Problem 24 - A Complete Resource Book in Chemistry for JEE Main

Question

\(\mathrm{A}, \mathrm{B}\) and \(\mathrm{C}\) have the oxidation numbers of \(+6,-2\) and \(-1\) respectively, the possible molecular formula when these atoms combine will be (a) \(\mathrm{A}_{2} \mathrm{BC}\) (b) \(\mathrm{AB}_{2} \mathrm{C}_{2}\) (c) \(\mathrm{ABC}_{2}\) (d) \(\mathrm{AB}_{2} \mathrm{C}\)

Step-by-Step Solution

Answer

The possible molecular formula is \(\mathrm{AB}_{2}\mathrm{C}_{2}\).

Step 1: Understanding Oxidation Numbers

The oxidation number is the charge an atom would have if the compound was composed of ions. In this problem, we are given that A has an oxidation number of +6, B has -2, and C has -1.

Step 2: Determine the Total Charge Balance

To form a stable compound, the sum of the oxidation numbers (charges) of all atoms in the molecule must equal 0. Therefore, we have: \(x(+6) + y(-2) + z(-1) = 0\), where \(x\), \(y\), and \(z\) are the number of atoms of A, B, and C, respectively.

Step 3: Trial Each Option for Neutrality

We evaluate each given option to see which one satisfies the condition from Step 2. This involves checking if the sum of the products of the oxidation numbers and the number of atoms per element is zero.

Step 4: Check Option (a)

For \(\mathrm{A}_{2}\mathrm{BC}\): - Contribution from A: \(2(+6) = +12\) - Contribution from B: \(1(-2) = -2\) - Contribution from C: \(1(-1) = -1\)- Total: \(+12 - 2 - 1 = +9\) (Not zero, thus not neutral).

Step 5: Check Option (b)

For \(\mathrm{AB}_{2}\mathrm{C}_{2}\): - Contribution from A: \(1(+6) = +6\) - Contribution from B: \(2(-2) = -4\) - Contribution from C: \(2(-1) = -2\)- Total: \(+6 - 4 - 2 = 0\) (Sum is zero, thus neutral).

Step 6: Check Option (c)

For \(\mathrm{ABC}_{2}\): - Contribution from A: \(1(+6) = +6\) - Contribution from B: \(1(-2) = -2\) - Contribution from C: \(2(-1) = -2\)- Total: \(+6 - 2 - 2 = +2\) (Not zero, thus not neutral).

Step 7: Check Option (d)

For \(\mathrm{AB}_{2}\mathrm{C}\): - Contribution from A: \(1(+6) = +6\) - Contribution from B: \(2(-2) = -4\) - Contribution from C: \(1(-1) = -1\)- Total: \(+6 - 4 - 1 = +1\) (Not zero, thus not neutral).

Step 8: Conclusion: Identify the Correct Formula

Among the given options, only \(\mathrm{AB}_{2}\mathrm{C}_{2}\) results in a total oxidation number of zero, satisfying the condition for a stable molecule.

Key Concepts

Understanding Charge Balance in Chemical Formulas

An essential principle in chemistry is the charge balance. This concept ensures that a compound is neutrally charged. In any stable molecule, the sum of all the charges, or oxidation numbers, must equal zero. This is critical because any imbalance may result in an unstable or non-existent molecule.

Consider the oxidation numbers as given in the original problem: A with +6, B with -2, and C with -1. When these elements combine to form a compound, we must calculate the total charge by multiplying each atom's oxidation number by the number of atoms present in the molecule.

• For example, in the hypothetical compound \( \mathrm{AB}_2\mathrm{C}_2 \), we calculate as follows: \( +6 \times 1 - 2 \times 2 - 1 \times 2 = 0 \).
• This means that \( \mathrm{AB}_2\mathrm{C}_2 \) achieves charge neutrality, making it a viable molecular formula.

Recognizing charge neutrality is key in determining if a compound can exist and remain stable.

Stable Compound Formation Criteria

A stable compound is one that will not spontaneously decompose under normal conditions. One core requirement for stability is charge balance. But beyond that, compounds exhibit further stability through other interactions and bonding arrangements between atoms.

• Atoms strive to achieve full outer electron shells, often involving sharing electrons (covalent bonds) or transferring electrons (ionic bonds) to reach more stable configurations.
• When atoms bond correctly, this not only neutralizes charges but also produces a structure that maintains this balance under expected conditions.

Examining this balance can predict stability. In our example, the molecular formula \( \mathrm{AB}_2\mathrm{C}_2 \) correctly balances the oxidation states, allowing for a potentially stable molecule under realistic conditions. Always checking for total charge neutrality is the first step towards identifying stable molecular entities.

Determining the Molecular Formula

Determining a compound's molecular formula involves correctly identifying the number and types of atoms that make up a molecule. It's a process that heavily relies on achieving a balance of charges and predicting stable forms of compound structures.

Given different atoms with known oxidation numbers, the goal is to find combinations where these numbers sum to zero, indicating charge neutrality and potential stability. Here are some steps one can follow:

• Express the relationship as an equation, as seen when finding all combinations of elements A, B, and C: \[ x(+6) + y(-2) + z(-1) = 0 \]
• Evaluate each potential formula by substituting different integers for \( x, y, \) and \( z \), which represent the number of atoms.
• Calculate to see if the total sum equals zero, identifying valid and stable molecular formulas.

Through this systematic approach, like in the solution provided, we determine that \( \mathrm{AB}_2\mathrm{C}_2 \) is the formula that satisfies the balance criteria, thus making it the correct molecular formula.