of conservation of mass (see
page 111) still applies. When reactions happen in open containers.
open containers, gases can enter or leave. The mass
of the remaining reaction mixture may decrease if a ✓ The mass decreases if a product in
gas escapes, or increase if a gas enters.
the gas state escapes.
Losing mass to air The magnesium reacts with
Some reactions produce a gas or dilute hydrochloric acid, ✓ The mass increases if a reactant in
gases. They may escape from the
reaction mixture, making the producing magnesium chloride the gas state enters.
remaining mass go down. solution and hydrogen gas.
The hydrogen escapes from the open
beaker, reducing the mass of the
remaining reaction mixture.

Magnesium ribbon
in an open beaker

Gaining Mass metal + oxygen metal oxide

from Air magnesium + oxygen magnesium oxide
+
When magnesium is heated 2Mg(s) O2(g) 2MgO(s)
in air, it reacts with oxygen
to form magnesium oxide.
Oxygen is gained by the
magnesium but lost from
the air. The total mass stays
the same, even though the
solid increases in mass.

Moles and Equations Quantitative Chemistry 113

The amount of a substance is measured in moles Key Facts
(mol). A balanced equation shows you the relative
amounts of reactants and products in a reaction. ✓ Numbers before formulas show
The ratio of the amounts of two substances is
called a mole ratio. This can be used to calculate the relative numbers of moles of
the amount of one substance from the known each substance.
amount of another substance in the reaction.
✓ Subscripts after chemical symbols

tell you the number of atoms of an
element in a compound.

✓ The ratio of moles of reactants and

products stays the same.

Balancing numbers tell you the Subscripts show if there is more
relative amounts of each than one atom of an element in
a unit of the substance.
substance in the reaction.

CH4 + 2O2 CO2 + 2H2O

1 mol of methane 2 mol of oxygen 1 mol of carbon dioxide 2 mol of water

methane oxygen carbon dioxide water

Molar Ratios

Question

Nitrogen reacts with hydrogen to form ammonia: N2 + 3H2 2NH3

Using this balanced equation, calculate the amount of ammonia formed from 6 mol of hydrogen.

Figuring it out

Divide the moles of hydrogen by the 3 in 3H2, then multiply by the 2 in 2NH3.

Amount of NH3 = 6 mol × 2 = 4 mol
3

Answer

4 mol of ammonia is formed from 6 mol of hydrogen.

114 Quantitative Chemistry

Balancing Equations Key Facts
Using Masses
✓ A balanced equation shows the formula of
You can balance an equation if you know the masses
of all the substances in that reaction as well as their each substance in a reaction, in the correct
relative masses (Ar or Mr). You can then calculate the amounts so no reactants are left over.
number of moles of each substance (see page 110).
✓ You can balance an equation if you

know the formulas of all the reactants
and products.

Using Reacting Masses: An Example

Question Mass of crucible (g) 30.00
Mass of crucible + magnesium (g) 30.48
Two students carried out an experiment. They Mass of crucible + magnesium oxide (g) 30.80
heated a piece of magnesium in a crucible so that
it reacted with oxygen to form magnesium oxide.
Use the results to determine the balanced
chemical equation for the reaction.

Figuring it out
1. Calculate the mass of each substance.

Mass of magnesium = 30.48 − 30.00 = 0.48 g
Mass of magnesium oxide = 30.80 − 30.00 = 0.80 g
Mass of oxygen = 30.80 − 30.48 = 0.32 g

2. Calculate the relative formula mass (see page 107) of each substance.

Ar of Mg = 24 Mr of O2 = (2 × 16) = 32 Mr of MgO = 24 + 16 = 40

3. Calculate the number of moles number of moles = mass of substance
relative formula mass of substance
of each substance using this equation:

Mg: 0.48 = 0.02 mol O2: 0.32 = 0.01 mol MgO: 0.80 = 0.02 mol
24 32 40

4. Simplify the ratios by dividing all the numbers by the smallest number (in this example 0.01). If

some numbers are not whole, multiply them all by the same amount so they are all whole numbers.

Mg: 0.02 = 2 O2: 0.01 = 1 MgO: 0.02 = 2
0.01 0.01 0.01

Answer

The balanced chemical equation for the reaction is 2Mg + O2 2MgO

Limiting Reactants Quantitative Chemistry 115

A chemical reaction carries on until one of the reactants Key Facts
is completely used up. This reactant is called the limiting
reactant. The other reactants in the reaction are described ✓ Reactions stop when the limiting
as being in excess. As the amount of the limiting reactant
increases, the amount of product formed increases. reactant runs out.

A color change reaction ✓ The other reactants are in excess.
Iodine dissolves in water to form a brown solution. ✓ The amount of product formed is
Zinc reacts with the iodine to form colorless zinc iodide.
directly proportional to the
amount of the limiting reactant.

Zinc metal is added. All the iodine has
reacted with the
The iodine zinc, producing a
solution is brown. colorless zinc iodide

solution.

The iodine is Unreacted zinc
gradually used up, metal is left over.
and so the solution
It is in excess.
becomes paler.

Maximum Product Calculations Figuring it out

If you know the mass of a product formed by a mass of Mg in second reaction = 6.0 = 2.5
given mass of a limiting reactant, you can mass of Mg in first reaction 2.4
predict the mass formed by a different mass.
So 2.5 times more magnesium was used in the
Question second reaction.
Mass of hydrogen in second reaction = 2.5 × 0.2 = 0.5 g
0.2 g of hydrogen is produced when 2.4 g of
magnesium ribbon reacts completely with Answer
excess dilute hydrochloric acid. Calculate
the mass of hydrogen produced when 6.0 g So 0.5 g of hydrogen is produced when 6.0 g of
of magnesium reacts completely instead. magnesium reacts completely with excess dilute
hydrochloric acid.

116 Quantitative Chemistry Key Facts

Calculating Masses ✓ The amount of limiting reactant is
in Reactions
calculated from its mass and its Mr.
The mass of the limiting reactant (see page 115)
determines the masses of the products that can be ✓ The maximum amount of product is
formed in a reaction. You can calculate the maximum
mass of a product using the relative formula masses calculated from the amount of limiting
of the limiting reactant and product, the balanced reactant and mole ratio.
chemical equation, and the mass of limiting reactant.
✓ The maximum mass of product is

calculated from its amount and its Mr.

Question

Iron reacts with chlorine to form iron chloride:

2Fe + 3Cl2 2FeCl3

Iron + chlorine iron chloride

What is the maximum mass of iron chloride that can be
produced when 2.24 g of iron reacts with excess chlorine?

