Download 3. Moles and Formulae

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Counting atoms and molecules
When conducting a chemical reaction, it is often important
to mix reactants in the correct proportions. This prevents
contamination of the products by wasted reactants.
However, atoms are very
small and impossible to count
out. In order to estimate the
number of atoms in a sample
of an element, it is necessary
to find their mass.
The mass of an atom is
quantified in terms of
relative atomic mass.
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Relative atomic mass
The relative atomic mass (Ar) of an element is the mass of
one of its atoms relative to 1/12 the mass of one atom of
carbon-12.
relative atomic mass
average mass of an atom × 12
=
(Ar)
mass of one atom of carbon-12
Most elements have more
than one isotope. The Ar of
the element is the average
mass of the isotopes, taking
into account the abundance of
each isotope. This is why the
Ar of an element is frequently
not a whole number.
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Relative molecular mass
The relative molecular mass (Mr) of a covalent substance
is the mass of one molecule relative to 1/12 the mass of
one atom of carbon-12.
Mr can be calculated by adding together the masses of
each of the atoms in a molecule.
Example: what is the Mr of H2SO4?
1. Count number of atoms
(2 × H) + (1 × S) + (4 × O)
2. Substitute the Ar values
(2 × 1.0) + (1 × 32.1) +
(4 × 16.0)
3. Add the values together
2.0 + 32.1 + 64.0 = 98.1
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Relative formula mass
The equivalent of relative molecular mass for an ionic
substance is the relative formula mass.
This is the mass of a formula unit relative to 1/12 the mass
of one atom of carbon-12. It is calculated in the same way
as relative molecular mass, and is represented by the same
symbol, Mr.
Example: what is the Mr of CaCl2?
1. Count number of atoms
(1 × Ca) + (2 × Cl)
2. Substitute the Ar values
(1 × 40.1) + (2 × 35.5)
3. Add the values together
40.1 + 71.0 = 111.1
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Calculating relative formula mass
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Moles and Avogadro's number
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Moles, mass and Ar / Mr
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Moles, mass and Mr calculations
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Avogadro’s law
In 1811 the Italian scientist Amedeo Avogadro developed a
theory about the volume of gases.
Avogadro’s law:
Equal volumes of different gases at the same pressure
and temperature will contain equal numbers of particles.
For example, if there are 2 moles of O2 in 50 cm3 of oxygen
gas, then there will be 2 moles of N2 in 50 cm3 of nitrogen
gas and 2 moles of CO2 in 50 cm3 of carbon dioxide gas at
the same temperature and pressure.
Using this principle, the volume that a gas occupies will
depend on the number of moles of the gas.
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Molar volumes of gases
If the temperature and pressure are fixed at convenient
standard values, the molar volume of a gas can be
determined.
Standard temperature is 273 K and pressure is 100 kPa.
At standard temperature and pressure, 1 mole of any gas
occupies a volume of 22.7 dm3. This is the molar volume.
Example: what volume does 5 moles of CO2 occupy?
volume occupied = no. moles × molar volume
= 5 × 22.7
= 113.5 dm3
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Ideal gas equation
How is the number of moles in a gas at other temperatures
and pressures calculated?
The ideal gas equation relates pressure, volume, number
of moles and temperature for a gas.
pV = nRT
p = pressure in Pa
n = number of moles
V = volume in m3
R = gas constant: 8.31JK-1 mol-1
T = temperature in Kelvin
A gas that obeys this law under all conditions is called
an ideal gas.
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Ideal gas equation: converting units
It is very important when using the ideal gas equation that
the values are in the correct units.
The units of pressure, volume or temperature often need
to be converted before using the formula.
Pressure
to convert kPa to Pa:
× 1000
Volume
to convert dm3 to m3:
to convert cm3 to m3:
÷ 1000 (103)
÷ 1 000 000 (106)
Temperature
to convert °C to Kelvin: + 273
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Calculating the Mr of gases
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Using the ideal gas equation
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Ideal gas calculations
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Types of formulae
The empirical formula of a compound shows the
relative numbers of atoms of each element present,
using the smallest whole numbers of atoms.
For example, the empirical formula of hydrogen peroxide
is HO – the ratio of hydrogen to oxygen is 1:1.
The molecular formula of a compound gives the actual
numbers of atoms of each element in a molecule.
The molecular formula of hydrogen peroxide is H2O2 – there
are two atoms of hydrogen and two atoms of oxygen in each
molecule.
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Determining empirical formulae
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Percentage by mass
Elemental analysis is an analytical technique used to
determine the percentage by mass of certain elements
present in a compound.
To work out the empirical
formula, the total mass of
the compound is
assumed to be 100 g, and
each percentage is turned
into a mass in grams.
If necessary, the mass of any elements not given by
elemental analysis is calculated. The empirical formula of
the compound can then be calculated as normal.
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Calculating empirical formulae
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Calculating molecular formulae
The molecular formula can be found by dividing the Mr by
the relative mass of the empirical formula.
Example: What is the molecular formula of hydrogen
peroxide given that its empirical formula is HO and
the Mr is 34?
1. Determine relative mass of empirical formula:
empirical formula mass = H + O = 1.0 + 16.0 = 17
2. Divide Mr by mass of empirical formula to get a multiple:
relative molecular mass = 34 = 2
multiple =
17
mass of empirical formula
3. Multiply empirical formula by multiple:
HO × 2 = H2O2
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Formulae calculations
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Glossary
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What’s the keyword?
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Multiple-choice quiz
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