In the third period, first ionization enthalpy generally increases from left to right due to increasing nuclear charge and decreasing atomic size.
However, certain exceptions arise due to electronic configuration stability.
Aluminium has a lower ionization enthalpy than silicon because aluminium has a $3p^1$ electron which is easier to remove compared to silicon’s $3p^2$ configuration.
Between silicon and phosphorus, ionization enthalpy increases as expected due to higher nuclear charge.
Sulfur has slightly lower ionization enthalpy than phosphorus because sulfur has paired electrons in the $3p$ orbital, causing extra repulsion.
Chlorine has the highest ionization enthalpy among the given elements due to its high effective nuclear charge.
Therefore, the correct increasing order is:
$$ \text{Al} < \text{Si} < \text{S} < \text{P} < \text{Cl} $$
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