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# Formulae

## Molecular formula

A molecular formula shows the number of the different atoms in a simple covalent molecule.

In a molecular formula, the chemical elements are represented by their symbols (e.g. "$\ce{O}$" for oxygen).

Subscripts (for example the "2" in $\ce{H2O}$) indicate how many atoms of each element are present in a molecule. If there is no subscript, then only one atom of that element is present.

Carbon dioxide has the formula $\ce{CO2}$. It consists of one carbon atom ($\ce{C}$) and two oxygen atoms ($\ce{O}$).

The letter in parentheses after the formulae indicates the state of the compound:

• (s) means the compound is a solid.
• (l) refers to a liquid.
• (g) indicates the substance is a gas.
• (aq) refers to a compound that is dissolved in water (aqueous).
Components of the molecular formula
Component Meaning Example
Element symbol Types of atoms in the molecule ${\definecolor{tred}{RGB}{136,24,28}\color{tred}\ce{CaCO}}\ce{_3}{(s)}$
Subscripts Number of atoms of each element in the molecule $\ce{CaCO}{\definecolor{tred}{RGB}{136,24,28}\color{tred}\ce{_3}}{(s)}$
Letters in parentheses Phase of the compound or element $\ce{CaCO3}\definecolor{tred}{RGB}{136,24,28}\color{tred}{(s)}$

## Empirical formulae

An empirical formula gives the relative number of each type of atom present in a molecule.

It is different from a molecular formula which indicates the absolute number of atoms of different elements in a molecule.

Empirical formulae are always listed with the simplest possible whole number ratios.

The empirical formula for ethene ($\ce{C2H4}$) is ($\ce{CH2}$) because there are two hydrogen atoms for each carbon atom.

Empirical formulae are the only possible formulae to use for ionic compounds and giant molecular substances because they are not simple, individual molecules.

The formula for silicon dioxide (quartz) is $\ce{SiO2}$ because there is one silicon atom for every 2 oxygen atoms in the giant molecular structure.

Empirical formulae are often used when dealing with molecules because they are easier to determine from experimental evidence than molecular formulae.

## Calculating empirical formulae

The empirical formula of a compound can be calculated if the percentage mass of each element in the compound are known.

We first assume that there are 100 grams of the compound. Then the mass of each element can be calculated and converted to moles using molar mass values.

Pentene is approximately 85.7% carbon and 14.3% hydrogen by mass. 100 grams of pentene thus contain 85.7 grams of carbon and 14.3 grams of hydrogen.

These masses are equivalent to 7.14 moles of carbon and 14.16 moles of hydrogen.

The number of moles of each element should then be compared using ratios to determine the empirical formula.

In the case of pentene, the molar ratio of carbon to hydrogen is approximately 7:14, which reduces to 1:2. The empirical formula is thus $\ce{CH2}$.

## Calculating molecular formulae

The molecular formula can be determined from the empirical formula if the molar mass of the compound is known.

The following steps are taken to calculate the molecular formula:

• Find the molar mass of the actual compound.
• Calculate the molar mass given by the empirical formula.
• Divide the molar mass of the compound by the molar mass from the empirical formula.
• Multiply the subscripts in the empirical formula using the previous result to obtain the molecular formula

Pentene has an empirical formula of $\ce{CH2}$ and a molar mass of approximately 70 g/mol. The molar mass of the empirical formula is approximately 14 g/mol.

The molecular formula thus must have a molar mass 5 times greater than that of the empirical formula, and the ratio of hydrogen to carbon atoms must stay the same.

The molecular formula is therefore $\ce{C5H10}$.

## Ion charge imbalances

A cation has more protons than electrons. The superscript number indicates the exact imbalance.

$\ce{Li^+}$ has 3 protons but just 2 electrons. It has an imbalance of 1. $\ce{Be^2+}$ has 4 protons but just 2 electrons. It has an imbalance of 2.

The overall charge is positive in these cases because protons are positively charged while electrons are negatively charged.

An anion has more electrons than protons. The superscript number indicates the exact imbalance.

$\ce{F^-}$ has 9 protons but 10 electrons. It has an imbalance of 1. $\ce{O^2-}$ has 8 protons but 10 electrons. It has an imbalance of 2.

The overall charge is negative because the negatively charged electrons outnumber the positively charged protons.

## Ionic bonding charges

Superscripts in a chemical formula denote charges of ions.

$\ce{Mg^2+}$ has a charge of $+2$ and $\ce{O^2-}$ has a charge of $-2$.

When $n=1$ (i.e. the charge is one), the number $1$ is usually omitted. We write $\ce{Li+}$ instead of $\ce{Li^1+}$ and $\ce{F^-}$ instead of $\ce{F^1-}$.

Common ions and their charges
Element Name of ion Formula Charge
$\ce{Li}$ Lithium $\ce{Li+}$ $+1$
$\ce{Mg}$ Magnesium $\ce{Mg^2+}$ $+2$
$\ce{Al}$ Aluminium $\ce{Al^3+}$ $+3$
$\ce{N}$ Nitride $\ce{N^3-}$ $-3$
$\ce{O}$ Oxide $\ce{O^2-}$ $-2$
$\ce{F}$ Fluoride $\ce{F-}$ $-1$

## Formulae of ionic compounds

Ionic compounds always have a neutral overall charge.

This means that the sum of the negative charges of all the anions in a compound must equal the sum of the positive charges of all the cations.

$$\text{Charge of all anions}- \text{Charge of all cations} = 0$$

In the ionic compound sodium oxide, sodium ($\ce{Na}$) loses 1 electron to become $\ce{Na^+}$, satisfying the octet rule.

Oxygen gains 2 electrons to become $\ce{O^2-}$ to satisfy the octet rule.

Because the overall charge of the ionic compound must be zero, 2 sodium ions must bind with 1 oxide ion. The sum of all the charges is then $$2\times(+1) + 1\times(-2) = 2 - 2 = 0.$$

The formula for sodium oxide is therefore $\ce{Na2O}$.

The blue dots on the valence shell of oxygen represent electrons donated by the sodium atoms.

## Ionic compounds and empirical formulae

An ionic compound formula is written to give the relative number of ions present in the compound structure. This formula is called the empirical formula.

The formula of the ionic compound magnesium chloride is $\ce{MgCl2}$.

Solid ionic compounds are in lattice form instead of molecular form. The ions are held together in a single large structure.

The subscripts therefore represent the ratio of one ion to another instead of the absolute number of ions in the structure.

Sodium chloride has the formula $\ce{NaCl}$, but it is not a single molecule containing one sodium (blue spheres) and one chloride (green spheres) ion.

When writing empirical formulae, the ratio between subscripts of the different ions is always reduced to the simplest form (the set of the smallest whole numbers).

The compound containing $\ce{Mg^2+}$ and $\ce{S^2+}$ is written as $\ce{MgS}$ rather than as $\ce{Mg2S2}$ because there is one $\ce{Mg}$ for every $\ce{S}$ in the large lattice structure.