Figuring it out Fine
particles
1. Calculate the relative formula mass of iron
chloride
(see page 107) of iron chloride.
The iron
Relative atomic masses (Ar): Fe = 56, Cl = 35.5 wool glows
Relative formula mass (Mr) of FeCl3 = 56 + (3 × 35.5) = 162.5 as it reacts
with the
2. Calculate the amount in moles of the limiting reactant chlorine.

from its mass and relative formula mass. Iron is the limiting Iron wool
reactant because we know chlorine is in excess.
Yellow–
number of moles = mass = 2.24 = 0.04 mol green
relative mass 56 chlorine
gas
3. Calculate the amount in moles of the product formed.
Iron reacting with chlorine
Use the mole ratio from the balanced chemical equation.

Mole ratio is 2Fe : 2FeCl3 which simplifies to 1 : 1
So 0.04 mol of Fe forms 0.04 mol of FeCl3

4. Calculate the mass of product formed. Use your answer

to step 3 and the Mr from step 1.

mass = moles × relative mass = 0.04 × 162.5 = 6.5 g

Answer

The maximum mass of iron chloride that can be produced is 6.5 g.

Quantitative Chemistry 117

The Volume of Gas Key Facts

The volume of any substance in the gas state depends on ✓ Volume of gas and moles are related
how many molecules of gas there are, its temperature, and
its pressure. The volume does not depend on the type of by the molar gas volume.
gas. One mole of any gas occupies 24 dm3 at room
temperature (20 °C) and pressure (101 kPa). ✓ The molar gas volume is 24 dm3 at

room temperature and pressure.

Molar Gas Volume Question

Room temperature (20°C) and Calculate the volume occupied by 0.25 mol of carbon dioxide at RTP.
atmospheric pressure is called volume of gas at RTP (dm3) = amount of gas (mol) × 24
RTP. One mole of any gas
occupies 24 dm3 (24,000 cm3) Figuring it out
at RTP. You can calculate the
volume of a gas at RTP if you Volume = 0.25 mol × 24 = 6.0 dm3
know its amount in moles.
Answer

At RTP, the volume occupied by 0.25 mol of carbon dioxide is 6.0 dm3.

Amount of Gas Volume of Gas from Its Mass

You can calculate the amount of any gas in You can calculate the volume occupied by a known mass of a gas
moles if you know its volume. Remember if you know its relative formula mass (Mr). For a reminder about
that the molar gas volume is 24 dm3 or the equation used here, see page 110.
24,000 cm3.

Question Question

Calculate the amount of oxygen that Calculate the volume occupied by 1.5 g of hydrogen
occupies 3.0 dm3 at RTP. at RTP. (Mr of H2 = 2.0)

mass (g) = amount (mol) × Mr

amount of = volume of gas Figuring it out
gas (mol) at RTP (dm3)
molar volume 1. Calculate the amount of gas in moles.

1.5 g = amount (mol) × 2.0 1.5 = 0.75 mol
number of moles (hydrogen) = 2

Figuring it out 3 2. Calculate the volume of gas using the equation
24
amount of gas (mol) = = 0.125 mol at the top of this page.
volume (dm3) = 0.75 mol × 24 = 18 dm3

Answer Answer

At RTP, 0.125 mol of oxygen At RTP, the volume occupied by 1.5 g of
occupies 3.0 dm3. hydrogen is 18 dm3.

118 Quantitative Chemistry Key Facts

Empirical Formulas ✓ The empirical formula of a compound

The empirical formula of a compound is the is the simplest whole-number ratio of
simplest whole-number ratio of the atoms of each atoms of each element in the
element found in the compound. Since compound.
ionic compounds have giant structures,
they’re always described with empirical ✓ The formulas of ionic compounds are
formulas. Compounds with covalent
bonding are usually given a molecular always empirical formulas.
formula, but it’s possible to figure
out an empirical formula ✓ The charges of the ions in the
for them, too.
empirical formulas of an ionic
The oxygen ions compound add up to zero.
have a 2− charge.
The lithium
ions have a
1+ charge.

Lithium oxide Oxygen atom
Lithium oxide is an ionic compound Phosphorus
with a giant ionic structure. Its atom
empirical formula is Li2O, because
two lithium ions are needed to Phosphorus pentoxide
balance the charge of the oxide ion.

Calculating an Empirical Formula

The idea of empirical formula is also applied to covalent compounds.

Question

What is the empirical formula of phosphorus pentoxide, which
has the molecular formula of P4O10?

Figuring it out
1. Find the highest common factor: the highest common factor

of 4 and 10 is 2.

2. Divide the molecular formula by the highest common factor.

4 10
P= 2 =2 O= 2 =5

Answer

The empirical formula is P2O5.

A Reacting Masses Quantitative Chemistry 119
Experiment
Key Facts
You can calculate the empirical formula of a
metal oxide by carrying out the experiment ✓ An empirical formula is the smallest
below. You need to know the mass of the metal
before it reacts with oxygen, and the mass of the whole-number ratio of atoms in a
metal oxide formed. Magnesium is a reactive compound.
metal that is suitable for this type of experiment.
✓ An empirical formula can be determined
The empirical formula of magnesium oxide
To calculate the empirical formula of using experimental results.
magnesium oxide (see page 120), you
need to know the mass of magnesium, and ✓ You need to find the masses of reactants
the mass of magnesium oxide it forms.
and products in your experiment.
4. Allow the crucible to
✓ Measure each mass carefully.
cool, then reweigh the ✓ Wear eye protection and gloves during
crucible and lid with the
the experiment.
contents. Be careful, it
will be very hot. 1. Record the mass of

the crucible and its lid.

2. Loosely coil a clean piece of magnesium

and put it in the crucible. Record the mass of
the crucible, lid, and magnesium together.

3. Heat the crucible, lifting the lid from time

to time to let air in. Continue heating for about
10 minutes until the magnesium turns white
and then turn the Bunsen burner off.

Recording Your Results

You need to record your results so that you can
calculate the empirical formula (see page 120).
Here are two calculations you need:

1. mass of magnesium
= (mass at step 2) − (mass at step 1)

2. mass of oxygen
= (mass at step 4) − (mass at step 2)

Heatproof mat

120 Quantitative Chemistry Key Facts

Calculating the ✓ Set out your work in columns to make it
Reacting Mass
easier to follow.
You can use the information gathered in the
reacting masses experiment outlined on ✓ Figuring out the mass of each element and
page 119 to determine the empirical
formula of the compound magnesium oxide. divide by its relative atomic mass.

✓ Find the simplest whole-number ratio.

Question Mass of crucible (g) 30.00
Mass of crucible + magnesium (g) 30.48
The table shows the results collected in the Mass of crucible + magnesium oxide (g) 30.80
experiment on page 119. Determine the empirical
formula of magnesium oxide using these results.
Relative atomic masses (Mr): Mg = 24, O = 16

Figuring it out Magnesium Oxygen

Before figuring out the empirical formula, calculate Magnesium oxide
the mass of each element in magnesium oxide
(see page 119).

