Understanding the Problem

We are given the first and second ionisation enthalpies of a metal as 496 kJ mol^–1 and 4560 kJ mol^–1, respectively. The large difference between these values (4560 >> 496) indicates that it is relatively easy to remove the first electron (low first ionisation enthalpy) but very difficult to remove the second electron (high second ionisation enthalpy). This is a characteristic property of an alkali metal (Group 1 element), which typically forms a +1 ion. Therefore, the metal in question is most likely to form M⁺ ions, and its hydroxide will be MOH.

Step-by-Step Solution

Step 1: Determine the Valency of the Metal

The large jump in ionisation enthalpy from first to second confirms that the metal prefers to lose only one electron to achieve a stable noble gas configuration. Thus, the valency of the metal is 1. Its hydroxide is MOH (a strong base).

Step 2: Write the Chemical Reactions

Reaction with HCl:
MOH (a base) reacts with HCl (an acid) in a neutralization reaction to form a salt and water. $\text{MOH}+\text{HCl}\to \text{MCl}+{\text{H}}_2\text{O}$
From the balanced equation, 1 mole of MOH reacts with 1 mole of HCl.

Reaction with H₂SO₄:
MOH reacts with H₂SO₄ (a dibasic acid). Since the metal has a valency of 1, the salt formed will be M₂SO₄. $2\text{MOH}+{\text{H}}_2\text{SO}{4}_{}\to {\text{M}}_2\text{SO}{4}_{}+2{\text{H}}_2\text{O}$
From the balanced equation, 2 moles of MOH react with 1 mole of H₂SO₄.

Step 3: Calculate Moles of Acid for 1 Mole of Metal Hydroxide

We have 1 mole of the metal hydroxide (MOH).

• Moles of HCl needed = 1 mole (from the 1:1 ratio).
• Moles of H₂SO₄ needed = 1/2 = 0.5 mole (from the 2:1 ratio, MOH:H₂SO₄).

Final Answer: 1 mole of HCl and 0.5 mole of H₂SO₄.
This corresponds to the option: 1 and 0.5.

Related Topics & Formulae

Ionisation Enthalpy: The energy required to remove an electron from an isolated gaseous atom. A large increase in successive ionisation energy indicates a change in the primary energy shell (e.g., moving from a valence electron to a core electron), which helps determine the group of the element.

Acid-Base Neutralization: A reaction between an acid and a base to form salt and water. The stoichiometry depends on the basicity of the acid (number of H⁺ ions it can donate) and the acidity of the base (number of OH^– ions it can donate or metal valency).

General Formulae for Reaction of Metal Hydroxide M(OH)_n with an Acid H_mX:
The balanced reaction is: $n\text{M(OH)}{}_n+m{\text{H}}_m\text{X}\to {\text{M}}_n{\text{X}}_m+m\times n{\text{H}}_2\text{O}$
The mole ratio of Acid : Metal Hydroxide is $m:n$.