Define ionisation energy and write its equations
Represent first and successive ionisation energies with gaseous species and explain their shared electrostatic basis.
Section 1 · Atomic structure
AS Level · Cambridge International Chemistry 9701, 2025–2027 syllabus. Electronic configurations are limited to ground-state atoms and ions of elements H to Kr. Written practice is self-checked; it does not replace cumulative exam practice or human subject-teacher review.
Before you begin
- Use atomic symbols and the Periodic Table, and distinguish an atom from an ion.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
From which state is an electron removed in an ionisation-energy equation?
What you will learn
- Define first ionisation energy
- Write equations for first, second and later ionisation energies
- Explain ionisation energy as attraction between nucleus and an outer electron
A first ionisation energy is an energy change per mole
The first ionisation energy is the energy required to remove one mole of electrons from one mole of gaseous atoms to form one mole of gaseous 1+ ions. The definition includes the gaseous state and applies to one mole of atoms, not one isolated atom.
The process is endothermic because energy must be supplied to overcome the electrostatic attraction between the positive nucleus and the negative outer electron. Do not confuse ionisation energy with electron affinity, which concerns adding an electron.
Successive equations start from the ion already formed
For X, the first equation is X(g) → X⁺(g) + e⁻. The second is X⁺(g) → X²⁺(g) + e⁻. More generally, the nth ionisation removes one electron from gaseous X⁽ⁿ⁻¹⁾⁺ to form Xⁿ⁺(g).
Every equation must show a gaseous atom or ion and one electron on the product side. Successive ionisation energies usually increase because the remaining electrons are held more strongly by a progressively more positive ion; large jumps can signal that removal has reached an inner shell.
Pause and explain
Which species is the reactant in the second ionisation equation of X?
Worked example
Write the equation for the third ionisation energy of aluminium and explain why it is endothermic.
Show the worked solution
- The third electron is removed from gaseous Al²⁺.
- The product is gaseous Al³⁺ and one electron.
- Energy is needed to overcome attraction between the ion and the electron.
Answer Al²⁺(g) → Al³⁺(g) + e⁻. The process is endothermic because energy must overcome electrostatic attraction between the positive ion and the electron being removed.
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Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Write the first and second ionisation equations for magnesium.
Give me a hint
Use one electron product in each equation and show each reactant in the gas state.
Compare my reasoning
- The first electron is removed from Mg(g).
- The second is removed from Mg⁺(g).
- Check charge is balanced in each equation.
Mg(g) → Mg⁺(g) + e⁻; Mg⁺(g) → Mg²⁺(g) + e⁻.
Look for these in your work
- Correct starting species
- Gas states shown
- Charge balanced
A learner writes IE₃ for calcium as Ca⁺(g) → Ca²⁺(g) + e⁻. Correct it and explain the numbering error.
Give me a hint
Count how many electrons have already been removed before the third.
Compare my reasoning
- The second ionisation forms Ca²⁺.
- The third therefore starts with Ca²⁺.
- The product after removal is Ca³⁺.
Ca²⁺(g) → Ca³⁺(g) + e⁻. The learner wrote the second ionisation equation: Ca⁺ loses the second electron, not the third.
Look for these in your work
- Initial charge corresponds to number already removed
- Final charge increments once
Explain why an electron must be supplied with energy to leave a gaseous positive ion.
Give me a hint
Name the two charged particles and the direction of their electrostatic interaction.
Compare my reasoning
- The ion has a positive charge and the electron has a negative charge.
- Opposite charges attract.
- Energy is needed to overcome that attraction.
The electron is attracted to the positively charged nucleus in the ion. Energy must be supplied to overcome this electrostatic attraction and remove the electron, so ionisation is endothermic.
Look for these in your work
- Opposite-charge attraction identified
- Energy requirement explained
Common mistakes
- Leaving out state symbols
- Starting the second ionisation equation from a neutral atom
- Putting the electron on the reactant side
- Defining first ionisation energy for one atom rather than one mole of atoms
What can you explain now?
From which state is an electron removed in an ionisation-energy equation?
Compare with the explanation
A gaseous atom or ion
Ionisation energy equations use gaseous species.
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Make it stick
What three details make a successive ionisation equation correctly numbered and chemically balanced?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.