Problem 89 - A Complete Resource Book in Chemistry for JEE Main

Question

The correct statement among the following is (a) the first ionization potential of \(\mathrm{Al}\) is less than the first ionization potential of \(\mathrm{Mg}\). (b) the second ionization potential of \(\mathrm{Mg}\) is greater than the second ionization potential of \(\mathrm{Na}\). (c) the first ionization potential of \(\mathrm{Na}\) is less than the first ioniation potential of \(\mathrm{Mg}\). (d) the third ionization potential of \(\mathrm{Mg}\) is greater than the third ionization potential of Al.

Step-by-Step Solution

Answer

The correct statement is (b).

Step 1: Understanding Ionization Potential

Ionization potential (or ionization energy) refers to the energy required to remove an electron from an atom or ion in its gaseous state. Generally, it increases across a period and decreases down a group in the periodic table.

Step 2: Examine Each Statement

Let's evaluate each statement based on known periodic trends and electron configurations.(a) The first ionization potential of \( \mathrm{Al} \) compared to \( \mathrm{Mg} \)- \( \mathrm{Al} \) has a lower ionization energy than \( \mathrm{Mg} \), following periodic trends.(b) The second ionization potential of \( \mathrm{Mg} \) versus \( \mathrm{Na} \)- \( \mathrm{Mg}^+ \) loses an electron from a filled orbital, while \( \mathrm{Na}^+ \) loses from a partially filled one, making \( \mathrm{Mg}^+ \) harder to ionize; hence the second ionization potential of \( \mathrm{Mg} \) is indeed greater.(c) The first ionization potential of \( \mathrm{Na} \) versus \( \mathrm{Mg} \)- \( \mathrm{Na} \) has a lower ionization energy than \( \mathrm{Mg} \).(d) The third ionization potential of \( \mathrm{Mg} \) is less than that of \( \mathrm{Al} \), not greater, since \( \mathrm{Mg}^{2+} \) has a filled shell while \( \mathrm{Al}^{2+} \) has yet to achieve a filled shell.

Step 3: Final Comparison and Conclusion

Among the options, (a), (b), and (c) align with known periodic trends, but only (b) clearly states a correct fact about ionization potentials and their specific comparison. Thus, the correct statement is (b): "the second ionization potential of \( \mathrm{Mg} \) is greater than the second ionization potential of \( \mathrm{Na} \)."

Key Concepts

Periodic Trends

Periodic trends refer to specific patterns in the periodic table that help us understand element behavior. These trends enable us to predict how elements will behave chemically and physically.

For ionization energy, the trend is as follows:

• Across a period (left to right), ionization energy increases. This happens because electrons are more strongly attracted to the nucleus as the atomic number rises.
• Down a group (top to bottom), ionization energy decreases. This is because, as you move down a group, the outer electrons are further from the nucleus and experience more shielding from the inner electrons.

These periodic trends are essential in analyzing and comparing the ionization potential of different elements, providing insight into their reactivity and stability.

Ionization Potential

Ionization potential, also known as ionization energy, is the energy required to remove an electron from an atom or ion in its gaseous state. There are several key points to understand about ionization potential:

• It measures how tightly an electron is bound to an atom.
• The first ionization energy refers to the energy needed to remove the first electron.
• Subsequent ionization energies (second, third, etc.) are always higher as it becomes increasingly difficult to remove additional electrons.

By examining ionization potential, you can determine an element's likelihood to form compounds. For example, metals usually have lower ionization energies and tend to lose electrons more easily, forming positive ions or cations. Understanding these concepts helps us explain the behavior observed in the correct solution to the exercise.

Electron Configuration

Electron configuration describes how electrons are distributed in the atomic orbitals of an atom. Understanding electron configuration is vital to evaluate ionization potential and periodic trends as it influences both.

Each element has a unique electron configuration, such as:

• Sodium ( ext{Na} : 1s² 2s² 2p⁶ 3s¹)
• Magnesium ( ext{Mg} : 1s² 2s² 2p⁶ 3s²)

In the exercise, we need to look at these configurations:

• When sodium loses an electron, it empties its 3s orbital and forms ext{Na}^+ : 1s² 2s² 2p⁶ ; making it more stable.
• Magnesium's ext{Mg}^+ loses an electron but from a filled ext{3s} orbital, leading to a stable ext{Mg}^{2+} configuration (1s² 2s² 2p⁶).

Knowing electron configurations thus helps explain why certain ionization potentials are higher or lower based on the electron removal process and the resulting stability of the ions.