How would you explain the fact that the first ionisation enthalpy of sodium is lower than that of magnesium but its second ionisation enthalpy is higher than that of magnesium?

Explanation

To explain why the first ionization enthalpy of sodium is lower than that of magnesium, but its second ionization enthalpy is higher than that of magnesium, we can follow these steps:

### Step 1: Understand Ionization Enthalpy
Ionization enthalpy is the energy required to remove an electron from an atom in the gaseous state. The first ionization enthalpy (IE1) refers to the removal of the first electron, while the second ionization enthalpy (IE2) refers to the removal of the second electron.

### Step 2: Write Electronic Configurations
- Sodium (Na) has the electronic configuration: \(1s^2 2s^2 2p^6 3s^1\) (or simply \(Ne 3s^1\)).
- Magnesium (Mg) has the electronic configuration: \(1s^2 2s^2 2p^6 3s^2\) (or simply \(Ne 3s^2\)).

### Step 3: Analyze First Ionization Enthalpy (IE1)
- For sodium, removing one electron from \(3s^1\) leads to a stable noble gas configuration (\(Ne\)). This removal is energetically favorable, resulting in a lower IE1.
- For magnesium, removing one electron from \(3s^2\) results in a \(3s^1\) configuration, which is less stable than the fully filled \(3s^2\) configuration. Therefore, it requires more energy to remove an electron, resulting in a higher IE1.

### Step 4: Analyze Second Ionization Enthalpy (IE2)
- For sodium, after the first ionization, Na becomes \(Na^+\) with the configuration \(Ne\) (or \(3s^0\)). Removing another electron from this stable noble gas configuration requires a significant amount of energy, leading to a high IE2.
- For magnesium, after the first ionization, Mg becomes \(Mg^+\) with the configuration \(Ne 3s^1\). Removing the second electron from \(3s^1\) is easier than removing an electron from a noble gas configuration, thus resulting in a lower IE2 compared to sodium.

### Conclusion
- **First Ionization Enthalpy**: Sodium has a lower IE1 than magnesium because it achieves a stable noble gas configuration upon losing one electron, while magnesium has a stable filled configuration that is harder to break.
- **Second Ionization Enthalpy**: Sodium has a higher IE2 than magnesium because removing an electron from the stable noble gas configuration of \(Na^+\) is much more difficult compared to removing an electron from the \(Mg^+\) configuration.

### Summary
- **IE1 (Na < Mg)**: Sodium loses an electron easily to achieve stability.
- **IE2 (Na > Mg)**: Sodium's stable noble gas configuration makes further removal of electrons very difficult.