Mass of magnesium (Mg) = 30.48 − 30.00 = 0.48 g

Mass of oxygen (O) = 30.80 − 30.48 = 0.32 g

1. Write the symbols of the 4. Divide Step 2 numbers by Step 3 numbers.

elements in columns. Mg O 0.48 0.32
24 16
= 0.02 = 0.02

2. Write the mass of each 5. Divide Step 4 numbers by their smallest number.

element. 0.48 g 0.32 g 0.02 0.02
0.02 0.02
=1 =1

3. Write the relative atomic 24 16 6. If needed, simplify the ratio, then write the formula.

mass of each element. Mg1O1 = MgO

Answer

The empirical formula of magnesium oxide is MgO.

Quantitative Chemistry 121

Water of Key Facts
Crystallization
✓ Salt crystals may contain water of
Some salts contain water molecules. These molecules are in
the salt’s crystal lattice, but are only loosely held there – the crystallization.
water can be removed by heating. A salt containing water of
crystallization is described as “hydrated”. A salt without ✓ The water can be removed from a
any water of crystallization is described as “anhydrous”.
hydrated salt by heating.

✓ A salt without water of

crystallization is an anhydrous salt.

Dehydration of hydrated copper sulfate Water is released.
Hydrated copper sulfate is blue. You can
remove its water of crystallization by heating, 5. Let the basin
forming white anhydrous copper sulfate.
cool then reweigh it
1. Record the mass of an 2. Add some hydrated copper sulfate with its contents.

evaporating basin. and record the mass of the basin and

hydrated copper sulfate together.

3. Heat the evaporating

basin. Take care to avoid

any hot solid spitting out.

4. Continue heating to

remove the water until the

copper sulfate turns white.

Turn the Bunsen burner off.

Hydrated and Water molecule The hydration bonds break when
(H2O) heated and the water evaporates,
Anhydrous Copper Sulfate leaving behind anhydrous copper
(II) sulfate.
Anhydrous copper sulfate is CuSO4.
The general formula for hydrated Sulfate ion Copper ion
copper sulfate is CuSO4·×H2O where (SO42−) (Cu2+)
× is a whole number. The dot (·)
separates the two parts of the Water
formula. In the hydrated form, water molecules
of crystallization (H2O) is held within (H2O)
the structure by very weak bonds.

CuSO4·3H2O

122 Quantitative Chemistry Key Facts

Calculating Water ✓ Set up your work in columns.
of Crystallization ✓ Figure out the mass of each

You can use the masses collected in the experiment compound and divide by its relative
outlined on page 121 to determine the amount of water formula mass.
of crystallization (water in the crystal lattice) involved.
If you know the mass of hydrated salt and anhydrous ✓ Find the simplest whole-number
salt, you can figure out the mass of water lost.
ratio to get the value of x.

Question Mass of basin (g) 30.25
Mass of basin + hydrated copper sulfate (g) 45.22
Determine the value of x in Mass of basin + anhydrous copper sulfate (g) 39.82
CuSO4·xH2O using the results in this
table. Give the formula of the
hydrated copper sulfate.
Relative formula masses (Mr):
CuSO4 = 159.6, H2O = 18

Figuring it out Sulfur ion
(SO42-)
Before figuring out the value of x, calculate the mass of
anhydrous copper sulfate and the mass of water lost. Copper ion
(Cu2+)
Mass of anhydrous copper sulfate
= 39.82 − 30.25 = 9.57 g Anhydrous copper sulfate
Mass of water
= 45.22 − 39.82 = 5.40 g

1. Write the formulas of 4. Divide Step 2 numbers by Step 3 numbers.

the compounds in CuSO4 H2O 9.57 = 0.06 5.40 = 0.3
columns. 159.6 18

2. Write the mass of each 5. Divide Step 4 numbers by their smallest number.

compound. 9.57 g 5.40 g 0.06 = 1 0.3 = 5
0.06 0.06

3. Write the relative 159.6 18 6. If needed, simplify the ratio, then write the value

formula mass of each of x.
compound. 1:5 so x = 5

Answer

x = 5 so the formula of the hydrated copper sulfate is: CuSO4.5H2O

Concentration Quantitative Chemistry 123

A solute can dissolve in a solvent to form a Key Facts
solution. The greater the mass or the amount of
dissolved solute in a given volume, the greater the ✓ A solute dissolves in a solvent to form
concentration. Concentrations in terms of mass
are measured in g/dm3. Concentrations in terms a solution.
of amount of substance are measured in mol/dm3.
✓ The concentration of a solution is a

measure of how “crowded” the solute
particles are.

✓ Concentration is measured in g/dm3

or mol/dm3.

Converting cm3 to dm3 Divide by 1,000 to convert from cm3 to dm3
Volumes used in
concentration calculations are Multiply by 1,000 to convert from dm3 to cm3
in cubic decimeters (dm3). For example, 125 cm3 = 125 = 0.125 dm3
Convert from cm3 to dm3 first
in a concentration calculation. 1,000

1 dm3 = 1,000 cm3

Calculating concentration concentration = mass of solute (g)
To calculate a concentration, (g/dm3) volume of solution (dm3)
you need to know the mass or
amount of solute, and volume
of solution.

concentration = amount of solute (mol)
(mol/dm3) volume of solution (dm3)

An Example

Question Figuring it out Answer
1. Convert the volume to dm3.
10 g of sodium The concentration
hydroxide is Volume of solution = 250 = 0.25 dm3 of the solution
dissolved in water 1,000 formed is 40 g/dm3.
to make 250 cm3
of solution. 2. Substitute values into the concentration equation above.
Calculate the
concentration Concentration = 10 g = 40 g/dm3
of this solution. 0.25 dm3

124 Quantitative Chemistry Key Facts

Titration ✓ Titrations involve finding out the
Calculations
volumes of acid and alkali that
Titration is a technique that is used to find unknown neutralize each other.
concentrations (see page 136). You carry out an experiment
to find the volumes of acid and alkali that exactly neutralize ✓ You can use the results to calculate
each other. If you know the concentration of one substance,
you can figure out the concentration of the other. an unknown concentration.

✓ You need to know both volumes,

and the known concentration.

Titrations concentration (mol/dm3) = amount of solute (mol)
In a titration, the concentration of one volume of solution (dm3)
solution is known and the other is
unknown. If you know the volumes that
react together, you can calculate the
unknown concentration.

An Example

Question

15 cm3 of 2.0 mol/dm3 hydrochloric acid neutralizes 25 cm3 of a sodium hydroxide solution:

HCl + NaOH NaCl + H2O. Calculate the concentration of the sodium hydroxide solution.

