Comprehensive Study Notes on d-Block and f-Block Elements (JEE Main 2023)

Redox Chemistry of Potassium Dichromate

Potassium dichromate ($K_2Cr_2O_7$) is a powerful oxidizing agent widely utilized in analytical and synthetic chemistry, particularly in acidic solutions. In these an acidic environment, the dichromate ion ($Cr_2O_7^{2-}$) undergoes reduction to the chromic ion. The chemical process involves the chromium atom shifting from an oxidation state of $+6$ in the dichromate ion to an oxidation state of $+3$ in the resulting chromium(III) ion.

The half-reaction for this reduction in acidic medium is represented as: $Cr_2O_7^{2-} + 14H^+ + 6e^- \rightarrow 2Cr^{3+} + 7H_2O$

Because there is a decrease in oxidation number from $+6$ to $+3$, potassium dichromate acts as an oxidizing agent by accepting electrons from other species in the solution.

Oxidation States and Oxidizing Nature of Transition Metals

Transition metals are characterized by their ability to exhibit a wide range of oxidation states due to the participation of both $(n-1)d$ and $ns$ electrons in bonding. Several specific observations regarding these oxidation states are notable:

1. Manganese ($Mn$) exhibits its highest oxidation state of $+7$ in its oxide form, specifically in manganese heptoxide ($Mn_2O_7$).
2. For heavier transition elements in Group 8, such as Ruthenium ($Ru$) and Osmium ($Os$), the oxidation state can reach as high as $+8$ in their respective oxides, $RuO_4$ and $OsO_4$.
3. Scandium ($Sc$) typically shows an oxidation state of $+3$. The claim that it exhibits a $+4$ oxidation state that is oxidizing in nature is incorrect, as $+3$ is the stable and most common state for Scandium.
4. Chromium ($Cr$) is highly oxidizing when it is in the $+6$ oxidation state. This is seen in compounds like the dichromate ion ($Cr_2O_7^{2-}$) and the chromate ion ($CrO_4^{2-}$).

Chromium Pentoxide and Coordination Compounds in Medicine

A specific test for chromium involves the formation of Chromium pentoxide ($CrO_5$). When a solution of acidified dichromate is treated with hydrogen peroxide in the presence of an organic solvent like amyl alcohol, a deep blue color is observed. This color is due to the formation of $CrO_5$, which is stabilized in the amyl alcohol layer. The structure of $CrO_5$ is famously described as a "butterfly" structure, featuring two peroxo groups.

In the field of medicine, coordination compounds play a vital role. Specifically, to inhibit the growth of tumors, platinum-based coordination compounds are employed. The most prominent example is Cis-platin ($Cis-[Pt(NH_3)_2Cl_2]$), which is a neutral coordination complex used effectively in chemotherapy to treat various types of cancers. Other compounds mentioned in similar contexts include EDTA and D-Penicillamine, though these are typically utilized as chelating agents for treating heavy metal poisoning rather than as primary anti-tumor agents.

Oxidation Reactions of Potassium Permanganate ($KMnO_4$)

Potassium permanganate acts as a strong oxidizing agent, but its behavior and the products it forms depend heavily on the $pH$ of the reaction medium. When reacting with iodide ions ($I^-$), the results differ as follows:

1. In an acidic solution: $KMnO_4$ oxidizes the iodide ion ($I^-$) to molecular iodine ($I_2$). In this process, the permanganate ion ($MnO_4^-$) is reduced to $Mn^{2+}$.
2. In a neutral or faintly alkaline solution: $KMnO_4$ oxidizes the iodide ion ($I^-$) to the iodate ion ($IO_3^-$). In this medium, the permanganate ion is typically reduced to manganese dioxide ($MnO_2$).

Electronic Configurations of Lanthanides and Post-Transition Ions

The electronic configuration of lanthanide ions is essential for understanding their chemical properties. For the Neodymium ion ($Nd^{2+}$), we must first consider the ground state configuration of Neodymium ($Z=60$), which is $[Xe] 4f^4 6s^2$. Upon losing two electrons to form the divalent cation ($Nd^{2+}$), the electrons are removed from the $6s$ orbital, resulting in a configuration of $[Xe] 4f^4$.

In the context of half-filled f-orbitals (the $f^7$ configuration), we look at specific lanthanides:

• Samarium ($Sm$, $Z=62$): Ground state is $[Xe] 4f^6 6s^2$.
• Europium ($Eu$, $Z=63$): Ground state is $[Xe] 4f^7 6s^2$. This contains a half-filled f-orbital.
• Gadolinium ($Gd$, $Z=64$): Ground state is $[Xe] 4f^7 5d^1 6s^2$. This also contains a half-filled f-orbital.
• Terbium ($Tb$, $Z=65$): Ground state is $[Xe] 4f^9 6s^2$.
• Promethium ($Pm$, $Z=61$): Ground state is $[Xe] 4f^5 6s^2$.

Therefore, Europium ($Eu$) and Gadolinium ($Gd$) are the elements that possess half-filled f-orbitals in their ground states.

Acidity and Basicity of Vanadium Oxides

For transition metal oxides, the basicity generally decreases as the oxidation state of the metal increases. This is because higher oxidation states lead to higher charge density, increasing the covalent character of the bond and the acidity of the oxide. In the case of Vanadium oxides:

• $V_2O_3$ contains Vanadium in the $+3$ oxidation state.
• $V_2O_4$ contains Vanadium in the $+4$ oxidation state.
• $V_2O_5$ contains Vanadium in the $+5$ oxidation state.

The correct order of basic nature is $V_2O_3 > V_2O_4 > V_2O_5$. Thus, $V_2O_3$ is the most basic, while $V_2O_5$ is amphoteric but predominantly acidic.

Ionization Enthalpies and Structural Properties of Manganese Heptoxide

The first ionization enthalpy of elements in the $3d$ series is generally higher than that of Group 2 metals. This is attributed to the successive filling of the $d$-orbitals across the period, which leads to an increase in effective nuclear charge that is not fully shielded by the inner electrons.

Regarding the structure of Manganese heptoxide ($Mn_2O_7$), which represents Manganese in its highest oxidation state ($Mn$ in $+7$), several structural features are observed:

1. Each Manganese atom is tetrahedrally surrounded by four oxygen atoms.
2. The structure contains an $Mn-O-Mn$ bridge, connecting the two manganese centers.
3. There is no direct $Mn-Mn$ bond in the $Mn_2O_7$ molecule.

Stability of Copper Ions in Aqueous Solution

A common phenomenon in aqueous chemistry is that the divalent copper ion ($Cu^{2+}$) is more stable than the monovalent copper ion ($Cu^+$), despite $Cu^+$ having a completely filled $d^{10}$ configuration. The primary reason for this is the hydration enthalpy. The enthalpy of hydration ($\Delta H_{hyd}$) for $Cu^{2+}$ is significantly more negative (more exothermic) than that for $Cu^+$. This large release of energy during hydration more than compensates for the high second ionization enthalpy required to remove the second electron from copper. Thus, in an aqueous environment, $Cu^{2+}$ is the more stable species.