The first ionisation potential of Na is 5.1 eV. The value of electron gain enthalpy of Na+ will be
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Q: Why is the answer negative?

Energy is required (absorbed) to remove an electron, making ionisation energy positive. When the electron is added back to the cation, that exact same amount of energy is released, making the electron gain enthalpy negative.

Q: Is electron gain enthalpy always negative?

Not always! For neutral atoms like noble gases or alkaline earth metals, adding an electron can require energy (positive enthalpy) due to electron-electron repulsion. However, adding an electron to a positive cation is always highly exothermic (negative).

Q: What is the difference between electron affinity and electron gain enthalpy?

They are closely related but have a subtle thermodynamic difference. Electron affinity is defined at absolute zero, while electron gain enthalpy includes a small temperature-dependent term ($\frac{5}{2}RT$). Also, by convention, a positive electron affinity often corresponds to a negative electron gain enthalpy.

Q: Can I apply this logic to the second ionisation energy?

Yes! The second ionisation energy of an atom (e.g., $\text{Mg}^+ \rightarrow \text{Mg}^{2+} + e^-$) is equal in magnitude and opposite in sign to the electron gain enthalpy of the divalent cation ($\text{Mg}^{2+} + e^- \rightarrow \text{Mg}^+$).

Q: Why are we using electron volts (eV) instead of kJ/mol?

Electron volts are a very convenient unit for measuring energy on the atomic scale, representing the energy gained by a single electron accelerated through a 1-volt potential difference. You can convert it to macroscopic units using $1 \text{ eV} \approx 96.48 \text{ kJ/mol}$.

Question

The first ionisation potential of $	ext{Na}$ is $5.1 	ext{ eV}$. The value of electron gain enthalpy of $	ext{Na}^+$ will be

Options:

(A) $- 2.55 	ext{ eV}$

(B) $- 5.1 	ext{ eV}$

(C) $-10.2 	ext{ eV}$

(D) $+ 2.55 	ext{ eV}$

Sigma Percentile · Accepted Answer

### The Beauty of Reversibility

Imagine pushing a heavy boulder up a steep hill. You have to expend a specific amount of energy to get it to the top. Now, what happens if you let that boulder roll back down to its exact starting position? It releases that exact same amount of energy.

This fundamental principle of energy conservation applies perfectly to the microscopic world of atoms and electrons.

### Analyzing the Forward Process

The problem states that the first ionisation potential of sodium ($	ext{Na}$) is $5.1 	ext{ eV}$.

What does this actually mean? It means we need to supply $5.1 	ext{ eV}$ of energy to a neutral, gaseous sodium atom to strip away its outermost electron.

We can write this process as a chemical equation:

$	ext{Na}_{(g)} \longrightarrow 	ext{Na}^+_{(g)} + e^-$

Since energy is absorbed by the system, the enthalpy change for this process is positive: $\Delta H_{IE} = +5.1 	ext{ eV}$.

### The Reverse Journey

Now, the question asks for the electron gain enthalpy of the sodium ion ($	ext{Na}^+$).

Let's write down the equation for this process. We are taking that positively charged sodium ion and giving it an electron back:

$	ext{Na}^+_{(g)} + e^- \longrightarrow 	ext{Na}_{(g)}$

Look closely at this equation. It is the **exact reverse** of the ionisation process we just discussed!

### The Final Calculation

Because enthalpy is a state function, reversing a chemical reaction simply reverses the sign of its enthalpy change.

If it took $+5.1 	ext{ eV}$ to pull the electron away, the system must release $-5.1 	ext{ eV}$ when the electron falls back into its original orbital.

Therefore, the electron gain enthalpy of $	ext{Na}^+$ is:

$\Delta H_{eg} = -5.1 	ext{ eV}$

This elegant symmetry is a powerful tool in chemical thermodynamics. Always remember: the ionisation energy of an atom is equal in magnitude but opposite in sign to the electron gain enthalpy of its corresponding cation!

Animated Solution for Chemistry - Periodicity in Properties: The first ionisation potential of $Na$ is $5.1 eV$ . The value of electron gain enthalpy of $Na^{+}$ will be

Select Answer:

Visualized Solution

$Ionisation Energy$

$Electron Gain Enthalpy$

$Energy Conservation$

$Final Answer$

$Conceptual Extension$

The Sigma Insight: Periodic Table and Periodic Properties

The Beauty of Reversibility

Analyzing the Forward Process

The Reverse Journey

The Final Calculation

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Animated Solution for Chemistry - Periodicity in Properties: .math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The first ionisation potential of Na is 5.1 eV. The value of electron gain enthalpy of Na+ will be