Problem 112 - A Complete Resource Book in Chemistry for JEE Main

Question

Each of the compounds \(\mathrm{Pt}\left(\mathrm{NH}_{3}\right)_{6} \mathrm{Cl}_{4}, \mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{6} \mathrm{Cl}_{3}\), \(\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{3}\) and \(\mathrm{K}_{2} \mathrm{PtCl}_{6}\) has been dissolved in water to make its \(0.001 \mathrm{M}\) solution. The order of their increasing conductivity in solution is (a) \(\mathrm{K}_{2} \mathrm{PtCl}_{6}<\mathrm{Pt}\left(\mathrm{NH}_{3}\right)_{6} \mathrm{Cl}_{4}<\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{6} \mathrm{Cl}_{3}<\) \(\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{3}\) (b) \(\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{6} \mathrm{Cl}_{3}<\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{3}<\mathrm{Pt}\left(\mathrm{NH}_{3}\right)_{6} \mathrm{Cl}_{4}<\) \(\mathrm{K}_{2} \mathrm{PtCl}_{6}\) (c) \(\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{3}<\mathrm{K}_{2} \mathrm{PtCl}_{6}<\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{6} \mathrm{Cl}_{3}<\) \(\mathrm{Pt}\left(\mathrm{NH}_{3}\right)_{6} \mathrm{Cl}_{4}\) (d) \(\mathrm{Pt}\left(\mathrm{NH}_{3}\right)_{6} \mathrm{Cl}_{4}<\mathrm{K}_{2} \mathrm{PtCl}_{6}<\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{3}<\) \(\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{6} \mathrm{Cl}_{3}\)

Step-by-Step Solution

Answer

The correct order is option (c): Co(NH3)4Cl3 < K2PtCl6 < Cr(NH3)6Cl3 < Pt(NH3)6Cl4.

Step 1: Determine Ion Contribution

To find the order of increasing conductivity of the solutions, we need to consider the dissociation of each compound into ions because conductivity depends on the number of ions in solution. Each compound will dissociate into different ions, providing different contributions to the conductivity.

Step 2: Analyze Pt(NH3)6Cl4

The compound \(\mathrm{Pt(NH}_{3}\mathrm{)_{6}Cl}_{4})\) is a coordination complex. It dissociates as follows:\[\mathrm{Pt(NH}_{3}\mathrm{)_{6}Cl}_{4} \rightarrow \mathrm{[Pt(NH}_{3}\mathrm{)_{6}]}^{4+} + 4 \mathrm{Cl}^-\]This results in 5 ions (1 complex cation and 4 chloride ions).

Step 3: Analyze Cr(NH3)6Cl3

The compound \(\mathrm{Cr(NH}_{3}\mathrm{)_{6}Cl}_{3})\) is another coordination complex and dissociates as follows:\[\mathrm{Cr(NH}_{3}\mathrm{)_{6}Cl}_{3} \rightarrow \mathrm{[Cr(NH}_{3}\mathrm{)_{6}]}^{3+} + 3 \mathrm{Cl}^-\]This results in 4 ions (1 complex cation and 3 chloride ions).

Step 4: Analyze Co(NH3)4Cl3

The compound \(\mathrm{Co(NH}_{3}\mathrm{)_{4}Cl}_{3})\) dissociates as:\[\mathrm{Co(NH}_{3}\mathrm{)_{4}Cl}_{3} \rightarrow \mathrm{[Co(NH}_{3}\mathrm{)_{4}Cl}^{2+} + 2 \mathrm{Cl}^-\]This forms 3 ions (1 complex ion and 2 chloride ions as it is a partial coordination complex).

Step 5: Analyze K2PtCl6

The compound \(\mathrm{K}_{2}\mathrm{PtCl}_{6}\) dissociates completely as:\[\mathrm{K}_{2}\mathrm{PtCl}_{6} \rightarrow 2\mathrm{K}^+ + \mathrm{PtCl}_{6}^{2-}\]This results in 3 ions (2 potassium ions and 1 complex anion).

Step 6: Order by Number of Ions

Now, sort the compounds by the increasing number of ions they produce in solution, as conductivity increases with the number of ions:* \(\mathrm{Co(NH}_{3}\mathrm{)_{4}Cl}_{3}\) and \(\mathrm{K}_{2}\mathrm{PtCl}_{6}\) each provide 3 ions.* \(\mathrm{Cr(NH}_{3}\mathrm{)_{6}Cl}_{3}\) provides 4 ions.* \(\mathrm{Pt(NH}_{3}\mathrm{)_{6}Cl}_{4}\) provides 5 ions.Hence, the order of increasing conductivity is: \(\mathrm{Co(NH}_{3}\mathrm{)_{4}Cl}_{3} < \mathrm{K}_{2}\mathrm{PtCl}_{6} < \mathrm{Cr(NH}_{3}\mathrm{)_{6}Cl}_{3} < \mathrm{Pt(NH}_{3}\mathrm{)_{6}Cl}_{4}\).

Key Concepts

Coordination Compounds

Coordination compounds, also known as complex compounds, are fascinating structures where transition metal atoms are bonded to various molecules or ions. These bonds are special because they involve the donation of electron pairs from the ligands to the metal center. Ligands are typically neutral molecules like ammonia (NH₃) or ions such as chloride (Cl⁻).

A central metal atom or ion is surrounded by a set number of ligands, forming a coordination complex. The coordination number, which is basically the total number of sites occupied by ligands on the central metal, can usually range from 2 up to 12.

Coordination chemistry helps us understand the structure, reactivity, and properties of a vast number of metal-based systems, making it critical in fields like catalysis, biological systems, and material science. The unique arrangements of the ligands around the metal ion can significantly influence the resultant properties, such as color, magnetism, and, notably, conductivity.

Dissociation of Compounds

Dissociation is a chemical process where compounds are split into smaller components, typically ions, when they are dissolved in liquid. In the context of solutions, especially those involving ionic or coordination compounds, dissociation is crucial for conductivity. When a substance dissolves in water, it might break into its constituent ions, which can move and thus conduct electricity.

Each compound will dissociate differently based on its structure and the strength of the bonds formed in its crystalline state. For example:

• Pt(NH₃)₆Cl₄: A complete dissociation results in five ions - one large cation complex and four individual Cl⁻ ions.
• Cr(NH₃)₆Cl₃: Splits into four ions comprising a trication and three Cl⁻ ions.
• Co(NH₃)₄Cl₃: Yields three ions since it forms one partial cation complex and two Cl⁻ ions.
• K₂PtCl₆: Produces three ions due to complete breakdown into two K⁺ ions and one complex anion.

Dissociation levels directly impact how well a solution can conduct electricity because more free-moving ions mean higher conductivity.

Ion Contribution to Conductivity

Conductivity in chemistry refers to the ability of a solution to conduct electricity, hinging largely on the presence and movement of ions. When a compound dissolves in water and dissociates into ions, these charged particles facilitate the flow of electric current.

• More ions equate to higher conductivity because they enable more charge to be carried through the solution.
• A solution's conductivity increases as the number of ions increases. Hence, compounds like Pt(NH₃)₆Cl₄, which dissociate into five ions in solution, show higher conductivity compared to compounds dissociating into fewer ions.
• Variations in the degree of ionization among different compounds result in differing levels of conductivity outcomes.

It's essential to understand that while the number of ions contributes significantly to conductivity, the nature of the ions, i.e., their size and charge, can also impact the overall conductivity of a solution. Bigger or multipositive/multinegative ions might move slower, reducing the effect a higher number of ions might have.