Problem 16 - A Complete Resource Book in Chemistry for JEE Main

Question

Considering \(\mathrm{H}_{2} \mathrm{O}\) as a weak field ligand, the number of unpaired electrons in \(\left[\mathrm{Mn}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}\) will be (Atomic no of \(\mathrm{Mn}=25\) ) (a) 2 (b) 3 (c) 4 (d) 5

Step-by-Step Solution

Answer

There are 5 unpaired electrons in exttt{[Mn(H extsubscript{2}O) extsubscript{6}] extsuperscript{2+}}.

Step 1: Determine the Electron Configuration of Mn

The atomic number of manganese (Mn) is 25. Therefore, its electron configuration is extbf{ exttt{[Ar] 3d extsuperscript{5} 4s extsuperscript{2}}}. Since we are considering exttt{Mn extsuperscript{2+}}, we remove two 4s electrons, resulting in exttt{[Ar] 3d extsuperscript{5}}.

Step 2: Understand the Nature of the Ligand

Water ( extrm{H}_2 extrm{O}) is a weak field ligand, which means it does not cause pairing of electrons in the extit{d}-orbitals of exttt{Mn}. Thus, Hund's rule of maximum multiplicity will apply, and the electrons will stay unpaired.

Step 3: Assign Electrons to the d-Orbitals

In the exttt{[Mn(H extsubscript{2}O) extsubscript{6}] extsuperscript{2+}} complex, manganese is in the exttt{d extsuperscript{5}} electronic configuration. According to Hund's rule, each of the five extit{d}-orbitals will have one unpaired electron.

Step 4: Count the Unpaired Electrons

Since there are five extit{d}-orbitals and each has one electron, the total number of unpaired electrons in exttt{[Mn(H extsubscript{2}O) extsubscript{6}] extsuperscript{2+}} is five.

Key Concepts

Electron Configuration

Electron configuration is a way of knowing where electrons are located around an atom. Manganese, often written as Mn, has an atomic number of 25. This means it ranks 25th on the periodic table and typically houses 25 electrons. Under normal conditions, Mn's electron setup is \\[ [\text{Ar}] \, 3d^5 \, 4s^2 \].\When we're looking at the special case of \( \text{Mn}^{2+} \), it's because the atom has lost 2 electrons. These electrons are lost mostly from the outermost layer, or shell. So, for \( \text{Mn}^{2+} \), we remove the two electrons from \( 4s \). This leaves \[ [\text{Ar}] \, 3d^5 \]. The electrons in the \( 3d \) orbitals will guide us in understanding how other atoms attach, like in coordination compounds.

Unpaired Electrons

Unpaired electrons are those that do not have a partner in the same orbital. Imagine these electrons as kids who prefer to sit alone on a school bus, occupying separate seats based on a rule called Hund's rule. Each \( d \)-orbital gets one child or electron until they are all occupied. This concept is vital in predicting the magnetic properties of compounds. In the case of \( [\text{Mn} (\text{H}_2\text{O})_6]^{2+} \), Mn's electron configuration in its \( 3d \) orbitals is \( d^5 \). This setup features five unpaired electrons, highlighting its magnetic nature. Each \( d \)-orbital has one unpaired electron, demonstrating why Mn in this compound is paramagnetic, meaning it's attracted to magnets.

Weak Field Ligand

A weak field ligand is important in the world of chemistry because it describes how strong a molecule like water is when it connects with others. In the coordination compound \( [\text{Mn}(\text{H}_2\text{O})_6]^{2+} \), water is a weak field ligand. This means the water doesn't provide enough energy to pair up the electrons in Mn's \( 3d^5 \) orbitals. Simply put, weak field ligands allow electrons to remain single and unpaired in their orbitals.
This concept also correlates to the color and reactivity attributes of the compound as weak field ligands lead to specific electron arrangements. In this case, water, as a weak field ligand, means that all five \( 3d \) electrons stay unpaired. Therefore, the \( [\text{Mn}(\text{H}_2\text{O})_6]^{2+} \) compound ends up having five unpaired electrons, shining light on its magnetic properties.