The second ionisation energies are higher than the first ionisation energies. This is mainly due to the fact the after the removal of the first electron, the atom changes into monovalent positive ion. In the ion, the number of electrons decreases but the nuclear charge remains the same. as a result of this, the remaining electrons are held more tightly by the nucleus and it becomes difficult to remove the second electron. therefore, the value of second ionisation energy. `(IE_(2))`, is greater than that of the first ionisatio energy `(IE_(1))`. similarly third ionisation energy `(IE_(3))` is greater than that of second `IE_(2)`.
Q. `IE_(1) and IE_(2)` of Mg metal are 178 and 348 kcal/mol respectively. the energy required for the given reaction is:
`Mg(s) to Mg^(+2)+2e^(-)`

Options

A. `+170` kcal/mol
B. `+526` kcal/mol
C. `-170` kcal/mol
D. `-526` kcal/mol

Answer

To solve the problem, we need to calculate the total energy required to convert solid magnesium (Mg) into a magnesium ion with a +2 charge (Mg²⁺) by removing two electrons. The ionization energies provided are:

- First ionization energy (IE₁) = 178 kcal/mol
- Second ionization energy (IE₂) = 348 kcal/mol

### Step-by-Step Solution:

1. **Understand the Process**: The reaction we are considering is:
\[ \text{Mg(s)} \rightarrow \text{Mg}^{2+} + 2e^- \]
This means we need to remove two electrons from magnesium.

2. **Calculate Total Ionization Energy**: The total energy required to remove two electrons is the sum of the first and second ionization energies:
\[ \text{Total Energy} = \text{IE}_1 + \text{IE}_2 \]
Substituting the values:
\[ \text{Total Energy} = 178 \, \text{kcal/mol} + 348 \, \text{kcal/mol} \]

3. **Perform the Addition**:
\[ \text{Total Energy} = 526 \, \text{kcal/mol} \]

4. **Determine the Sign of the Energy**: Since energy is required to remove the electrons, the value will be positive. Therefore, the energy required for the reaction is:
\[ +526 \, \text{kcal/mol} \]

5. **Select the Correct Option**: Based on the calculated energy, the correct answer is option 2: +526 kcal/mol.

### Final Answer:
The energy required for the reaction is **+526 kcal/mol**.

---