Problem 5 - A Complete Resource Book in Chemistry for JEE Main

Question

A complex compound of \(\mathrm{Co}^{3+}\) with molecular formula \(\mathrm{CoCl}_{\mathrm{x}} \cdot \mathrm{yNH}_{3}\) gives a total of 3 ions when dissolved in water. How many Cl- ions satisfy both primary as well as the secondary valencies in this complex? (a) 3 (b) 1 (c) 4 (d) zero

Step-by-Step Solution

Answer

(b) 1

Step 1: Understanding Coordination Chemistry

The complex compound provided is made up of cobalt (\(\mathrm{Co}^{3+}\)), chlorine \((\mathrm{Cl}^-)\), and ammonia \((\mathrm{NH}_3)\). Cobalt (III) has a primary valency of 3, which corresponds to the number of ions detached when dissolved in water, i.e., charge. This compound splits into ions to give a total of 3 ions; the rest are bound to satisfy the metal's secondary valency (coordination number).

Step 2: Analyzing the Ionization

Since the compound gives a total of 3 ions upon dissolution, and considering one of these ions is the complex ion itself \([\mathrm{Co}\mathrm{NH}_3^y\mathrm{Cl}_w]^{z+}\), the other ions will be chlorine ions. Thus, the exterior chlorine ions ionize to give \( x-2 = 2 \) chloride ions, which implies 2 Cl- ions are free, not part of the coordination sphere. Consequently, this fits with \((\mathrm{Co}\mathrm{Cl}_x \cdot \mathrm{yNH}_3)\) resulting in three ions: 2 free Cl- ions and one complex ion.

Step 3: Applying Coordination Chemistry

The secondary valency will be filled by Ammonia \(\mathrm{NH}_3\) and the remaining chlorine ions \(w\), which are directly bonded to the cobalt ion. To satisfy the metal's coordination number \(w + y = 6\). Since the free chloride ions are outside the coordination sphere, the remaining Cl ion(s) must be inside, completing the coordination sphere.

Step 4: Solving the Equation

The cobalt ion \(\mathrm{Co}^{3+}\) forms a coordination number of 6. We've deduced there are 3 free ions, so 3 more are left to fulfill the coordination: \( x - 2 + y = 6\). Assigning free ions \(x - 2 = 2\) from Step 2, we find \(x = 3\) and thus \(y = 3\). This confirms that all 3 chloride ions are involved in primary valency, and one is coordinated (secondary valency) causing chlorine ions to satisfy both primary and secondary valencies, and fulfill the charge.

Key Concepts

Complex Compounds

Complex compounds are fascinating structures in chemistry formed when a central metal atom binds with surrounding molecules or ions. This often happens through coordinate covalent bonds. These compounds are also known as coordination complexes.

• **Central Ion or Atom**: Generally, this is a transition metal, like cobalt (4Co4) in our exercise.
• **Ligands**: Molecules or ions that donate a pair of electrons to the metal are called ligands. Ammonia (NH_3) and chlorine ions (Cl^-) often serve this function.

Complex compounds have broad applications, such as in catalysis and biological systems. Understanding the composition and behavior of these complexes is crucial in coordination chemistry.

Coordination Number

The coordination number of a complex compound is a key concept in understanding its structure. It signifies the number of ligand atoms bound to the central metal ion. In the given exercise, cobalt (III) has a coordination number often equaling 6, a common scenario for such metals. This means six entities (either ligands or their functions) surround the cobalt ion.

• **Impacts Structure**: The coordination number informs us about the geometric arrangement of the ligands around the central ion.
• **Reflects Bonding**: It shows how many connections are formed, critical for complexes' stability and reactions.

By deciphering the coordination number, we can deduce how the atoms are arranged and predict how the compound might react.

Primary Valency

Primary valency refers to the oxidation state or the principal valency of the central metal ion in a complex. It is similar to the charge on the ion. In our example, cobalt (III) has a primary valency of +3. This primary valency helps determine the number of ions a compound can release into the solution when dissolved. In our case, when the complex dissolves in water, it produces three ions in total, aligning with cobalt's primary valency.

• **Free Ions**: These are ions that satisfy the primary valency by being free to move in solution.
• **Charge Balance**: The compound's primary valency ensures that the total number of ions effectively balances its overall charge.

Mastering the concept of primary valency allows us to predict how compounds dissociate in solutions and their potential electrolytic behavior.

Secondary Valency

Secondary valency pertains to the number of coordinate bonds formed between the metal ion and its surrounding ligands within a complex compound. These bonds reflect the coordination number discussed earlier. In the cobalt compound example, the secondary valency is filled by ligands like ammonia and remaining chlorine ions within the coordination sphere. It is this secondary valency that leads to the formation of the coordination sphere.

• **Coordination Sphere**: The structural core where ligands like NH_3 and Cl^- directly bond with the metal.
• **Stability**: The secondary valency contributes significantly to the stability and geometry of the complex.

Understanding secondary valency provides insight into the spatial arrangement of atoms and stability preferences of complex compounds.