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 of calculating the energy required for the reaction \( \text{Mg}(s) \rightarrow \text{Mg}^{2+} + 2e^{-} \), we will use the provided first and second ionization energies of magnesium.

### Step-by-Step Solution:

1. **Identify Ionization Energies**:
- The first ionization energy (IE1) of magnesium is given as 178 kcal/mol.
- The second ionization energy (IE2) of magnesium is given as 348 kcal/mol.

2. **Understanding the Reaction**:
- The reaction involves the conversion of solid magnesium (Mg) to a magnesium ion with a +2 charge (\( \text{Mg}^{2+} \)) while releasing two electrons (\( 2e^{-} \)).
- This process requires energy to remove the electrons from the magnesium atom.

3. **Calculate Total Energy Required**:
- The total energy required for the reaction can be calculated by adding the first and second ionization energies:
\[ \text{Total Energy} = \text{IE1} + \text{IE2} \]
- Substituting the values:
\[ \text{Total Energy} = 178 \, \text{kcal/mol} + 348 \, \text{kcal/mol} \]
- Performing the addition:
\[ \text{Total Energy} = 526 \, \text{kcal/mol} \]

4. **Conclusion**:
- The energy required for the reaction \( \text{Mg}(s) \rightarrow \text{Mg}^{2+} + 2e^{-} \) is 526 kcal/mol.

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

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