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

Question

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

Step-by-Step Solution

Answer

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

Step 1: Identify Components and Their Charges

The complex ion given is \( \left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{2} \right]^{+} \). We will first identify the charges of each component. Ammonia (\( \mathrm{NH}_{3} \)) is a neutral ligand, so it contributes no charge. Each chloride ion (\( \mathrm{Cl}^- \)) contributes a \(-1\) charge. Since there are two chloride ions, their total contribution is \(-2\).

Step 2: Use Total Charge to Find Oxidation State

The overall charge of the complex ion is given as \(+1\). Thus, the sum of the oxidation state of chromium (\( \mathrm{Cr} \)) and the charge of the ligands should equal \(+1\).

Step 3: Set Up the Equation

Let \( x \) be the oxidation state of \( \mathrm{Cr} \). The equation representing the charges is: \[ x + (4 \times 0) + (2 \times -1) = +1 \] which simplifies to: \[ x - 2 = +1 \]

Step 4: Solve for \( x \)

Solve the equation \( x - 2 = +1 \) to find \( x \). Add 2 to both sides to find \( x = +3 \).

Step 5: Conclusion

The oxidation state of \( \mathrm{Cr} \) in \( \left[ \mathrm{Cr}(\mathrm{NH}_{3})_{4} \mathrm{Cl}_{2} \right]^{+} \) is \(+3\).

Key Concepts

Chromium Complexes

Chromium complexes are a fascinating subject in chemistry with a variety of industrial and scientific applications. Chromium can form several different oxidation states, most commonly ranging from

• +2
• +3
• +6

These oxidation states are associated with different properties and uses of the element. In the context of ligand chemistry, chromium often serves as the central metal atom in complex ions. This means it connects to other atoms or groups of atoms, known as ligands.
For students analyzing chromium-containing compounds, understanding the charge or oxidation state of chromium is crucial. It reveals how chromium interacts with ligands and influences the properties of the entire complex. In the given complex, \[\left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{2}\right]^{+}\]chromium exhibits an oxidation state of +3. This affects the color, magnetism, and reactivity of the complex, making it an essential point of study for chemistry students.

Coordination Compounds

Coordination compounds consist of a central metal atom or ion bonded to a surrounding array of molecules or ions, called ligands. These compounds have a wide range of uses, from catalysis to electronic materials.
The central metal, such as chromium in our complex, is typically a transition metal that can exchange electrons with the ligands. This interaction primarily determines the physical and chemical properties of the coordination compound. For example,

• Color of the compound
• Magnetic properties
• Stability

In the complex\[\left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{2}\right]^{+}\]chromium coordinates with four ammonia molecules and two chloride ions. This set-up leads to a specific geometry and arrangement, which students may be asked to identify or explain. Understanding these arrangements helps in predicting the behavior and reactivity of coordination compounds.

Ligand Chemistry

Ligands are ions or molecules that donate a pair of electrons to a central metal atom to form coordination bonds. In the study of coordination chemistry, the nature and type of ligands significantly impact the characteristics of a complex.
Ligands like ammonia \(\left(\mathrm{NH}_{3}\right)\)are neutral, whereas chloride \(\left(\mathrm{Cl}^-\right)\)is a negatively charged ligand. These ligands play a pivotal role in defining the chemical behavior of a complex.

• Neutral ligands do not add additional charge to the complex.
• Anionic ligands decrease the oxidation state of the central metal by contributing negative charges.

In our specific example with chromium, ammonia contributes no charge, whereas chloride contributes -1 per ion. When calculating the overall charge or oxidation state of a complex, understanding the charge of each ligand is essential. Proper knowledge of ligand behavior and their electron-donating capabilities helps predict the reaction pathways and stability of coordination compounds.