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 are required to react completely with 1 mole of a metal hydroxide (MOH) formed by a metal (M) with the given ionization enthalpies.

### Step-by-Step Solution:

1. **Identify the Metal**:
The first ionization enthalpy is 496 kJ/mol and the second is 4560 kJ/mol. The significant jump in ionization energy suggests that the metal is likely from Group 1 (alkali metals). This is because after losing one electron, the metal achieves a stable electron configuration (octet) and requires much more energy to remove the second electron.

2. **Write the Reaction with HCl**:
The metal hydroxide (MOH) will react with hydrochloric acid (HCl) as follows:
\[ \text{MOH} + \text{HCl} \rightarrow \text{MCl} + \text{H}_2\text{O} \]
From this reaction, we can see that 1 mole of MOH reacts with 1 mole of HCl.

3. **Write the Reaction with H₂SO₄**:
The metal hydroxide (MOH) will also react with sulfuric acid (H₂SO₄):
\[ \text{MOH} + \frac{1}{2} \text{H}_2\text{SO}_4 \rightarrow \frac{1}{2} \text{M}_2\text{SO}_4 + \text{H}_2\text{O} \]
This indicates that 1 mole of MOH reacts with 0.5 moles of H₂SO₄.

4. **Calculate the Moles Needed**:
- For HCl: 1 mole of MOH requires 1 mole of HCl.
- For H₂SO₄: 1 mole of MOH requires 0.5 moles of H₂SO₄.

5. **Final Answer**:
Therefore, to completely react with 1 mole of the metal hydroxide (MOH), we need:
- **1 mole of HCl**
- **0.5 moles of H₂SO₄**

### Conclusion:
The answer is 1 mole of HCl and 0.5 moles of H₂SO₄.

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