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I had a little confusion regarding ionisation energies.

I get that in general, the second ionisation energy > first ionisation energy, due to increased effective nuclear charge on the second electron.
However, in the case of an element of group 15, say phosphorus, shouldn't it be the other way around because of the half-filled orbital configuration ([Ne]3s23p3, for phosphorus)? Won't it be harder to ionise the first electron because of increased stability?

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  • $\begingroup$ You're right in saying that the ionisation energy of phosphorus should be greater than that of sulphur due to its half-filled p subshell. This is one of the many exceptions... There's also the second group alkaline earth metals whose ionisation energy is greater compared to that of the thirteenth group elements, due to a fully filled s subshell... $\endgroup$ – Abhigyan Chattopadhyay Nov 10 '17 at 18:28
  • $\begingroup$ Periodic trends are just that, trends. They give you a general idea of what to expect, but each case needs to be examined individually. $\endgroup$ – Michael Lautman Nov 10 '17 at 22:16
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This is a common misconception if you don’t think through the concept of ionisation energy enough. By your proposal, the second ionisation energy of certain elements (e.g. phosphorus) should be lower than the first. But that is never the case; all second ionisation energies are higher than the first.

The first ionisation energy corresponds to the following reaction: $$\ce{P(g) -> P+ (g) + e-}\tag{1}$$ The second ionisation energy corresponds to this reaction: $$\ce{P+(g) -> P^2+ (g) + e-}\tag{2}$$

It is very simple to see why the second ionisation energy must be greater than the first. While in the first, you are separating a positive and a negative charge, which already requires force (and thus energy), when moving on to the second ionisation you are removing a negative charge from an already positively charged body. Since electromagnetic attraction depends on the value of the charge, the second electron is drawn to the doubly-ionised ion twice as strongly as the first.

Therefore, there is no element whose second ionisation energy is lower than the first.

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