Chapter 1 Stoichiometric relationships
1.1 The particulate nature of matter
1.1.1
States of matter
Solid
Liquid
Gas
Particles closely
packed
Particles slightly more spread out
Particles very spread out
Strong forces between
particles, they vibrate
about fixed positions
Weaker forces between particles,
they can move past each other
Negligible forces between
particles, they move
randomly
Fixed shape
Take the shape of the container
No fixed shape
Fixed volume
Fixed volume
No fixed volume
Changes of state
Change of state
Description
Is energy absorbed or
released?
Sublimation
Solid to gas with no liquid state
Absorbed
Deposition
Gas to solid with no liquid state
Released
Evaporation
Liquid to gas
Absorbed
Boiling
Liquid to gas
Absorbed
Condensation
Gas to liquid
Released
Freezing
Liquid to solid
Released
Melting
Solid to liquid
Absorbed
Changes from a more-ordered state to a less-ordered state (such as a liquid to a gas) are
endothermic. Changes from a less-ordered state to a more-ordered state (such as a liquid to a
solid) are always exothermic.
State symbols:
State
Symbol
Examples
Solid
(s)
Na (s), Mg (s), C (s)
Liquid
(l)
H2O (l), Br2 (l)
Gas
(g)
O2 (g), CO2 (g)
In aqueous solution
(aq)
NaCl (aq), H2SO4 (aq)
Density
Mass per unit volume
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1.1.2 Elements and compounds
An atom of an element is the smallest particle that shows the characteristic properties
of that element.
An element is made up of the same kind of atom and cannot be broken down by
chemical means into a simpler substance.
A compound is made up of two or more different elements that are chemically
combined.
A molecule consists of two or more atoms that are chemically bonded together. The
atoms can be the same, as in O2, or different, as in H2O.
1.1.3 Mixtures
 A homogeneous mixture has the same composition throughout
 A heterogeneous mixture has a non-uniform composition.
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1.1.3 Chemical reactions and equations
Chemical reactions involve the formation of new chemical substances.
The chemical change taking place during a reaction can be represented by a
chemical equation.
The law of the conservation of mass states that mass is conserved in a chemical
reaction.
Predicting the products
o Combustion: H2O and CO2
o Acid + base: Salt and water
1.2.1 Relative atomic mass
The relative formula (or molecular) mass (Mr) of a compound is the weighted average mass
of the compound compared to 1/12 the mass of an atom of carbon-12. As it is a relative scale,
values for relative formula (or molecular) masses are dimensionless (do not have units).
The relative atomic mass (Ar) is the weighted average mass of an atom compared to 1/12 the
mass of an atom of carbon-12. As it is a relative scale, values for relative atomic masses are
dimensionless (do not have units).
The relative formula (or molecular) mass (Mr) of a compound is the weighted average mass
of the compound compared to 1/12 the mass of an atom of carbon-12. As it is a relative scale,
values for relative formula (or molecular) masses are dimensionless (do not have units).
1.2.2 The mole concept
A mole is a standard scientific unit for measuring large quantities of very small entities such
as atoms, defined as containing exactly 6.02214076 × 1023 elementary entities.
The molar mass (M) is the mass in grams of one mole of a substance. The unit for molar
mass is grams per mole (g mol-1).
1.2.3 Empirical and molecular formula
An empirical formula is the lowest whole number ratio of atoms (or ions) in a
compound.
A molecular formula is the actual number of atoms in a compound.
1.3.1 Limiting and excess reagents
 The coefficients in a balanced chemical equation tell us the molar ratio of the
reactants and products.
 The limiting reactant (reagent) limits the amount of product that can be made in a
chemical reaction.
 The excess reactant (reagent) is the reactant that remains at the end of a reaction.
Procedure:
1) Convert from mass in grams to amount (in mol).
2) Divide each amount (in mol) by the coefficient in the balanced equation.
3) The lowest value(s) is/are the limiting reactant(s) and the highest is the excess
reactant.
1.3.2 Theoretical yield
 The theoretical yield is the maximum amount of product that can be produced
assuming that all the limiting reactant has reacted.
 The actual yield is the amount of product that is actually produced in a chemical
reaction.
Gases
4 magnitudes:
 Pressure
 Temperature
 Volume
 Number of moles
1.3.3 Avogadro's law and molar volume of a gas
 The kinetic molecular theory of gases:
o The particles in a gas are in constant, random, straight-line motion.
o There are negligible forces of attraction (intermolecular forces) between the
particles.
o Collisions between particles or with the walls of the container are perfectly
elastic (no energy is lost).
o The distance between the particles is much greater than the size of the
particles, therefore, gas particles have negligible volume.
o The kinetic energy of the particles in a gas is directly proportional to the
absolute temperature (in kelvin).
Representation of gases:

The pressure exerted by a gas in a container is determined by how frequently the
particles hit the walls of the container. SI unit Pascal (Pa) N*m-2 , but commonly given
I bars where 105Pa=1bar.

