The first and second ionisation enthalpies of a metal are 496 and 4560\,kJ mol-1, respectively. How many moles of HCl…

🧠 The big jump in IE means Group 1 First IE is $496$, second IE is $4560$. That huge jump is the giveaway — after losing one electron, the next is being pulled out of a noble gas core. So the metal is monovalent (like Na), and the hydroxide is $\ce{MOH}$.

🗺️ Reactions, one at a time With HCl: $\ce{MOH + HCl -> MCl + H2O}$. Ratio $1:1$. So $1$ mole of $\ce{MOH}$ needs $1$ mole of HCl.

With $\ce{H2SO4}$: $\ce{2MOH + H2SO4 -> M2SO4 + 2H2O}$. One $\ce{H2SO4}$ molecule eats $2$ hydroxides. So $1$ mole of $\ce{MOH}$ only needs $0.5$ mole of $\ce{H2SO4}$.

⚠️ Common mistake Students often forget that $\ce{H2SO4}$ is diprotic. Each molecule supplies $2$ H$^+$, so half the moles are enough. If you treat it like HCl ($1:1$), you wrongly mark option (a).

$\boxed{\text{Answer: (d)}}$