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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.

Relative atomic mass

relative atomic mass

(Ar)

average mass of an atom × 12

mass of one atom of carbon-12

=

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.

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.

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?

(2 × H) + (1 × S) + (4 × O)

1. Count number of atoms

(2 × 1.0) + (1 × 32.1) + (4 × 16.0)

2. Substitute the Ar values

2.0 + 32.1 + 64.0 = 98.1

3. Add the values together

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 × Ca) + (2 × Cl)

1. Count number of atoms

(1 × 40.1) + (2 × 35.5)

2. Substitute the Ar values

40.1 + 71.0 = 111.1

3. Add the values together

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 50cm3 of oxygen gas, then there will be 2 moles of N2 in 50cm3 of nitrogen gas and 2 moles of CO2 in 50cm3 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.

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 273K and pressure is 100kPa.

At standard temperature and pressure, 1 mole of any gas occupies a volume of 22.7dm3. This is the molar volume.

Example: what volume does 5 moles of CO2 occupy?

volume occupied = no. moles × molar volume

= 5 × 22.7

= 113.5dm3

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

V = volume in m3

n = number of moles

R = gas constant: 8.31JK-1mol-1

T = temperature in Kelvin

A gas that obeys this law under all conditions is called an ideal gas.

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)

÷ 1000000 (106)

Temperature

to convert °C to Kelvin:

+ 273

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.

The molecular formula of a compound gives the actual numbers of atoms of each element in a molecule.

For example, the empirical formula of hydrogen peroxide is HO – the ratio of hydrogen to oxygen is 1:1.

The molecular formula of hydrogen peroxide is H2O2 – there are two atoms of hydrogen and two atoms of oxygen in each molecule.

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 100g, 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.

Calculating molecular formulae

relative molecular mass

34

=

= 2

multiple =

17

mass of empirical formula

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:

3. Multiply empirical formula by multiple:

HO × 2 = H2O2

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