Problem 158 - A Complete Resource Book in Chemistry for JEE Main

Question

The oxidation state of \(\mathrm{Cr}\) in \(\left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{2}\right]^{+} \quad\) (a) 0 (b) \(+1\) (c) \(+2\) (d) \(+3\)

Step-by-Step Solution

Answer

The oxidation state of \(\mathrm{Cr}\) is \(+3\).

Step 1: Understand the Coordination Compound

We need to determine the oxidation state of Chromium (Cr) in the complex ion \(\left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{2}\right]^{+}\). In this coordination compound, \(\mathrm{NH}_3\) is a neutral ligand, and each chloride ion (\(\mathrm{Cl}^-\)) has a charge of \(-1\). Overall the compound has a +1 charge.

Step 2: Assign Charges to Ligands and Aim for Overall Charge

The compound consists of four ammonia (\(\mathrm{NH}_3\)) molecules, which are neutral and contribute \(0\) charge each, and two chloride ions (\(\mathrm{Cl}^-\)), which contribute a total charge of \(-2\). Since the entire complex has a charge of \(+1\), the sum of all the charges should equal \(+1\).

Step 3: Calculate the Charge for the Metal

Let \(x\) be the oxidation state of \(\mathrm{Cr}\). Hence, the equation is \(x + 4(0) + 2(-1) = +1\). Simplifying gives \(x - 2 = +1\).

Step 4: Solve for the Oxidation State

Solve the equation \(x - 2 = +1\) for \(x\). Add 2 to both sides to get \(x = +3\). Thus, the oxidation state of \(\mathrm{Cr}\) in the compound is \(+3\).

Key Concepts

Oxidation State

The oxidation state of an element in a compound is essentially the degree of oxidation of that element. It represents the number of electrons an atom can lose, gain, or share when it is in a compound. This is a crucial concept because it helps understand how compounds are formed and how they behave in chemical reactions. In coordination chemistry, determining the oxidation state of the central atom, like Chromium (Cr) in our example, is indispensable for understanding the chemical composition and bonding. Usually, the oxidation state is indicated by a Roman numeral, like Cr(III) for an oxidation state of +3. To determine this, you add up the charges contributed by all ligands and set it to the known charge of the entire complex, solving for the central atom's oxidation state.

Coordination Compounds

Coordination compounds are a fascinating topic in chemistry, defined by the presence of a central metal atom or ion bonded to surrounding molecules or ions, known as ligands. These compounds, like \([\mathrm{Cr}(\mathrm{NH}_3)_4\mathrm{Cl}_2]^+\), consist of a metal atom (often a transition metal) surrounded by ligands, creating a complex ion. The central metal, such as Chromium in our case, coordinates with the ligands, forming coordinate covalent bonds. Many properties of coordination compounds, such as their color, magnetism, and reactivity, depend significantly on how the metal atom bonds with its ligands. The nature of these bonds and the geometric arrangement can dramatically affect how these compounds interact with other molecules and ions.

Ligand Charge Assignment

In coordination chemistry, understanding how to assign charges to ligands is fundamental for determining the overall charge of the compound. Ligands can be neutral or charged, influencing the oxidation state of the central metal atom.

• For instance, in the compound [Cr(NH_3)_4Cl_2]^+, ammonia \((\mathrm{NH}_3)\) is a neutral ligand, contributing zero charge per molecule.
• In contrast, chloride ions \((\mathrm{Cl}^-)\) are negatively charged, each contributing a -1 charge.

To determine the oxidation state accurately, consider the charges of all ligands and the total charge of the coordination compound. This systematic approach allows for calculating the oxidation state of the central metal, as the total charges from ligands and the metal must equal the overall charge of the compound. This understanding is crucial for appreciating the chemical behavior and reactivity of coordination compounds.