Question

If first ionization enthalpy of Mg is \(738 \, \text{kJ/mol\) then second ionization enthalpy of Mg in kJ/mol will be :

• A. \(-640 \, \text{kJ/mol}\)
• B. \(-527 \, \text{kJ/mol}\)
• C. \(658 \, \text{kJ/mol}\)
• D. \(1450 \, \text{kJ/mol}\)

Answer 1

The Correct Option is D

The problem states that the first ionization enthalpy of magnesium (Mg) is given as \(738 \, \text{kJ/mol}\), and we need to determine its second ionization enthalpy. Let's break down the process step-by-step:

Explanation:

Definition of Ionization Enthalpy:

• The ionization enthalpy (or ionization energy) is the energy required to remove an electron from an atom in its gaseous state.
• The first ionization enthalpy refers to the energy needed to remove the first electron. For magnesium, this is given as \(738 \, \text{kJ/mol}\).
• The second ionization enthalpy refers to the energy required to remove a second electron from the positively charged ion created after the first electron is removed (i.e., \(\text{Mg}^+\)).

Ionization Process for Magnesium:

• The first ionization step for Mg can be expressed as:
• The second ionization step is:

Understanding the Increase in Ionization Enthalpy:

• The second ionization enthalpy is typically larger than the first because it involves removing an electron from a positively charged ion, which is more difficult compared to removing it from the neutral atom.
• This is because the electron is pulled more strongly towards the nucleus in \(\text{Mg}^+\) compared to the neutral \(\text{Mg}\) atom due to the reduction in electron-electron repulsion and the stronger effective nuclear charge.

Conclusion:

• Given the options, \(1450 \, \text{kJ/mol}\) is the only value significantly larger than the first ionization enthalpy of \(738 \, \text{kJ/mol}\), which is consistent with the typical increase in enthalpy for the second ionization process.
• Therefore, the second ionization enthalpy of Mg is \(1450 \, \text{kJ/mol}\).