Ionisation enthalpy and electron gain enthalpy

Ionisation enthalpy

The first ionisation enthalpy, $\Delta_i H_1$, is the energy needed to remove the most loosely held electron from an isolated gaseous atom in its ground state:

• $\text{X(g)} \rightarrow \text{X}^+\text{(g)} + e^-$

It is given in $\text{kJ mol}^{-1}$: the energy for a mole of atoms. Energy is always needed, so it is always positive.

The second ionisation enthalpy removes an electron from the positive ion. It is always larger than the first, because the electron leaves a positive ion that holds it more strongly. For sodium the first is $496\ \text{kJ mol}^{-1}$ but the second is $4562\ \text{kJ mol}^{-1}$. The second electron comes from the filled inner shell.

Shielding and the effective nuclear charge

An outer electron does not feel the full charge of the nucleus. The electrons between it and the nucleus shield it. What it feels is the effective nuclear charge:

• $Z_{\text{eff}} = Z - S$, where $Z$ is the number of protons and $S$ the shielding by the other electrons.

Inner electrons shield well. Electrons in the same shell shield only a little. Among orbitals of one shell, an s electron goes closer to the nucleus than a p electron, so it is held more firmly and shields the p electrons.

The trends

Across a period the nuclear charge grows while the electrons stay in one shell. $Z_{\text{eff}}$ rises, the atom shrinks, and the ionisation enthalpy rises. Down a group the outer electron is in a higher shell, farther away and better shielded, so the ionisation enthalpy falls.

Two dips that make sense

• Boron is lower than beryllium. Beryllium's outer electrons are in $2s$. Boron's outermost electron is in $2p$, which is shielded by the $2s$ electrons and held less firmly.
• Oxygen is lower than nitrogen. Nitrogen is $2s^2 2p^3$: three $2p$ electrons, one in each orbital. In oxygen, $2p^4$, two electrons share one orbital and repel each other. Removing one of them is easier.

Period 3 shows the same two dips, at aluminium and at sulphur.

Electron gain enthalpy

The electron gain enthalpy, $\Delta_{eg}H$, is the enthalpy change when an isolated gaseous atom takes an electron:

• $\text{X(g)} + e^- \rightarrow \text{X}^-\text{(g)}$

When energy is released, it is negative. The more negative, the more readily the atom accepts the electron.

• The halogens have the most negative values: one more electron completes their shell.
• The noble gases have positive values: the new electron must enter a new, higher shell. Neon is $+116\ \text{kJ mol}^{-1}$.
• Chlorine is more negative than fluorine. The fluorine atom is so small that an added electron is crowded by the electrons already in its compact $2p$ subshell. Oxygen and sulphur behave the same way.
• Across a period it becomes more negative, and down a group generally less negative.

Practise with new numbers

Try it in Python

The program walks across period 2 and marks every step where the ionisation enthalpy goes down instead of up.

Common mistakes

• Forgetting the gas. Ionisation enthalpy is defined for isolated gaseous atoms, not for a solid metal.
• Expecting a smooth rise. Groups 13 and 16 dip below the element before them.
• Thinking fluorine gains an electron most readily. Chlorine releases more energy, because fluorine is so small.
• Mixing up the signs. A negative electron gain enthalpy means energy is released.
• Treating the second ionisation enthalpy like the first. It is always larger, and much larger when the electron comes from an inner shell.

Remember these

• $\Delta_i H_1$: $\text{X(g)} \rightarrow \text{X}^+\text{(g)} + e^-$, always positive.
• $Z_{\text{eff}} = Z - S$. It rises across a period, so atoms shrink and hold their electrons harder.
• Ionisation enthalpy rises across a period and falls down a group. Dips at groups 13 and 16.
• Electron gain enthalpy is most negative for the halogens, positive for the noble gases, and less negative for fluorine than for chlorine.

Check yourself

Try each one on your own first. If you are stuck, open a hint. Then check with Show the answer.

1. Write the equation for the first ionisation of a magnesium atom.

2. Why is the first ionisation enthalpy of oxygen lower than that of nitrogen?

3. Why does the first ionisation enthalpy fall from lithium to caesium?

4. The electron gain enthalpy of argon is positive. What does that tell you?

5. Which needs more energy: removing an electron from $\text{Na}^+$ or from a sodium atom? Why?