Problem 105 - A Complete Resource Book in Chemistry for JEE Main

Question

The successive ionization energy values for an element \(\mathrm{X}\) are given below: (a) 1st ionization energy \(=410 \mathrm{~kJ} \mathrm{~mol}^{-1}\) (b) 2 nd ionization energy \(=820 \mathrm{~kJ} \mathrm{~mol}^{-1}\) (c) 3 rd ionization energy \(=1100 \mathrm{~kJ} \mathrm{~mol}^{-1}\) (d) 4 th ionization energy \(=1500 \mathrm{~kJ} \mathrm{~mol}^{-1}\) (e) 5 th ionization energy \(=3200 \mathrm{~kJ} \mathrm{~mol}^{-1}\) Find out the number of valence electron for the atom, \(\mathrm{X} .\) (a) 4 (b) 3 (c) 5 (d) 2

Step-by-Step Solution

Answer

The atom X has 4 valence electrons (option a).

Step 1: Understanding Ionization Energies

Ionization energy is the amount of energy required to remove an electron from an atom. It increases with the removal of each successive electron because of the increased positive charge, which more strongly attracts the remaining electrons.

Step 2: Analyzing the Given Data

We are given several ionization energies. The first significant jump in ionization energy indicates where electrons are being removed from a more stable, inner shell.

Step 3: Identify the Large Increase

Note that the jump from the 4th to the 5th ionization energy is the largest (from 1500 to 3200 kJ/mol). This large increase suggests that 4 electrons were removed from the valence shell, and the 5th electron is being removed from a more stable inner shell.

Step 4: Determine Number of Valence Electrons

Since the largest increase is between the 4th and 5th ionization energy, element X has 4 valence electrons, as the first four are easier to remove than the fifth, which also supports the stability of a new electron shell being completed with those 4 electrons.

Key Concepts

Valence Electrons

Valence electrons are the electrons located in the outermost shell of an atom. These electrons play a crucial role in chemical bonding because they are the ones involved in forming bonds with other atoms. Understanding the number of valence electrons helps in predicting an atom's chemical properties.

The element's reactivity and its tendency to form certain types of bonds depend on the valence electrons. When atoms interact, they tend to lose, gain, or share valence electrons to achieve a more stable electron configuration, often seen as having a full outer shell. For example, elements like oxygen need two electrons to fill their outer shell, making them likely to form bonds where they can gain or share electrons.

In the context of ionization energy, the removal of valence electrons requires less energy compared to removing electrons from an inner shell. This is because valence electrons are further from the nucleus and experience less electrostatic pull from the protons in the nucleus. Therefore, identifying the point at which ionization energy significantly increases can suggest the number of valence electrons, as it indicates a shift from removing valence to core electrons.

Successive Ionization Energies

Successive ionization energies refer to the energy required to remove electrons from an atom one by one in succession. Each removal requires more energy than the previous one due to the increased positive charge of the ion, which results in a stronger attraction to the remaining electrons.

With each electron removed, less shielding exists between the nucleus and the electrons, which increases the nuclear effective charge on the remaining electrons. As a result, removing additional electrons becomes progressively harder. This is why the ionization energy for each subsequent electron is higher.

When analyzing ionization energies, a large jump between any two successive energies indicates that electrons are being removed from closer to the nucleus, generally moving from outer shells to inner ones. For example, if a large increase is observed from one ionization energy to the next, it typically marks the transition from removing a valence electron to removing an inner-shell electron. This insight was key in identifying that element X in our exercise has 4 valence electrons.

Electron Configuration

Electron configuration describes how electrons are distributed among the orbitals of an atom. It gives insight into the atom's chemical behavior and properties. Electrons fill orbitals in a way that lowers the atom's energy, typically filling from lower to higher energy levels or shells (aufbau principle).

Electrons arrange themselves in a way that obeys the Pauli exclusion principle and Hund's rule. The Pauli exclusion principle states that no two electrons can have the same set of quantum numbers, while Hund's rule indicates electrons will singly fill orbitals of the same energy before doubling up in any.

By knowing the electron configuration, we can determine the number of valence electrons, as these are located in the outermost shell. For example, in a configuration such as 1s² 2s² 2p⁶ 3s², the 3s² shows that there are two valence electrons in the outer shell. The number and arrangement of these valence electrons determine how an atom will interact chemically with other substances, and whether they'll tend to lose, gain, or share electrons in chemical reactions.