Figuring it out 2. Substitute the values for hydrochloric acid into the
1. Convert the volumes into dm3.
concentration equation (because you know its concentration).
15 cm3 = 15 = 0.015 dm3
25 cm3 = 1,000 2.0 mol/dm3 = amount of HCl
0.015 dm3
25 = 0.025 dm3
1,000 3. Rearrange the equation above, then solve.

amount of HCl = 2.0 × 0.015 = 0.03 mol

4. Figure out the amount of sodium hydroxide using the mole ratio in the balanced chemical equation.

1 mol of HCl reacts with 1 mol of NaOH, so 0.30 mol of HCl reacts with 0.30 mol of NaOH.

concentration of NaOH = 0.03 mol = 1.2 mol/dm3
0.025 (dm3)

Answer

The concentration of the sodium hydroxide solution is 1.2 mol/dm3.

Atom Economy Quantitative Chemistry 125

One of the ways to evaluate a chemical process is Key Facts
to calculate its atom economy. This is a measure of
its efficiency in converting reactants into a desired ✓ Reactions often make more than one
product. In many chemical processes, the desired
product is not the only one—other products called product. Some will be useful, but others
by-products may be produced, too. will be waste.

✓ Atom economy is a measure of how

efficiently reactants form a product.

✓ The higher the atom economy, the less

waste there is.

Equation percentage atom = total Mr of the desired product × 100
The atom economy of a economy total Mr of all reactants
reaction gives the percentage
of atoms in the reactants that
become atoms in the desired
product. You can calculate it
using this equation.

Calculating Atom Economy methane steam carbon dioxide hydrogen
(reactant) (reactant) (by-product) (desired
product)

Question

Most hydrogen is manufactured by CH4(g) + 2H2O(g) CO(g) + 4H2(g)
reacting methane with steam. Calculate
the atom economy of this process.

Figuring it out 3. Calculate the total relative formula
1. Calculate the relative formula masses (Mr) of the
masses of the reactants.
reactants and the desired product (if not given to you).
See page 107 for a reminder of how to do this. Carbon Mr of CH4 + Mr of 2H2O
dioxide (CO2) is a waste product so isn’t included here. = 16 + (2 × 18) = 52

Mr of CH4 = 12 + (4 × 1) = 16 4. Put your answers to steps 2 and 3 into
Mr of H2O = (2 × 1) + 16 = 18
Mr of H2 = 2 × 1 = 2 the equation above to calculate the
percentage atom economy.
2. Calculate the total relative formula mass of the desired
% atom economy = 8 × 100 = 15.4%
product. 52

Mr of 4H2 = 4 × (2 × 1) = 8

Answer

The atom economy of this process is 15.4%.

126 Quantitative Chemistry

The Advantages Key Facts

of Atom Economy ✓ Processes with high atom

Processes with high atom economies are more efficient economies reduce waste and the
than those with low atom economies (see page 125). use of raw materials.
They reduce the use of raw materials and limit harm to
the environment. They are important for sustainable ✓ High atom economy is important
development (see page 263), ensuring we meet our
needs without preventing people in the future from for sustainable development
meeting their needs. and profitability.

✓ The atom economy of a reaction

can be increased by finding a use
for waste products.

Resources steam hydrogen
Reactions with a low atom
economy can waste resources, C(s) + 2H2O(g) CO2(g) + 2H2(g)
which makes those resources
unsustainable. One way to Coal is mainly composed of carbon Carbon dioxide is a
make hydrogen involves and is a nonrenewable resource— waste by-product.
reacting coal with steam. it will run out if we keep using it.
This process has a low atom
economy, just 8.3%, so it
wastes a lot of coal.

Profits sulfur carbon disulfide
If you are making a lot of
waste, or the waste is CH4(g) + 4S(g) CS2(g) + 2H2S(g)
hazardous, a chemical
process may not be profitable. Methane is expensive. Hydrogen sulfide is a very
Carbon disulfide is a useful poisonous and corrosive gas.
industrial solvent. It is made It is expensive to remove and
by reacting methane with
sulfur. The atom economy dispose of responsibly.
for this reaction is 52.8%,
so just under half the mass
of the products is waste.

By-products C6H12O6(aq) ethanol
The atom economy of a
process can be increased plant sugars 2C2H5OH(aq) + 2CO2(g)
by finding a use for the
waste products, rather Waste carbon dioxide can be sold to
than throwing them away. manufacturers to carbonate drinks.
Ethanol is a useful biofuel. This increases the atom economy to
The atom economy for
making it is 51.1%. 100% as no waste is produced.

Percentage Yield Quantitative Chemistry 127

In chemical reactions, no atoms are made or Key Facts
destroyed, so the total mass stays the same. The
theoretical yield of a product is the maximum ✓ The actual yield is the mass actually
mass it is possible to make from a given mass of
reactants. However, you may not get the mass that made in a reaction.
you expect. The percentage yield of a reaction is
the mass of product actually made, compared to ✓ The theoretical yield is the maximum
the maximum theoretical mass of products.
possible mass that can be made.

✓ The percentage yield varies from 0%

(no product made) to 100% (maximum
mass of product made).

Theoretical yield Red–brown pieces of copper
You may be given the theoretical yield to use form in the reaction when
in a percentage yield calculation. It is copper oxide powder and
possible to calculate the theoretical yield if carbon are heated.
you know the mass of the limiting reactant.
For a reminder about limiting reactants, see
page 115. For a reminder about calculating
masses in reactions, see page 116.

percentage yield = mass of product actually made × 100
maximum theoretical
mass of product

An Example

Question Figuring it out Answer

When heated, copper oxide reacts The percentage yield can vary from The percentage
with carbon. Copper and carbon 100% (no product has been lost) to 0% yield is 75%.
dioxide are produced in the (no product has been made or collected).
reaction. In an experiment, the
actual yield of copper was 0.90 g percentage yield = 0.9 g × 100 = 75%
but the theoretical yield of copper 1.2 g
was 1.2 g. Calculate the percentage
yield of copper in the experiment.

128 Quantitative Chemistry Key Facts

100% Yield ✓ Actual yields are always less than 100%.
✓ Reversible reactions do not go to
Actual yields are less than theoretical yields.
The mass of product made is usually less than completion, so yields will be less
expected for two main reasons. Some of the than 100%.
product can revert to the original reactants in
reversible reactions (see page 191), and unwanted ✓ Side reactions result in unwanted
side reactions form by-products. Also, some of the
product is lost during separation and purification. by-products.

✓ Some product gets lost during

separation from the reaction mixture.

Reversible reactions N2 + 3H2 2NH3
Reversible reactions do not go to
completion. Some reactants will be nitrogen hydrogen This symbol means ammonia
left, so the yield is less than 100%. For the reaction is
example, nitrogen reacts with reversible.
hydrogen to form ammonia, and
ammonia breaks down to form
nitrogen and hydrogen.

