The first and second ionisation enthalpies of a metal are 496 and `4560 KJ mol ^(-1)` , respectively. How many moles of HCI and `H_2SO_4` Respectively , will be needed to react completely with 1 mole of the metal of the metal hydroxide ?

Options

A. 1 and 1
B. 1 and 2
C. 2 and 0.5
D. 1 and 0.5

Answer

To solve the problem, we need to determine how many moles of HCl and H2SO4 will react with 1 mole of a metal hydroxide based on the given ionization enthalpies.

### Step 1: Understand the Ionization Enthalpies
The first ionization enthalpy of the metal is 496 kJ/mol, and the second ionization enthalpy is 4560 kJ/mol. This indicates that the metal prefers to lose only one electron to achieve a stable oxidation state of +1.

### Step 2: Determine the Reaction with HCl
When the metal hydroxide (let's denote it as M(OH)) reacts with hydrochloric acid (HCl), the reaction can be represented as:
\[ \text{M(OH)} + \text{HCl} \rightarrow \text{MCl} + \text{H}_2\text{O} \]

From the balanced equation, we see that:
- 1 mole of metal hydroxide reacts with 1 mole of HCl.

Thus, for 1 mole of M(OH), we will need:
- **1 mole of HCl.**

### Step 3: Determine the Reaction with H2SO4
Now, when the metal hydroxide reacts with sulfuric acid (H2SO4), the reaction can be represented as:
\[ 2 \text{M(OH)} + \text{H}_2\text{SO}_4 \rightarrow \text{M}_2\text{SO}_4 + 2 \text{H}_2\text{O} \]

From the balanced equation, we see that:
- 2 moles of metal hydroxide react with 1 mole of H2SO4.

Thus, for 1 mole of M(OH), we will need:
- **0.5 moles of H2SO4.**

### Final Answer
- **1 mole of HCl** is needed.
- **0.5 moles of H2SO4** is needed.

### Summary
To react completely with 1 mole of the metal hydroxide:
- **HCl required:** 1 mole
- **H2SO4 required:** 0.5 moles