

\( 3\text{NiS} + 2\text{HNO}_3 + 6\text{HCl} \rightarrow 3\text{NiCl}_2 + 2\text{NO} + 3\text{S} + 4\text{H}_2\text{O} \)
The problem asks for the number of protons that are not involved in hydrogen bonding in the final product B, which is formed through a sequence of two reactions.
1. Redox Reaction: The first reaction involves Nickel(II) sulfide (NiS) reacting with nitric acid (HNO₃) and hydrochloric acid (HCl). This is a redox reaction where nitric acid acts as an oxidizing agent. The products are determined by the oxidation of sulfide and the reduction of nitrate.
2. Coordination Chemistry (Qualitative Analysis): The second reaction is a characteristic test for the Nickel(II) ion (\(Ni^{2+}\)). \(Ni^{2+}\) reacts with dimethylglyoxime (DMG), \(H_3C-C(=NOH)-C(=NOH)-CH_3\), in an ammoniacal (basic) medium to form a stable, brightly colored coordination complex.
3. Hydrogen Bonding: This is an electrostatic attraction between a hydrogen atom covalently bonded to a highly electronegative atom (like O, N, F) and another nearby electronegative atom. Protons attached to carbon atoms (C-H bonds) are generally considered non-polar and do not participate in conventional hydrogen bonding.
4. Structure of Nickel(II) dimethylglyoximate: The complex formed, \(Ni(DMG)_2\), has a specific square planar geometry with intramolecular hydrogen bonds, which must be analyzed to count the different types of protons.
Step 1: Identify the product A from the first reaction.
The first reaction is:
\[ NiS + HNO_3 + HCl \longrightarrow A + NO + S + H_2O \]In this reaction, the sulfide ion (\(S^{2-}\)) in NiS is oxidized to elemental sulfur (S). The nitrate ion (\(NO_3^-\)) from nitric acid is reduced to nitric oxide (NO). The nickel ion remains in its +2 oxidation state and, in the presence of HCl, forms nickel(II) chloride. The balanced reaction is:
\[ 3NiS + 2HNO_3 + 6HCl \longrightarrow 3NiCl_2 + 2NO + 3S + 4H_2O \]Therefore, the compound A is Nickel(II) chloride, \(NiCl_2\).
Step 2: Identify the product B from the second reaction.
The second reaction is:
\[ A + NH_4OH + \text{Dimethylglyoxime} \longrightarrow B + NH_4Cl + H_2O \]Substituting A = \(NiCl_2\), we have the reaction of Nickel(II) chloride with dimethylglyoxime (DMG) in an ammoniacal solution (\(NH_4OH\)). This is a classic confirmatory test for \(Ni^{2+}\), which forms a stable, bright red precipitate of Nickel(II) dimethylglyoximate. The overall reaction is:
\[ NiCl_2 + 2(C_4H_8N_2O_2) + 2NH_4OH \longrightarrow Ni(C_4H_7N_2O_2)_2 + 2NH_4Cl + 2H_2O \]Thus, the product B is the complex Nickel(II) dimethylglyoximate, often written as \(Ni(DMG)_2\). Its chemical formula is \(C_8H_{14}N_4NiO_4\).
Step 3: Analyze the structure of product B, \(Ni(DMG)_2\).
In the complex \(Ni(DMG)_2\), the central \(Ni^{2+}\) ion is coordinated to two dimethylglyoximate ligands. Each ligand is bidentate, bonding to the nickel ion through its two nitrogen atoms. This results in a square planar geometry around the nickel atom. The structure is stabilized by two strong intramolecular O-H···O hydrogen bonds between the two ligands.
Step 4: Identify and count the different types of protons in the structure of B.
The structure of \(Ni(DMG)_2\) contains two types of hydrogen atoms (protons):
We need to find the number of protons that do not involve in hydrogen bonding.
Total number of methyl protons = (Number of methyl groups) × (Protons per group)
\[ \text{Number of protons not involved in H-bonding} = 4 \times 3 = 12 \]The number of protons that do not involve in hydrogen bonding in the product B is 12.
What will be the equilibrium constant of the given reaction carried out in a \(5 \,L\) vessel and having equilibrium amounts of \(A_2\) and \(A\) as \(0.5\) mole and \(2 \times 10^{-6}\) mole respectively?
The reaction : \(A_2 \rightleftharpoons 2A\)

Cobalt chloride when dissolved in water forms pink colored complex $X$ which has octahedral geometry. This solution on treating with cone $HCl$ forms deep blue complex, $\underline{Y}$ which has a $\underline{Z}$ geometry $X, Y$ and $Z$, respectively, are

What will be the equilibrium constant of the given reaction carried out in a \(5 \,L\) vessel and having equilibrium amounts of \(A_2\) and \(A\) as \(0.5\) mole and \(2 \times 10^{-6}\) mole respectively?
The reaction : \(A_2 \rightleftharpoons 2A\)
A black body is at a temperature of 2880 K. The energy of radiation emitted by this body with wavelength between 499 nm and 500 nm is U1, between 999 nm and 1000 nm is U2 and between 1499 nm and 1500 nm is U3. The Wien's constant, b = 2.88×106 nm-K. Then,