Side reactions Product loss
Reactants may react in an unexpected When a liquid is filtered
way, forming unintentional products. to remove a solid,
For example, magnesium burns in air, some liquid or solid
reacting with oxygen to make magnesium always gets lost.
oxide. It also reacts with nitrogen in the
air to make magnesium nitride as it burns. Some liquid will get
left on the inside of
This is the intended reaction:
the beaker when
2Mg + O2 2MgO it’s transferred.

magnesium oxygen desired product Some liquid remains Some solid is
on the solid and in left on the
the filter paper. filter paper.

This side reaction happens at the same time:

3Mg + N2 Mg3N2

magnesium nitrogen unwanted
by-product

The
Chemistry

of Acids

130 The Chemistry of Acids Key Facts

The pH Scale ✓ The pH scale is a measure of

The pH scale is a way of measuring how acidic or how acidic or alkaline substances
alkaline a substance is. On this scale pH 7 is neutral are, and most substances fall within
—neither alkaline, nor acid. Values below 7 are acidic, the range of 0 to 14.
while values of 8 to 14 are alkaline. The pH of a
solution can be measured using a pH indicator (see ✓ Acidic substances have
below and page 134)—these change color at different
pH levels. lower pHs.

Universal indicator ✓ Alkaline substances have
The approximate pH can be determined by adding a
few drops of universal indicator to a sampled solution higher pHs.
and comparing the color against a color chart. The
range of colors for universal indicator is shown below. ✓ A substance with a pH of 7 is

neutral–neither acidic nor alkaline.

Sulfuric acid Vinegar Lemon juice Rainwater
The pH of lemon
A car battery Vinegar contains juice is usually Dissolved carbon
contains sulfuric ethanoic acid, around 2.5. dioxide makes rainwater
slightly acidic. Its pH is
acid with a pH and typically has typically around 5.5.
of about 1. a pH of about 2.

pH 0 1 2 3 4 5 6

Increasing acidity

The Chemistry of Acids 131

A Digital pH Meter 3.22 The pH is displayed as
a number, usually to
The pH of a substance can two decimal places.
be measured electronically
using an electronic probe The pH probe
that detects the number of is placed in
hydrogen ions (H+) in a the solution.
solution. The more hydrogen
ions there are, the more
acidic the solution is, and the
lower the pH.

A pH meter dipped in orange juice

Pure water Dishwashing liquid Bleach Sodium hydroxide

The pH of pure The pH of liquid Household bleach (dilute The pH of sodium
water is 7—it’s detergents varies a sodium hypochlorite hydroxide, which is used to
neutral, so neither lot, but is usually
alkaline nor acid. around pH 8. solution) has an alkaline clean drains, is around
pH of around 12. 14—it is very alkaline.

7 8 9 10 11 12 13 14

Neutral Increasing alkalinity

132 The Chemistry of Acids

Acids Key Facts

Acids are substances that release hydrogen ions (H+) ✓ When dissolved in water, acids
when added to water. A solution is described as acidic if
it has a pH of less than 7. Strong acids can be corrosive release hydrogen ions (H+).
while weak acids, such as citric acid (lemon juice) and
ethanoic acid (vinegar), are common in foods. ✓ A solution is acidic if has a pH of

Forming acids less than 7.
Ethanoyl chloride reacts instantly when added to
water to produce hydrogen chloride and ethanoic ✓ Acids are commonly found in foods
acid. Some of the hydrogen chloride escapes
from the beaker as gas, and some dissolves in and give them a sour taste.
the water to form hydrochloric acid.
How Acids Work

Ethanoyl chloride Acids ionize (break apart) in water to
(CH3COCl) is added to produce positive hydrogen ions (H+) and
a beaker of cold water. negative ions—for example, when the
covalent compound hydrogen chloride
(HCl) gas is dissolved in water.

A glass rod dipped in Water Positive hydrogen
ammonia is used to ions (H+)
test for hydrogen
chloride gas. Negative chloride
ions (Cl-)
Ammonia reacts
with hydrogen
chloride gas to form
ammonium chloride,
which produces
visible fumes.

Ethanoic acid and
hydrochloric acid
form in the beaker.

Hydrogen chloride gas
dissolved in water

The Chemistry of Acids 133

Bases Key Facts

A base is any substance that can neutralize an acid. ✓ A base is a substance that can
A soluble base—which releases hydroxide ions (OH−)
when added to water—is called an alkali. Bases have neutralize acids.
a pH greater than 7. Common household bases include
sodium bicarbonate, often used in baking and soaps. ✓ Soluble bases, called alkalis, release

Potassium reacts hydroxide ions (OH−) when mixed
with water to form an with water.
alkaline solution of
potassium hydroxide. ✓ Bases have a pH greater than 7.

How Alkalis Work

Alkalis ionize (break apart) in water to
release negative hydroxide ions (OH−) and
positive ions—for example, when potassium
hydroxide is added to water.

Negative Positive Water
hydroxide potassium
ions (OH−)
ions (K+)

Forming an alkali Phenolphthalein
When a Group 1 metal, such as indicator turns
potassium, is added to water, it pink in the
reacts to form hydrogen gas and an presence of alkalis
alkali metal hydroxide. This is why (see page 134).
Group 1 metals are also known as
the alkali metals. Bases

Alkalis and bases Alkalis
All alkalis are bases, (soluble
but many bases are bases)
insoluble (they do not
dissolve in water), so
these are not alkalis.

Potassium hydroxide
in water

134 The Chemistry of Acids Key Facts

Indicators ✓ Indicators are substances that change

Indicators are substances that change color color when mixed with acids and alkalis.
in acidic or alkaline conditions. There are many
types of indicator that produce vastly different ✓ Different colors appear at different,
colors, with specific colors appearing at certain pH
values. Universal indicator (see page 130) is a specific pH values.
mixture of several different indicators, and can be
used to measure the approximate pH of a solution. ✓ Universal indicator is a mixture of several

Litmus different indicators.
Litmus is an indicator made from lichen. It
changes from red (acid) to purple (neutral) to When red litmus
blue (alkaline). Blue litmus paper is used to paper is dipped
indicate the presence of acid, while red litmus
paper is used to check for alkalis. in an alkali, it
turns blue.
When blue litmus paper is
dipped in acid, it turns red. The solution
turns bright
Phenolphthalein pink when
Phenolphthalein is colorless in acidic
solutions but turns bright pink in the the pH is
presence of an alkali solution. The color above 8.
change is sharp and easy to see, and it’s a
popular choice in titrations (see page 136) The solution
with strong alkalis, such as sodium hydroxide. turns yellow
above about
Phenolphthalein indicator
is colorless below pH 8. pH 4.5.

Methyl orange
Methyl orange turns from red (acidic) to
orange to yellow (more alkaline). It changes
color over a range of pH values, so methyl
orange is used in titrations where
phenolphthalein will not work.

