Ionisation enthalpy

Ionisation enthalpy ($\Delta_i H$, also called ionisation energy) is the minimum energy required to remove the most loosely bound electron from an isolated gaseous atom in its ground state, forming a gaseous cation:

where: M(g) is the neutral atom in the gas phase, M$^+$(g) is the resulting cation, and $e^-$ is the removed electron. The gas-phase condition matters — this is a property of an isolated atom, unrelated to reactions in solution.

Successive ionisation enthalpies remove a second, third, ... electron from the already-formed cation:

where: $\Delta_i H_2$ is the second ionisation enthalpy, always measured starting from the +1 ion, not the neutral atom. Successive values always increase, $\Delta_i H_1 < \Delta_i H_2 < \Delta_i H_3 < \ldots$, because each electron is pulled from an increasingly positive, smaller ion, so the remaining electrons are held more tightly. A very large jump between two successive values signals that the next electron must come from a completed, lower (more stable) shell — this is how a table of successive ionisation enthalpies reveals the number of valence electrons an atom has.

Trend across a period: ionisation enthalpy generally increases left to right, because the effective nuclear charge, $Z_{eff}$, increases as electrons are added to the same shell — same-shell electrons shield each other poorly, so the growing nuclear charge is felt more strongly, making the outermost electron progressively harder to remove.

Trend down a group: ionisation enthalpy decreases, because the valence electron sits in a progressively larger, higher-$n$ shell, farther from the nucleus and screened by more complete inner shells — it becomes easier to remove despite the larger nuclear charge.

Two irregularities within a period interrupt the otherwise steady rise:

• Group 2 to Group 13 (e.g. Be to B, Mg to Al): ionisation enthalpy drops slightly. Group 2's outermost electron sits in a filled, extra-stable $ns^2$ configuration, while Group 13's outermost electron occupies a higher-energy $np^1$ orbital that is also partly shielded by the filled $ns^2$ pair beneath it — easier to remove despite the higher nuclear charge.
• Group 15 to Group 16 (e.g. N to O, P to S): ionisation enthalpy drops slightly. Group 15's $np^3$ configuration is exactly half-filled — extra stable by Hund's rule — while Group 16's $np^4$ must pair two electrons in one orbital, and the resulting electron–electron repulsion makes that paired electron easier to remove.

The single idea behind every trend and every exception above is effective nuclear charge ($Z_{eff}$) — the net positive pull an outer electron actually feels once the repulsion (shielding) from inner electrons is accounted for, since inner electrons partly cancel the attraction of the nucleus. Moving across a period, each new electron enters the same outer shell as the previous ones. Electrons in the same shell shield each other only weakly, so the nuclear charge keeps climbing while the shielding barely does — $Z_{eff}$ rises steadily, the outermost electron is pulled in tighter, and it takes more energy to remove it. Moving down a group, the newest valence electron enters a higher shell altogether. It now sits behind an extra complete layer of inner electrons, which shields the nucleus very effectively, and it is also physically farther away — both effects make the electron easier to pull off even though the nucleus itself is more charged. The two exceptions are not failures of this reasoning; they are refinements of it. A filled subshell ($ns^2$) or an exactly half-filled subshell ($np^3$) is unusually stable because the electron arrangement minimises electron–electron repulsion (via Hund's rule for the half-filled case) and gains a small extra symmetry stabilisation. Removing the next electron — one entering a new, higher-energy $np^1$ orbital, or one forced to pair up in an already half-filled $np^4$ — costs less than the smooth $Z_{eff}$ trend alone would predict, because that next electron starts from a less stable arrangement to begin with. So both irregularities are really about comparing the stability of the starting configuration, not about the general $Z_{eff}$ rule breaking down.

Question: Explain why the first ionisation enthalpy of magnesium (Mg, $Z=12$) is higher than that of aluminium (Al, $Z=13$), even though Al has a higher nuclear charge.

Step 1. Write the valence configurations: Mg is $[\text{Ne}]3s^2$; Al is $[\text{Ne}]3s^23p^1$.

Step 2. Note that Mg's electron to be removed comes from a completely filled $3s^2$ subshell, which carries extra stability — both electrons are spin-paired in a fully occupied subshell.

Step 3. Note that Al's electron to be removed comes instead from the singly occupied $3p^1$ orbital, which is higher in energy than $3s$ and is additionally shielded, in part, by the filled $3s^2$ pair beneath it — so it is held less firmly despite Al's larger nuclear charge.

Step 4. Compare the two effects: the stability gained from Mg's filled subshell outweighs the small nuclear-charge increase from Mg to Al.

Answer: $\Delta_i H_1(\text{Mg}) > \Delta_i H_1(\text{Al})$ — an exception to the general "ionisation enthalpy increases across a period" trend, explained by subshell stability rather than by $Z_{eff}$ alone.

Competitive stretch

Question: The successive ionisation enthalpies of an element (arbitrary units) are $\Delta_i H_1 = 590$, $\Delta_i H_2 = 1145$, $\Delta_i H_3 = 4912$, $\Delta_i H_4 = 6491$. Deduce the element's likely group (number of valence electrons).

Step 1. List the successive jumps: $H_1 \to H_2 \approx 1.9\times$; $H_2 \to H_3 \approx 4.3\times$; $H_3 \to H_4 \approx 1.3\times$.

Step 2. Identify where the dramatically large jump occurs: between $\Delta_i H_2$ and $\Delta_i H_3$, meaning the third electron is far harder to remove than the first two.

Step 3. Interpret the pattern: two "easy" electrons followed by a big jump means the atom has 2 valence electrons, since the third electron must come from a stable, completed inner shell.

Answer: the element has 2 valence electrons and belongs to Group 2 — these are realistic values for calcium ($\Delta_i H_1 \approx 590$, $\Delta_i H_2 \approx 1145\ \text{kJ mol}^{-1}$).

• Assuming ionisation enthalpy increases smoothly and without exception across every period — the Group 2/13 and Group 15/16 dips are commonly tested and must be explained, not ignored.
• Confusing "successive ionisation enthalpy always increases" (true) with "the increase is always gradual" (false) — a large jump reveals a shell or subshell closure and is used to deduce the valence electron count.
• Mixing up the group trend direction — it is easy to misremember and say ionisation enthalpy increases down a group; it actually decreases, because the valence electron is farther from the nucleus and better shielded.
• Forgetting that ionisation enthalpy applies to a gaseous atom only — it is unrelated to lattice energy or solvation energy discussed elsewhere in the same unit.

Ask the tutor: if the Group 2/13 or Group 15/16 exception, or reading a successive-ionisation-enthalpy table, still feels confusing, ask the AI tutor to walk through a few more period-3 or period-2 examples with you.