Avogadro’s Law states that equal volumes of gases measured at the same conditions
(the same temperature and pressure) contain equal numbers of particles. This means
that we can relate the volume of any gas to the amount (in mol) of the gas, however
due to differences in molar mass, the mass will be different.
Temperature scales
 Working with gases we use absolute temperature scale, with the values in kelvin (K).
 To convert from oC to K, add 273; for example, 25 oC is equal to 298 K.
 Absolute zero (0 K) is the lowest possible temperature on the Kelvin scale.
o The motion of particles is minimal.
o A substance has no transferable heat energy.
o An ideal gas at constant pressure would reach zero volume.
STP – Standard temperature and pressure
 Temperature is a measure of average kinetic energy per molecule in a substance.
 T=273K=0℃
 TK= T℃ + 273
 Pressure is continuous physical force exerted on or against an object by something in
contact with it. Force applied perpendicular to the surface of an object per unit area
over which that force is distributed
p=F/A
 p= 100kPa (kilo Pascal)
SATP – Standard ambient temperature and pressure
 T=298K=25℃
 p= 100kPa
Reacting gas volume ratios
 Under the same conditions of temperature and pressure, the molar ratio of a balanced
equation also gives us the volume ratio of the gases.
2mol
20 cm3
1 mol
10 cm3
Molar volume of a gas
2mol
20 cm3
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The molar volume of a gas is the volume occupied by one mole of a gas at conditions
of standard temperature and pressure (STP).
This states that one mole of a gas at STP occupies a volume of 22.7 dm3
1.3.4 The gas laws
 Volume of a gas is the volume of its container.
 Pressure of a gas is a result of the particles of the gas colliding with the walls of the
container.
 Describes the behavior of a gas when subjected to changes in temperature and
pressure. The general trends in behavior with changing conditions of temperature and
pressure are the same for all gases.
 Ideal gases are gases that exhibits the five postulates of the kinetic molecular theory,
as well as obeying the gas laws.
Boyle's Law − the relationship between pressure and volume

At constant temperature and number of moles, the pressure and volume of a fixed
mass of an ideal gas are inversely proportional to each other. This means that if the
pressure of a fixed mass of gas at constant temperature is doubled, the volume halves.
Charles' Law − the relationship between temperature and volume
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At constant pressure and n of moles, the volume of a fixed mass of an ideal gas is
directly proportional to its absolute temperature (in kelvin).
This means that if the absolute temperature of a fixed mass of an ideal gas is doubled,
the volume of the gas will also double
Gay-Lussac's Law − the relationship between temperature and pressure

At constant volume and n of moles, the pressure of a fixed mass of an ideal gas is
directly proportional to its absolute temperature (in kelvin). This means that if the
absolute temperature of a fixed mass of an ideal gas is doubled, the pressure of the gas
will also double.
Relationships
P1*V1= P2*V2
T1/V1= T2/V2
P1/T1= P2/T2
The combined gas law
The general gas equation
1.3.5 The ideal gas equation
and
P is the pressure in pascals (kPa)
V is the volume in dm3
n is the amount of gas (in mol)
R is the universal gas constant (8.31 J K–1 mol-1)
T is the absolute temperature (in kelvin)
When using the ideal gas equation, be careful to use the correct units:
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Pressure, P: must be in Pa; if kPa are given, multiply by 103
Volume, V: must be in m3; if dm3 are given, divide by 103, or if cm3 are given, divide
by 106
Amount in mol, n: this can be calculated using n = m / M, where m is the mass in
grams and M is the molar mass.
Temperature, T: must be converted to kelvin (K); if °C is given, add 273 (or, more
precisely, add 273.15).
Solving tasks
If gases are at STP, use V=22.7dm3
- If gases are not at STP, use PV = nRT
- To solve for density, replace n with m/M
1.3.6 Real gasses
 Real gases deviate from ideal gas behavior under two conditions: at high pressures and
low temperatures.
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At very high pressure the gas particles are closer together. Under these conditions,
the actual volume of the particles becomes significant.
At low temperatures, the particles move less rapidly (have lower average kinetic
energy). This means that there is a greater opportunity for intermolecular forces
between the particles to have an effect.
1.3.7 Solutions and concentrations
Solution
 Substances dissolved in water will be in ionic form

Homogeneous mixture (uniform composition throughout)

The concentration of a solution is the amount (in mol) or mass (in g) of solute
per volume of solution.
Molar concentration: Square bracket notation is used to denote the molar
concentration of a solute in units of mol 𝑑𝑚−3.