Methyl orange is
red below pH 3.

Neutralization The Chemistry of Acids 135

Neutralization is a chemical reaction between an Key Facts
acid and a base. If the quantities of acid and base
are just right, the resulting solution will be neutral ✓ Neutralization is a reaction between
with a pH of 7. When acids and bases react with each
other, the products are always a salt and water. The an acid and base.
salt formed depends on the acid and base used.
✓ Hydrogen ions (H+) from the acid
Sodium hydroxide
(a base) is added to combine with hydroxide ions (OH−)
hydrochloric acid. from the base to form water (H2O)
and a salt.

✓ The salt produced depends on the

acid and base used.

Reacting hydrochloric acid and sodium hydroxide
A few drops of universal indicator have been used
to monitor the reaction when sodium hydroxide is
added to hydrochloric acid. At first, the solution
stays red as the pH is below 7 (acidic). But as
more base is added, the solution turns green
(neutral), and then blue as the pH is now more
than 7 (alkaline).

Hydrochloric acid The solution turns
with a few drops of blue after the acid
universal indicator. becomes alkaline.

acid + base salt + water

hydrochloric acid sodium hydroxide sodium chloride water
HCl + NaOH +
NaCl H2O

How H+ ions Na+ ions The OH− ions combine
Neutralization Works with the H+ ions to
form water (H2O).
Acidic solutions contain Cl− ions OH− ions
hydrogen ions, while alkaline The Na+ ions combine with
solutions contain hydroxide Hydrochloric Cl− ions to form sodium
ions. These react together to acid chloride (NaCl).
form salt and water.

Sodium
hydroxide

136 The Chemistry of Acids Key Facts

Titrations ✓ Titration is a chemical technique

Titration is a technique that is used to find the used to find the concentration of an
concentration of an unknown solution (an acid or unknown solution.
alkali) by reacting it with a solution of known
concentration. A few drops of indicator are added ✓ The concentration of acids or alkalis can
so the amount of solution needed to cause a color
change can be recorded. For more on titration be calculated by carrying out titrations.
calculations, see page 124.
4. At the end of the
Burette
A burette is a piece of laboratory glassware titration, the titer
used to measure very small volumes. Most (volume of acid
burettes are marked from 0 cm3 (at the top) added) is recorded. If
to 50 cm3 (at the bottom). In this example, the initial volume
the burette is filled with acid. wasn’t zero, the
starting volume must
Calculating the Mean Titer be subtracted from

Question this reading.

Determine the mean titer from the results given 2. The tap on the
in the table below using two concordant (close
together) results. For accuracy, titrations are burette is turned,
repeated at least twice. allowing acid to be
added drop by drop.
Start volume 0.00 12.00 23.20 5.50
(cm3) 12.00 23.20 34.35 17.00 3. Acid is added
12.00 11.20 11.15 11.50
Final volume until the indicator
(cm3) changes color,

Titer showing the solution
(cm3) has been neutralized.

Figuring it out 1. An accurate
1. The closest results are 11.20 cm3 and 11.15 cm3
2. The mean of closest results (to two decimal points) volume of alkali is
added to the flask,
11.20 + 11.15 = 11.18 cm3
2 along with a few
drops of indicator.
Answer

Mean titer = 11.18 cm3

Strong and The Chemistry of Acids 137
Weak Acids
Key Facts
In chemistry, the words “strong” and “weak”
have specific meanings. In water, acids ionize ✓ Strong acids completely ionize in water—
(break up) into hydrogen ions (H+) and anions
(negative ions). All of the molecules in strong all their molecules break into ions in water.
acids ionize in water, while only a small number
of the molecules in weak acids ionize in water. ✓ Weak acids barely ionize at all in

Comparing strong water—only a small number of their
and weak acids molecules break into ions in water.
These flasks contain
solutions of a strong acid ✓ Strong acids have a lower pH than weak
and a weak acid that have
the same concentration— acids of the same concentration as they
the same amount of acid have more H+ ions.
molecules compared to the
amount of water. Universal This orange-
indicator has been added yellow color
to show the pHs. indicates that the
pH is about 4.
This red color
shows the pH
of this solution

is about 2.

Strong acid Weak acid

Ionization in Acids All of the acid Only a very
molecules ionize tiny number of
In strong acids, the (break up) into H+ molecules ionize.
molecules ionize ions and negatively
completely into H+ ions Weak acid
and anions (negative ions). charged ions.
In weak acids, only some
of the molecules ionize, so H+ ion
fewer H+ ions are released
into the solution. Negatively
charged ion

Strong acid

138 The Chemistry of Acids

Dilute and Key Facts

Concentrated Acids ✓ A dilute acid has a low ratio of acid

A dilute acid solution has a low ratio of acid molecules molecules to water.
to water, while a concentrated solution has a higher
ratio of acid to water. Remember that “strong” and ✓ A concentrated acid has a higher ratio
“weak” relate to the level of ionization of acids in water
(see page 137), and “dilute” and “concentrated” of acid to water.
relate to the amount of acid dissolved in the solution.
✓ “Strong” and “weak” refer to how

ionized an acid is in water, and “dilute”
and “concentrated” refer to the
amount of acid a solution contains.

Comparing dilute and If more acid is added,
concentrated acids the solution becomes
A concentrated acid solution will
have a lower pH than a dilute one, more concentrated.
because more H+ ions are present.

As water is added, the
solution becomes
more diluted.

A small amount of acid
is dissolved in this
dilute solution.

A lot of acid is
dissolved in this
concentrated solution.

Dilute acid Concentrated acid

How Concentration Works There is a low ratio
of acid molecules
It is possible to have both a concentrated to volume of water.
and dilute solution of a weak acid.
Likewise, concentrated and dilute There is a higher ratio
solutions of strong acids are possible. of acid molecules to
The hazardousness of an acid depends volume of water.
on both its concentration and strength.

Dilute solution Concentrated solution
of a weak acid of a weak acid

Reactions The Chemistry of Acids 139
with Bases
Key Facts
Acids react with bases to produce a salt and water.
There are several different kinds of base, including ✓ Metal oxides and metal hydroxides
metal hydroxides, metal oxides, and metal carbonates.
In each case, the salt produced forms from the metal react with acids to form a salt
ion in the base and the negative ion in the acid. and water.

✓ These are neutralization reactions.
✓ We can predict the salt that will form

from the acid and the metal ion
present in the base.

