Problem 63 - A Complete Resource Book in Chemistry for JEE Main

Question

A compound contains atoms \(X, Y, Z\) the oxidation number of \(X\) is \(+2, Y\) is \(+5\) and \(Z\) is \(-2\) The possible form of the compound is (a) \(\mathrm{XY}_{1} \mathrm{Z}_{2}\) (b) \(\mathrm{Y}_{2}\left(\mathrm{XZ}_{3}\right)_{2}\) (c) \(\mathrm{X}_{3}\left(\mathrm{YZ}_{4}\right)_{2}\) (d) \(\mathrm{X}_{3}\left(\mathrm{Y}_{4} \mathrm{Z}\right)_{2}\)

Step-by-Step Solution

Answer

Option (c) \( \mathrm{X}_{3}(\mathrm{YZ}_{4})_{2} \) is the correct form of the compound.

Step 1: Understanding Oxidation Numbers

The oxidation numbers provided indicate how many electrons an atom of an element gains or loses to reach a stable state. Here are the given oxidation numbers: \( X = +2 \), \( Y = +5 \), and \( Z = -2 \). These values will be used to check if the sum of oxidation numbers in each compound equals zero, which is the condition for a stable compound.

Step 2: Option A - Evaluating \( \mathrm{XY}_{1} \mathrm{Z}_{2} \)

Calculate the total oxidation number for each element: \( X = +2 \), \( Y = +5 \), and two \( Z = 2 \times -2 = -4 \). The sum is \(+2 + 5 -4 = +3\). Since this sum is not zero, option (a) is incorrect.

Step 3: Option B - Evaluating \( \mathrm{Y}_{2}\left(\mathrm{XZ}_{3}\right)_{2} \)

Calculate the total oxidation number: For \( Y = 2 \times +5 = +10 \), and for \(\mathrm{XZ}_{3}\), each has \( X = +2 \), \(3 \times Z = 3 \times -2 = -6\), so \(\mathrm{XZ}_{3} = +2 -6 = -4\). Therefore, \(2 \times -4 = -8\). The sum is \(+10 -8 = +2\), which is not zero. Option (b) is incorrect.

Step 4: Option C - Evaluating \( \mathrm{X}_{3}\left(\mathrm{YZ}_{4}\right)_{2} \)

Calculate the total oxidation number: For the term \(\mathrm{X}_{3}\), \(3 \times X = 3 \times +2 = +6\); in \(\mathrm{YZ}_{4}\), \( Y = +5 \), \(4 \times Z = 4 \times -2 = -8\), so \(\mathrm{YZ}_{4} = +5 -8 = -3\). Thus, \(2 \times -3 = -6\). The sum is \(+6 -6 = 0\). Therefore, this configuration is balanced, meaning it forms a stable compound. Option (c) could be correct.

Step 5: Option D - Evaluating \( \mathrm{X}_{3}\left(\mathrm{Y}_{4} \mathrm{Z}\right)_{2} \)

Calculate the total oxidation number: For \(\mathrm{X}_{3}\), \( 3 \times X = 3 \times +2 = +6\); in \(\mathrm{Y}_{4} \mathrm{Z}\), \( Y_{4} = 4 \times +5 = +20\), \( Z = -2 \), so \(\mathrm{Y}_{4} \mathrm{Z} = +20 - 2 = +18\). Therefore, \(2 \times +18 = +36\). The sum is \(+6 + 36 = +42\), which is not zero. Option (d) is incorrect.

Key Concepts

Compound Stability

In chemistry, the stability of a compound can be assessed by its oxidation numbers. These numbers show how electrons are exchanged during reactions. A compound is stable when it maintains a balanced electrical charge.

• Oxidation numbers: Represent the charge an atom would have if the compound was composed of ions.
• Stability criterion: The sum of the oxidation numbers in a compound must be zero for it to be stable.

The calculations of oxidation numbers allow chemists to predict the stability of a compound. Sometimes, understanding whether a compound is stable can explain why some reactions occur and others do not. As seen in the exercise, option (c)'s compound achieves balance, confirming its stability.

Electrochemistry Concepts

Oxidation and reduction are the pillars of electrochemistry. This branch of chemistry focuses on the movement of electrons, which is crucial for creating stable chemical bonds.

• Oxidation: Loss of electrons by an atom, increasing its oxidation state.
• Reduction: Gain of electrons by an atom, decreasing its oxidation state.
• Redox reactions: A combination of reduction and oxidation where electrons are transferred between atoms.

In the context of the provided exercise, each element's capacity to lose and gain electrons to, or from other elements decides the potential configurations of a stable compound. Here, elements X, Y, and Z interchange electrons ensuring some configurations balance, like in option (c), and stabilize the compound.

Chemical Formula Evaluation

Evaluating chemical formulas involves analyzing the structure and distribution of atoms within molecules. Correct evaluation ensures that the chemical process and the resulting compound's stability are understood.

• Purpose: To ensure that combined elements result in an overall neutral compound.
• Calculation: Sum all oxidation numbers for each compound formula to check for zero balance.

In the exercise, each possible formula is evaluated step by step to determine if the sum of oxidation numbers equals zero. This systematic approach helps identify option (c) as the formula where balance is achieved.