Problem 155 - A Complete Resource Book in Chemistry for JEE Main

Question

Which of the following ions has the maximum magnetic moment? \(\quad\) (a) \(\mathrm{Mn}^{2+}\) (b) \(\mathrm{Fe}^{2+}\) (c) \(\mathrm{Ti}^{2+}\) (d) \(\mathrm{Cr}^{2+}\)

Step-by-Step Solution

Answer

\(\mathrm{Mn}^{2+}\) has the maximum magnetic moment.

Step 1: Understand Magnetic Moment

Magnetic moment is related to unpaired electrons. It can be calculated using the formula \(\mu = \sqrt{n(n+2)}\), where \(n\) is the number of unpaired electrons.

Step 2: Determine Electron Configurations

Find the electron configurations for each ion. \( \mathrm{Mn^{2+}}: [\mathrm{Ar}]\,3d^5\), \( \mathrm{Fe^{2+}}: [\mathrm{Ar}]\,3d^6 \), \( \mathrm{Ti^{2+}}: [\mathrm{Ar}]\,3d^2 \), \( \mathrm{Cr^{2+}}: [\mathrm{Ar}]\,3d^4\).

Step 3: Count Unpaired Electrons

Count the unpaired electrons for each ion. - \(\mathrm{Mn^{2+}}\): 5 unpaired electrons - \(\mathrm{Fe^{2+}}\): 4 unpaired electrons - \(\mathrm{Ti^{2+}}\): 2 unpaired electrons - \(\mathrm{Cr^{2+}}\): 4 unpaired electrons

Step 4: Calculate Magnetic Moment for Each Ion

Apply the formula \(\mu = \sqrt{n(n+2)}\): - \(\mathrm{Mn^{2+}}\): \(\mu = \sqrt{5(5+2)} = \sqrt{35} \approx 5.92 \mu_B\) - \(\mathrm{Fe^{2+}}\): \(\mu = \sqrt{4(4+2)} = \sqrt{24} \approx 4.90 \mu_B \)- \(\mathrm{Ti^{2+}}\): \(\mu = \sqrt{2(2+2)} = \sqrt{8} \approx 2.83 \mu_B \)- \(\mathrm{Cr^{2+}}\): \(\mu = \sqrt{4(4+2)} = \sqrt{24} \approx 4.90 \mu_B \)

Step 5: Compare Magnetic Moments

Compare the calculated magnetic moments. \(\mathrm{Mn^{2+}}\) has the highest magnetic moment with approximately 5.92 \(\mu_B\), compared to the others.

Key Concepts

Unpaired Electrons

Unpaired electrons greatly influence the magnetic properties of an atom, ion, or molecule. These electrons do not have a partner with opposite spin in the same orbital. When there are unpaired electrons, they create an internal magnetic field, contributing to the overall magnetic moment.

When a magnetic field is applied, substances with unpaired electrons, like certain metal ions, will interact with it. This interaction depends on the quantity of unpaired electrons:

• A single unpaired electron aligns with the field, resulting in paramagnetism.
• More unpaired electrons lead to stronger magnetic effects.

By understanding the number of unpaired electrons in a given substance, one can predict its magnetic behavior.

Electron Configurations

Electron configurations tell us about the arrangement of electrons in an atom or ion. This configuration gives us insight into the ion's properties, including its magnetic moment. For transition metal ions, the electron configuration often involves the filling of the 3d sub-shell.

Determining electron configurations involves identifying the number of electrons the ion has and arranging them in increasing energy levels:

• First to fill is the 1s orbital, then 2s, 2p, and so on until the 3d orbital.
• The arrangement follows the order of increasing atomic number and the Aufbau principle.
• Ions will sometimes have electrons removed or added depending on their charge, affecting the configuration.

Electron configuration helps predict reactivity, bonding and magnetism, which are all crucial in understanding chemical behavior.

Transition Metal Ions

Transition metal ions are unique because they have partially filled d orbitals. These ions arise from transition metals that can lose different numbers of electrons from s and d sub-shells, forming various oxidation states.

Some key features of transition metal ions involve:

• Variability: They exhibit different magnetic and chemical properties based on their specific electron configuration.
• Colored Compounds: Due to d-d electron transitions, these ions often form colored compounds.
• Paramagnetism: Many have unpaired d electrons, contributing to unique magnetic qualities.

Understanding these ions and their electron configurations is essential in predicting how they will behave in magnetic fields and in chemical reactions.