Acids and metal oxides

acid + metal oxide salt + water

hydrochloric + sodium sodium chloride + water
acid oxide
+ 2NaCl + H2O
2HCl Na2O

sulfuric acid + copper(II) oxide copper(II) sulfate + water

H2SO4 + CuO CuSO4 + H2O

Acids and metal hydroxides

acid + metal hydroxide salt + water

hydrochloric + sodium sodium chloride + water
acid hydroxide
+ NaCl + H2O
HCl NaOH

sulfuric acid + calcium calcium sulfate + water
hydroxide
H2SO4 + CaSO4 + 2H2O
Ca(OH)2

140 The Chemistry of Acids Key Facts

Reactions with ✓ Acids react with metal carbonates to
Metal Carbonates
form a salt, water, and carbon dioxide.
Acids react with metal carbonates to form a salt,
water, and carbon dioxide. This reaction between ✓ This is a neutralization reaction.
acids and metal carbonates is a neutralization ✓ You can predict the salt that will form
reaction (see page 135).
from the acid and the metal ion
Limestone and hydrochloric acid present in the carbonate.
Limestone is mostly calcium
carbonate (CaCO3), which reacts Hydrochloric acid is
with hydrochloric acid to form added to limestone.
carbon dioxide, water, and
calcium chloride salt. Limestone

Fizzing occurs when carbon
dioxide gas is produced.

Common Reactions

Metal carbonates react with acid to form a salt, water, and carbon dioxide.
We can figure out which salt forms by looking at the acid and the metal ion
in the metal carbonate. Some common examples are listed below:

acid + metal carbonate salt + water + carbon dioxide

hydrochloric acid + sodium sodium + water + carbon
carbonate chloride dioxide

2HCl + Na2CO3 2NaCl + H2O + CO2

sulfuric acid + calcium calcium + water + carbon
carbonate sulfate dioxide
H2SO4
+ CaCO3 CaSO4 + H2O + CO2

Making The Chemistry of Acids 141
Insoluble Salts
Key Facts
An insoluble salt may form when two solutions
containing soluble salts are mixed. In such cases, the ✓ Salts that don’t dissolve in water
insoluble salt (also known as the precipitate) can be
separated by filtration. A pure sample of the salt then are insoluble.
remains after the sample dries.
✓ An insoluble salt may form when
Making lead iodide
Lead iodide is a bright yellow compound that is insoluble two solutions containing soluble
in cold water. It can be made by mixing solutions of lead salts are mixed.
nitrate and potassium iodide, both of which are
colorless and soluble. ✓ The insoluble salt (precipitate)

1. Lead nitrate (Pb(NO3)2) 2. A bright yellow can be separated from the solution
by filtration, then dried to get a
is added to a solution of precipitate of lead pure sample.
potassium iodide (Kl).
iodide (PbI) forms. 3. A folded piece of filter
Pb(NO3)2 is
dissolved paper is placed in a funnel
in water. and the solution is passed
through it.
KI (in water)
4. A filtrate of lead iodide is left

in the filter paper and is rinsed
with distilled water to wash away
any traces of either soluble salt.

5. The lead iodide is

left to dry, resulting in
a pure, dry sample.

Reacting Potassium Iodide and Lead Nitrate Lead iodide is solid
and does not dissolve.
Potassium iodide and lead nitrate are both soluble. When their
solutions are mixed, the reaction between them produces
insoluble lead iodide and soluble potassium nitrate.

potassium + lead nitrate lead iodide + potassium
iodide nitrate

2KI(aq) + Pb(NO3)2(aq) PbI2(s) + 2KNO3(aq)

142 The Chemistry of Acids

Making Soluble Salts Key Facts

An acid reacts with a base to form a salt and water, ✓ To make a pure sample of a soluble
but unless you have precise quantities, the final
product will contain traces of one of the reactants. salt, you can either use precise
You can get around this by using a more insoluble quantities of acid and alkali so they
base than you need and filtering off the excess. react completely, or an excess of an
insoluble base.
Making pure copper sulfate
Copper(II) sulfate is a soluble, bright blue salt. ✓ When using an insoluble base, the
In this experiment it’s prepared by reacting
an excess of insoluble copper(II) oxide with excess solid is filtered off to leave a
a solution of sulfuric acid. pure solution of the soluble salt.

✓ Once the water has evaporated,

pure salt crystals are left.

3. Heating the filtrate 4. Remove the

gently removes some, evaporating basin
but not all, of the water. from the heat and
leave in a warm
It’s important not to place. This allows
overheat the sample, so the rest of the water
the evaporating basin is to evaporate slowly
and copper sulfate
heated on top of a crystals to form.
beaker of water.

Copper oxide 2. The product of the
powder
reaction is filtered to
1. An excess of
remove the unreacted
black copper(II)
oxide is mixed copper(II) oxide.
with sulfuric acid.

Making a Salt from Copper(II) Oxide and Sulfuric Acid

The reaction between copper(II) oxide and sulfuric acid produces a
soluble salt: copper(II) sulfate. An excess of copper(II) oxide is used to
make sure all the acid reacts. Here’s the equation for the above reaction.

copper(II) oxide + sulfuric acid copper(II) sulfate + water
+ H2O(l)
CuO(s) + H2SO4(aq) CuSO4(aq)

Metals
and Their
Reactivity

144 Metals and Their Reactivity

The Reactivity Series Key Facts

A reactivity series is a list of elements (most of them ✓ Some elements are more likely to
are metals) in order of their reactivity, from most
reactive at the top to least reactive at the bottom. chemically react than others.
Reactivity can mean how readily the element reacts
with other substances, but in this list it describes ✓ A reactivity series lists elements in
how easily the element loses electrons.
order of how readily they lose
List of elements electrons when they react.
These elements are commonly listed in a
reactivity series. A reactivity series can ✓ Elements that lose electrons easily
include all or just some of these elements.
are found at the top of reactivity
Most reactive series. Those that don’t are at
the bottom.
K
✓ These lists are usually made up of
Potassium
metals, but some nonmetals may
Na be included.

Sodium These elements are all very
reactive metals. They react
Li vigorously with water, oxygen,
and acids (see page 59).
Lithium
Calcium, magnesium, and
Ca aluminum are fairly reactive
metals and react with water.
Calcium
Carbon is often included in the reactivity
Potassium Mg series because it can be used to displace
Potassium is very reactive because its metals less reactive than it (see page 148).
atoms easily lose their outermost electrons Magnesium
during reactions. Zinc and iron are fairly reactive
Al metals and react with water.

Aluminum Hydrogen is often included in the reactivity
series because it can be used to displace
C metals less reactive than it.

