Problem 63 - A Complete Resource Book in Chemistry for JEE Main

Question

Among the following complex ions, the one with the highest paramagnetism is (a) \(\left[\mathrm{FeF}_{6}\right]^{2+}\) (b) \(\left[\mathrm{Cu}\left(\mathrm{H}_{2} \mathrm{O}\right)\right]^{2+}\) (c) \(\left[\mathrm{Zn}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}\) (d) \(\left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)\right]^{3+}\)

Step-by-Step Solution

Answer

The most paramagnetic ion is \([\mathrm{FeF}_{6}]^{2+}\).

Step 1: Identify the Electronic Configuration

Determine the electronic configuration for each metal ion in their oxidation states.(a) Fe in \([\mathrm{FeF}_{6}]^{2+}, Fe^{4+}\): \([Ar]3d^4\)(b) Cu in \([\mathrm{Cu(H}_{2}\mathrm{O})]^{2+}, Cu^{2+}\): \([Ar]3d^9\)(c) Zn in \([\mathrm{Zn(H}_{2}\mathrm{O})_{6}]^{2+}, Zn^{2+}\): \[\mathrm{[Ar]3d^{10}}\](d) Cr in \([\mathrm{Cr(NH}_{3})]^{3+}, Cr^{3+}\): \([Ar]3d^3\)

Step 2: Determine the Number of Unpaired Electrons

Count the number of unpaired electrons for each configuration as unpaired electrons cause paramagnetism.(a) \[\mathrm{Fe^{4+}}: 4\] unpaired electrons(b) \[\mathrm{Cu^{2+}}: 1\] unpaired electron(c) \[\mathrm{Zn^{2+}}: 0\] unpaired electrons(d) \[\mathrm{Cr^{3+}}: 3\] unpaired electrons

Step 3: Evaluate Paramagnetism

The ion with the most unpaired electrons is the most paramagnetic, since paramagnetism is due to the presence of unpaired electrons. Therefore:- (a) \[\mathrm{Fe^{4+}}: 4\] unpaired electrons- (b) \[\mathrm{Cu^{2+}}: 1\] unpaired electron- (c) \[\mathrm{Zn^{2+}}: 0\] unpaired electrons- (d) \[\mathrm{Cr^{3+}}: 3\] unpaired electronsThus, \[\mathrm{Fe^{4+}}\] has the highest paramagnetism.

Key Concepts

Unpaired Electrons

Unpaired electrons play a crucial role in determining the magnetic properties of a substance. When an atom or ion has unpaired electrons, it exhibits paramagnetism, which means it is attracted by an external magnetic field. The more unpaired electrons present, the stronger the paramagnetic behavior.

• In atoms with completely filled or half-filled orbitals, electrons pair up, leading to no unpaired electrons.
• In configurations with unpaired electrons, each unpaired electron contributes a magnetic moment.

In the context of complex ions, counting unpaired electrons helps determine which ion is more strongly paramagnetic. For instance, the ion \([\text{FeF}_{6}]^{2+}\) has the most unpaired electrons (four), making it the most paramagnetic compared to the others analyzed in the exercise.

Electronic Configuration

Understanding the electronic configuration of an atom or ion is essential to predict its chemical behavior and properties, including magnetism. Electronic configuration indicates the arrangement of electrons in various orbitals.

• This arrangement is written using a standard notation that shows the number of electrons in each orbital subshell, following the order of fill per the Aufbau principle.
• It helps identify the number of unpaired electrons in an atom or ion.

In the given exercise, calculating the electronic configuration helped identify the states of each metal ion in their respective complexes. For example, the electronic configuration of \(\text{Fe}^{4+}\) is \([\text{Ar}]3d^{4}\), indicating the presence of four unpaired electrons. This was key to determining which complex ion exhibits the most paramagnetism.

Complex Ions

Complex ions are species formed from a central metal atom or ion bonded to surrounding molecules or ions called ligands. These complex ions display varied properties, including unique electronic configurations and magnetic behaviors.

• The type of ligands and their specific arrangements affect the electronic distribution within the central metal ion.
• This distribution then influences properties like color and magnetism.

In relation to paramagnetism, the arrangement of ligands can alter the electronic structure of the central metal ion, thereby impacting the number of unpaired electrons. In the example of \([\text{FeF}_{6}]^{2+}\), fluoride ligands lead to a configuration where the central metal ion \(\text{Fe}^{4+}\) exhibits significant paramagnetism due to its four unpaired electrons. This analysis of complex ions helps in understanding their chemical and physical behavior.