Ionisation energies 

In a nutshell

Ionisation energy is the energy required to form one mole of gaseous ions by removing one electron from each atom in one mole of gaseous atoms/ions. The process of ionisation is an endothermic reaction. Factors such as nuclear charge, filled electron shells and shielding affects ionisation energy. 

Equations

There is a general equation to help write the chemical equation for any number of ionisation energy for a species. 

​$$X^{(n-1)+}(g)→X^{n+}(g)+e^- \newline n=number\>ionisation\>energy$$​​

Ionisation energy

Ionisation energy is the energy required to form one mole of gaseous ions by removing one electron from each atom in one mole of gaseous atoms/ions. 

The first ionisation energy is the energy required to form one mole of $$1+$$ gaseous ions by removing one electron from each atom in one mole of gaseous atoms. The chemical equation for the first ionisation energy of sodium is shown below.

Example

​$$Na(g) →Na^+(g) +e^-$$

One electron was removed forming one mole of gaseous sodium $$1+$$ ion.

Energy is required to remove the electron. This means the process of ionisation is an endothermic reaction.

Factors affecting ionisation energy  

The magnitude of the ionisation energy depends on the attraction between the nucleus and valence electrons. This determines how hard it is to remove the outer electron from the atom/ion. 

A high ionisation energy means that it's very hard to remove the outer electron from the gaseous atom/ion. A lower ionisation energy means that it's easier to remove the outer electron from the gaseous atom/ion.

The value of the ionisation energy depends on a few different factors.

Nuclear charge

The nuclear charge is the attraction between the nucleus and valence electrons. 

The number of protons increases as you move to the right of the periodic table. This means an element on the right hand side will have more protons than an element on the left hand side if they're in the same period (row). 

Atoms/ions with a higher amount of protons will have a higher ionisation energy. This is because there are more protons (with a positive charge) in the nucleus to attract the valence electrons. Therefore, it will be harder to remove an electron due to the strong electrostatic attraction between the nucleus and the valence electrons. 

Example

Determine which species has a higher ionisation energy.

$$K(g)→K^+(g)+e^- \newline Ca(g)→Ca^+(g)+e^-$$​​

Calcium has more protons than potassium and hence a larger nuclear charge. Therefore, calcium has a higher ionisation energy.

Filled electron shells

Large atoms/ions will have lots of filled electron shells. This means that the valence electrons will be less attracted to the nucleus as they are further away from it. Therefore, the electrostatic attraction between the nucleus and valence electrons will be weaker. This results in a lower ionisation energy.

Example

Predict which gaseous atoms have a higher ionisation energy, $$Na(g)$$ or $$Cs(g)$$. 

Gaseous sodium atoms have a higher ionisation energy as sodium atoms are smaller and have less filled electron shells compared to caesium.

Shielding

Lots of electrons in an atom/ion means that there are many electrons in between the nucleus and valence electrons. This means the valence electrons won't feel as attracted to the nucleus as the inner electrons are in the way. Therefore, valence electrons will be easier to remove resulting in a lower ionisation energy. 

Example

According to shielding effects, which gaseous atoms have a higher ionisation energy, $$K(g)$$ or $$Fr(g)$$?

Potassium atoms have fewer electrons and less shielding compared to iron atoms. Therefore, the potassium atoms have a higher ionisation energy.

Down a group

Down a group the number of electrons and filled electron shells increases. The electrostatic attraction between the valence electrons and nucleus will be weaker down a group. Therefore, the first ionisation energy typically decreases down a group. The decrease in the ionisation energy value for each group provided evidence that electron shells exist. 

Successive ionisation energies

Successive ionisation energy is the ionisation energy following the previous one. After the first ionisation energy is the second ionisation energy. The second ionisation energy is the energy required to form one mole of gaseous $$2+$$ ions by removing one electron from each ion in one mole of gaseous $$1+$$ ions. 

Example

Write the second ionisation energy for sulfur. 

​$$S^+(g)→S^{2+}(g)+e^-$$

A sulfur cation with a charge of $$+2$$​ is formed. 

The chemical equation for any number of ionisation energy can be worked out for any gaseous atom/ion using this general equation:

​$$X^{(n-1)+}(g)→X^{n+}(g)+e^- \newline n=number\>ionisation\>energy$$

Shell structure

Plotting each successive ionisation energy of a gaseous atom can determine which group it is in. The sudden large increase in ionisation energy suggests that an electron from another shell has been removed.

Each time an electron is removed from a shell, there will be a fewer number of electrons left. This means there will be less repulsion between the remaining electrons and it will be harder to remove the next electron from the shell compared to the previous one. Therefore, with each electron removed, the ionisation energy will increase.

When all the electrons from the same shell are removed, the next electron removed is from the next shell closer to the nucleus. This causes a sharp increase in ionisation energy as it is much harder to remove this electron due to the increased nuclear charge, with fewer electrons. A sharp increase in ionisation energy suggests that an electron from another shell has been removed.

Example

The first electron removed is from the fourth electron shell of a potassium atom. This is quite far from the nucleus and has low nuclear charge due to the presence of many electrons and filled electron shells. Therefore, the ionisation energy is lower for this electron compared to the rest of the electrons. 

The next electron removed is from the third shell of a potassium atom. This sharp increase in ionisation energy indicates that this electron has been removed from a new shell. 

Only one electron was present before this sharp increase in ionisation energy. Potassium is in Group $$1$$​ as it has one valence electron.