Question

What is the value of electron gain enthalpy of $Na^+$ if $IE_1$ of $Na = 5.1 \, eV$?

• A. + 10.2 eV
• B. -5.1 eV
• C. -10.2 eV
• D. + 2.55 eV

Answer 1

The Correct Option is B

To find the value of the electron gain enthalpy of Na^+, we need to understand the concepts of ionization energy and electron gain enthalpy.

The ionization energy (IE_1) refers to the energy required to remove an electron from an atom or ion. In the case of sodium (Na), the first ionization energy (IE_1) is given as 5.1 eV.

Electron gain enthalpy is defined as the energy change when an electron is added to a neutral atom or an ion in the gaseous state. For a cation like Na^+, gaining an electron is essentially the reverse of removing an electron to form Na^+ from Na.

Therefore, the electron gain enthalpy of Na^+ is the negative of the ionization energy of Na:

\text{Electron Gain Enthalpy of } Na^+ = -IE_1 \text{ of } Na = -5.1 \, eV

This implies that the energy change when an electron is added to Na^+ is -5.1 eV, indicating an exothermic process where energy is released.

Hence, the correct answer is -5.1 eV.

Let's review the provided options:

1. + 10.2 eV: Incorrect, as it states a positive value which is incorrect for electron gain enthalpy.
2. -5.1 eV: Correct, as explained above.
3. -10.2 eV: Incorrect, as it does not align with the magnitude of given ionization energy.
4. + 2.55 eV: Incorrect, as it is unrelated to the given data.