Dilute solutions
 A relatively small amount of solute dissolved in the solution.
 Concentration is expressed in parts per million (ppm), calculated using the
equation:
 This ppm to molarity formula for dilute solutions is:
ppm = moles/L * molar mass * 1000
A 25.0 g sample of river water contains 5.00 × 10-4 g of lead (Pb). Calculate the concentration
in ppm.

concentration (ppm) = (mass of solute / mass of solution) × 106

concentration = (5.00 × 10-4 g) / 25.0 g + 5.00 × 10-4 g) × 106

concentration = 20.0 ppm
Standard solutions
 A standard solution is a solution with an accurately known concentration. A
primary standard solution is made using a primary standard. A primary
standard is a substance that has the following properties:
o High purity (99.9 %).
o High molar mass.
o Low reactivity.
o Does not change composition in contact with air.
Making a primary standard solution:
Serial dilution
 Diluting a stock solution multiple times, usually by the same factor, which
results in an exponential decrease in concentration.
 Continued dilutions will decrease the concentration by a factor of ten each time.
A 1.00 cm3 sample of a 5.00 mol dm-3 solution is made up to 10.0 cm3 by adding 9.00 cm3
of distilled water. The procedure is carried out a total of five times. Determine the final
concentration of the solution.
 Each time, the concentration decreases by a factor of 10, so the final
concentration will be 5.00 × 10−5 mol dm-3.
Dissolution
Solid+liquid
NaCl(aq)
+
 Na (aq) +Cl (aq)
The water molecule is a polar molecule and applies a force able to break apart the ionic
attractions/structure of the NaCl, creating ions in the solution.
Density of charge (σ)
Dilution
Liquid+Liquid
HCl(aq)
+
 H (aq) +Cl (aq)
1.3.8 Volumetric analysis
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Precise measurement of volumes to calculate the concentration of a solution.
Relies on precise equipment.
Pieces of glassware (calibrated graduation, varying degrees of precision):
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(a)Beaker – a common piece of apparatus used to hold solutions. In general,
beakers should not be used to measure the volumes of a solution due to their
low precision.
(b) Erlenmeyer/conical flask – used in titrations, they are tapered at the top to
allow solutions to be swirled without the risk of spillage.
(c) Measuring cylinder – used to measure volumes of solutions. More precise
than a beaker but less precise than a volumetric pipette.
(d) Volumetric flask – used to make up a precise volume of a solution. They
range in size from 50 cm3 to 1 dm3.
(e) Volumetric pipette – used to precisely measure a specific volume of
solution.
(f) Burette – used to deliver a precise volume of solution in a titration.
Titration
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A method of volumetric analysis to determine concentration of a solution.
Repeat trials are necessary. repeat trials.
o 1st trial - rough titration, not used to calculate the average volume.
o Subsequent volumes should ideally be within 0.10 cm3 of each other
(concordant values). These volumes are then used to calculate the average
volume of the titrant used in the titration.
Practical steps
1. A burette is filled with a standard solution of known concentration (the titrant/titrating
agent).
2. A carefully measured volume of the solution with the unknown concentration (the
analyte) is placed in a conical flask below the burette.
3. An indicator is used to determine the end-point of the titration, added to the conical
flask.
Worked task
 We have a NaOH solution of unknown concentration.
 By titration (chemical reaction), we can calculate the yield of the titration and find the
initial concentration.
 Here, we can use a neutralization reaction:
 NaOH(aq) + HCl(aq)  NaCl(aq) + H2O
 Base
+ Acid  Salt
+ Water
 BTB indicator which changes color, yellow indicates acid, blue indicates base and
green indicates ph 7.
 HCl C=0.1mol*dm-3
 NaOH C=?
 Vi=0cm3
 Vi=10cm3
3
 Vf=39.5cm
 Vuseed=Vf-Vi=39.5cm3
 CB*VB= CA*VA
nB= nA
 CB*10cm3= 0.1*39.5cm3
CB= 0.1*39.5cm3 : 10cm3
CB= 0.395mol*dm-3= 0.4mol*dm-3
Back titration

Titration done in reverse

An excess of titrant is added to the analyte and the excess titrant is then titrated to
determine how much excess titrant remains
Formula collection
Density
Mass per unit volume
The mole concept
1.2.3 Empirical and molecular formula
1.3.2 Theoretical yield
1.3.7 Solutions and concentrations
Dilute solutions
1.3.3 Avogadro's law and molar volume of a gas
1.3.4 The gas laws
Relationships
P1*V1= P2*V2
T1/V1= T2/V2
P1/T1= P2/T2
The combined gas law
The general gas equation
1.3.6 The ideal gas equation
and
P is the pressure in pascals (kPa)
V is the volume in dm3
n is the amount of gas (in mol)
R is the universal gas constant (8.31 J K–1 mol-1)
T is the absolute temperature (in kelvin)