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 number of valence electrons for element X is 4.

Step 1: Understand Ionization Energy

Ionization energy is the energy required to remove an electron from an atom in its gaseous state. Successive ionization energies increase as more electrons are removed because the ion becomes increasingly positive, making it more difficult to remove the next electron.

Step 2: Analyze the Given Ionization Energies

Given the ionization energies: 1st: 410 kJ/mol 2nd: 820 kJ/mol 3rd: 1100 kJ/mol 4th: 1500 kJ/mol 5th: 3200 kJ/mol Notice the significant jump from the 4th to the 5th ionization energy.

Step 3: Identify the Jump in Ionization Energy

The large increase in ionization energy from the 4th (1500 kJ/mol) to the 5th (3200 kJ/mol) suggests that the 4th electron removed was the last valence electron. Removing a core electron requires significantly more energy.

Step 4: Determine Number of Valence Electrons

The significant jump between the 4th and 5th ionization energies indicates that there are 4 valence electrons. Thus, the electron configuration changes drastically after the 4th electron, which means option (a) 4 is correct.

Key Concepts

Successive Ionization Energies

Successive ionization energies refer to the energy needed to remove each electron sequentially from an atom. As more electrons are removed, the ionization energy generally increases. This increase is due to several factors:

• As electrons are removed, protons in the nucleus exert a stronger attractive force on the remaining electrons.
• The ion becomes more positively charged, which further increases the attraction to remaining electrons.
• This makes it progressively harder to remove each additional electron, leading to higher successive ionization energies.

In the given exercise, we note that for element \(\mathrm{X}\), the ionization energies rise from 410 \(\text{kJ/mol}\) for the first electron to a considerably higher 3200 \(\text{kJ/mol}\) by the fifth electron. The sharp increase between the fourth and fifth energies indicates a shift from removing valence electrons to core electrons.

Valence Electrons

Valence electrons are the outermost electrons of an atom and are crucial in determining many of an element's chemical properties. These electrons are generally involved in chemical bonding and reactions. Here are some key points:

• Valence electrons are usually found in the outermost shell of an atom.
• They have the highest energy compared to inner-shell electrons.
• The number of valence electrons determines an atom's reactivity, bonding behavior, and placement in the periodic table.

In the context of ionization energies, the point where there's a significant jump in energy indicates that the electrons being removed are transitioning from valence to core electrons. In our example, since the jump is observed after the 4th ionization, this tells us that element \(\mathrm{X}\) has 4 valence electrons.

Electron Removal

Electron removal in an atom progresses from valence to core electrons. Initially, it takes less energy to remove a valence electron because these are less tightly bound.

• Valence electrons are further from the nucleus, making them less tightly held.
• Core electrons are closer to the nucleus and held more strongly due to a higher effective nuclear charge.
• After removing all valence electrons, significantly more energy is required to remove a core electron.

In the scenario given, the ionization energies illustrate this concept well. Initially, the energies increase steadily—typical for valence electron removal. But the large jump from the 4th to the 5th ionization energy shows the increased difficulty of removing a core electron.