Carbon Copper, silver, and gold are
unreactive metals.
Zn

Zinc

Fe

Iron

H

Hydrogen

Cu

Copper

Ag

Silver

Gold Au
Gold isn’t very reactive because its atoms
don’t easily lose their outermost electrons Gold
during reactions.
Least reactive

Reactions with Acids Metals and Their Reactivity 145

Some metals react vigorously with acids. Metals that Key Facts
react spontaneously with acids at room temperature are
found at the top of the reactivity series (see opposite ✓ Some metals react more vigorously
page). When metals react with acids, their atoms lose
electrons. The most common products of this reaction with acids than other metals.
are a solution of a metal salt and hydrogen gas.
✓ When metals react with acids, they
Metals reacting with hydrochloric acid
Magnesium, zinc, iron, and lead all have different levels of usually produce hydrogen gas and
reactivity. When placed in hydrochloric acid, magnesium a solution of the metal salt.
reacts vigorously, but the lead barely reacts at all.
Only a few hydrogen gas bubbles
Lots of hydrogen gas bubbles are produced when an iron screw
are produced when magnesium is placed in hydrochloric acid.
reacts with hydrochloric acid.

Magnesium Zinc Iron Lead

Equation
A reaction between a metal and an acid produces a salt and hydrogen gas.

metal + acid metal salt + hydrogen

146 Metals and Their Reactivity

Reactions with Water Key Facts

Most metals react slowly with water, if they react at all. ✓ Group 1 and Group 2 metals
However, Group 1 and Group 2 metals are exceptions.
When placed in water at room temperature, they react are so reactive that they react
vigorously, leaving behind a metal hydroxide (alkaline spontaneously with water.
solution) and producing hydrogen gas. Some metals
even react with water vapor (see opposite page). ✓ When dropped in water, the

Metals react with water metals fizz and dissolve.
Potassium, sodium, and lithium (Group 1 metals) and
calcium (a Group 2 metal) react vigorously with water. ✓ Group 1 and Group 2 metals react

with water to produce a metal
hydroxide and hydrogen gas.

A lump of potassium Bubbles of Lithium reacts with water Calcium hydroxide forms
fizzes loudly and hydrogen gas. to produce large bubbles as a cloudy precipitate in
even jumps. of hydrogen gas.
the solution.

Potassium Sodium Lithium Calcium

Equation
A reaction between a metal and water produces a metal
hydroxide (alkaline solution) and hydrogen gas.

metal + water metal hydroxide + hydrogen

Metals and Their Reactivity 147

Reactions Key Facts
with Steam
✓ Some metals won’t react with liquid
Some metals will react with steam (water as a gas), also
known as water vapor, at high temperatures. In these water, but will react with steam at
cases, the products are a metal oxide and hydrogen gas. high temperatures.

✓ In these cases, the products are

a metal oxide and hydrogen.

Magnesium oxidized Test tube
A ribbon of magnesium burns in
steam to produce magnesium
oxide and hydrogen gas.

Damp cotton ball Ribbon of Gas tube
magnesium

1. The damp cotton ball 2. The ribbon of 3. This produces hydrogen

is gently heated by a magnesium starts gas, which is burned off at
Bunsen burner flame to
to react with steam the end of the test tube
produce steam.
and burn. (see page 231).
4. Magnesium starts to
5. The flame at the end of
react more vigorously,
producing clouds of the test tube grows as more
magnesium oxide. hydrogen gas is released.

metal + water metal oxide + hydrogen

148 Metals and Their Reactivity Key Facts

Extracting Metals ✓ Metals that are less reactive than
with Carbon
carbon can be extracted from their
Metals that are less reactive than carbon (see page ores by using carbon.
144) can be extracted from their ores by using
carbon. Copper and iron can both be produced in ✓ Iron can be separated from its ore
this way, although the sample is not very pure.
using carbon.
Iron ore is added to the
blast furnace, as well as ✓ This process is carried out in
coke and limestone, which
factories inside a blast furnace.
both contain carbon.
Blast furnace
Extracting iron involves a very hot reaction,
so the heated iron ore and carbon-
containing compounds are held in huge
vats. The symbol and word equations for
this reaction are shown below.

This reaction produces carbon
dioxide gas, which leaves the blast
furnace as a waste gas.

Carbon dioxide gas

A blast of hot air is added to the Molten iron is collected at the
blast furnace to help the bottom of the blast furnace.

reaction between iron oxide and
carbon take place.

Molten slag (useless
by-products of the reaction) is

funnelled out of the
blast furnace.

iron oxide + carbon iron + carbon dioxide

2Fe2O3 + 3C 4Fe + 3CO2

Redox Reactions Metals and Their Reactivity 149

The word redox is derived from the words Key Facts
“reduction” and “oxidation.” In redox reactions,
electrons are transferred from one substance to ✓ Redox is short for “reduction”
another. One substance is reduced (gains electrons)
while the other is oxidized (loses electrons). A and “oxidation.”
thermite reaction (a reaction that involves heating
metals) is an example of a redox reaction. ✓ In redox reactions, one substance

Thermite reaction transfers electrons to another.
Powdered aluminum metal reacts with
iron(III) oxide to form aluminum oxide ✓ A well-known redox reaction is
and iron metal. In this case, the iron is
reduced, while the aluminum is oxidized. thermite, in which aluminum loses
electrons while iron gains them.
The aluminum sparks brightly
during the reaction. The metal tray contains
the explosive reaction.

Thermite reaction formula equation aluminum oxide + iron
aluminum + iron oxide
Al2O3 + 2Fe
2Al + Fe2O3

150 Metals and Their Reactivity Key Facts

Group 7 Displacement ✓ In a displacement reaction, a more
Reactions
reactive element displaces a less
In a displacement reaction, a more reactive element reactive element from its compound.
displaces a less reactive element from its compound.
Group 7 elements react in this way. Their reactivity ✓ The reactivity of Group 7 elements
decreases down the group (see page 70), so a higher
element can displace those below it. decreases down the group.

✓ Chlorine, for example, can displace

both bromine and iodine from their
compounds.

Chlorine Chlorine water added Chlorine water added
displacement
Chlorine is more Chlorine displaces Chlorine displaces
reactive than both bromine and the iodine and the
bromine and iodine, solution turns yellow. solution turns
so it’ll displace both brown.
of them from their
compounds with Displacement of bromine Potassium Displacement of iodine
potassium. iodide solution

Potassium
bromide solution

Bromine Bromine water added Bromine water added
displacement
Bromine is more Bromine doesn’t Bromine displaces
reactive than iodine, displace chlorine in iodine and the
but less reactive than the solution, so the solution turns
chlorine—so it’ll only solution is the color brown.
displace iodine from of bromine water.
its compounds with
potassium. No displacement Potassium Displacement of iodine
iodide solution
Potassium
chloride solution

Iodine displacement Iodine solution added Iodine solution added
Iodine is less reactive
than chlorine or Iodine doesn’t displace Iodine doesn’t
bromine, so won’t chlorine in the solution, displace
displace either of so the solution is the bromine in the
them from their color of iodine solution. solution, so the
compounds with solution is the
potassium. color of iodine
solution.

Potassium No displacement Potassium No displacement
chloride solution bromide solution