Problem 109 - 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 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 \(\mathrm{Al}\)

Step-by-Step Solution

Answer

The correct statements are (a) and (c).

Step 1: Understand Ionization Potential

Ionization potential (ionization energy) is the energy required to remove an electron from an atom. The first ionization potential refers to the energy needed to remove the first electron, the second refers to the energy needed to remove the second electron, and so on.

Step 2: Analyze Ionization Potential Trends in the Periodic Table

In the periodic table, ionization potential generally increases across a period (from left to right) and decreases down a group (from top to bottom). Aluminum (Al) and Magnesium (Mg) are in the same period with Mg coming before Al, while Sodium (Na) is in a different group.

Step 3: Compare First Ionization Potentials of Al and Mg

Magnesium has two electrons in its outer shell (ns^2 configuration), while aluminum adds one more electron (p-orbital), resulting in similar shielding with a slightly lower effective nuclear charge requiring less energy to remove the first electron. Thus, the first ionization potential of Mg is greater than that of Al.

Step 4: Compare Second Ionization Potentials of Mg and Na

Magnesium's second ionization involves removing an electron from the fully paired ns^2 orbital, displaying a relatively high ionization potential. In contrast, after the first ionization, sodium attains a stable noble gas configuration, and its second ionization potential corresponds to removing an electron from a lower energy level, which is significantly higher.

Step 5: Compare First Ionization Potentials of Na and Mg

Since Na is in period 3 and group 1, it is expected to have a lower first ionization potential than Mg, which is also in period 3 but in group 2, making it more tightly bound and harder to remove the first electron.

Step 6: Compare Third Ionization Potentials of Mg and Al

After the first two electrons are removed, Mg has a stable configuration similar to helium (noble gas), which makes the third ionization potential extremely high. For Al, the third ionization is easier since it involves removing from a less stable configuration.

Step 7: Evaluate Statements Based on Comparisons

(a) True - The first ionization potential of Al is indeed less than that of Mg. (b) False - The second ionization potential of Mg is less than that of Na due to noble gas configuration stability. (c) True - The first ionization potential of Na is less than that of Mg. (d) False - The third ionization potential of Mg is greater than that of Al.

Key Concepts

Periodic Table Trends

The periodic table is structured in a way that showcases a number of trends, which are instrumental in predicting the behavior of elements. One of the most significant trends is the change in ionization potential. As you move across a period (from left to right), the ionization energy generally increases. This increase is due to the growing nuclear charge - the number of protons in the nucleus - which more strongly attracts the electrons, making them harder to remove. The electrons are pulled closer to the nucleus, increasing the energy required to dislodge them.

In contrast, moving down a group (from top to bottom), the ionization potential generally decreases. This occurs because the electrons are being added to higher principal energy levels, further away from the nucleus. While the nuclear charge does increase, the effect is mitigated by increased electron shielding, which reduces the overall pull felt by the outermost electrons. Thus, they are more easily removed. Understanding these trends is crucial for accurately predicting the ionization potential in chemical elements.

Electron Configuration

Electron configuration describes the distribution of electrons in an atom's orbitals. Electrons fill up orbitals in accordance to the "aufbau" principle, starting from the lowest energy level upwards. The configuration follows a specific order, with each orbital type able to hold a set number of electrons:

• p orbitals hold up to 6 electrons
• d orbitals hold up to 10 electrons
• f orbitals can hold 14 electrons
• s orbitals hold up to 2 electrons

For example, magnesium (Mg) has an atomic number of 12, so its electron configuration is ext{1s}^2 ext{2s}^2 ext{2p}^6 ext{3s}^2. In comparison, aluminum (Al) with an atomic number of 13 has one more electron: ext{1s}^2 ext{2s}^2 ext{2p}^6 ext{3s}^2 ext{3p}^1. This minor difference in configuration between Al and Mg results in differing ionization potentials, illustrating how subtle changes in electron configuration can greatly impact atomic properties.

Ionization Energy Series

Ionization energy is the energy required to remove an electron from an atom, with each successive ionization requiring more energy. This series begins with the first ionization energy, which pertains to removing the first electron, and continues as second, third and so on, each referring to subsequent electrons. Each progressive ionization energy is typically higher than the previous one, as removing an electron often leaves a positive ion that more strongly attracts remaining electrons.

For example, in magnesium, the first ionization involves removing an electron from a partially filled s-orbital, while the second ionization removes an electron from a fully filled s-orbital. This second action requires significantly higher energy due to the stability associated with a filled orbital. As we remove more electrons, reaching a noble gas configuration, the ionization energy heightens considerably. Analyzing ionization energy series helps us understand the stability and reactivity of elements and their comparative behavior in chemical reactions.

Atomic Structure

The atomic structure forms the foundation of chemistry, dictating how elements and compounds interact. At its core, an atom comprises three primary particles:

• Protons, which are positively charged and reside in the nucleus
• Neutrons, which are neutral and also located in the nucleus
• Electrons, which are negatively charged and orbit the nucleus

The structure is held together by the attraction between the positively charged nucleus and the negatively charged electrons. This balance of forces determines the atomic stability and the overall behavior during chemical reactions.
Elements in the periodic table are arranged to signal how many protons (or electrons) are present in an atom, which governs their electron configuration and influences their chemical properties and ionization potential. Understanding the atomic structure is key to grasping why different elements exhibit unique ionization energies and why certain trends exist across the periodic table.