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

Question

A, B and 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 correct formula is (b) \( \mathrm{AB}_{2} \mathrm{C}_{2} \).

Step 1: Identify Oxidation States

We are given the oxidation states: A is +6, B is -2, and C is -1. Our task is to ensure the compound is neutral, meaning the sum of the oxidation numbers in the compound must equal zero.

Step 2: Calculate Total Charge for Each Option

For each option, calculate the total charge: - Option (a): A2 (+6) + B0 (-2) + C1 (-1) = 12 - 2 - 1 = +9 - Option (b): A1 (+6) + B2 (-2) + C2 (-1) = 6 - 4 - 2 = 0 - Option (c): A1 (+6) + B0 (-2) + C2 (-1) = 6 - 0 - 2 = +4 - Option (d): A1 (+6) + B2 (-2) + C0 (-1) = 6 - 4 + 0 = +2

Step 3: Select the Correct Formula

The molecular formula must be neutral, so total charge should be zero. Only option (b) AC_{2} yields a total oxidation number sum of zero, making it the correct molecular formula.

Key Concepts

Understanding Molecular Formula

The molecular formula represents the combination of elements that make up a molecule. It not only indicates the types of atoms present but also how many of each kind are in the molecule. For example, when considering the choices provided (89 in the exercise, each option is a potential molecular formula. They are made up of elements A, B, and C, with specific quantities such as 8 subscript numbers9 which indicate the number of each atom involved.
The molecular formula is crucial for understanding the compound's composition and how the oxidation states sum up to create a neutral compound. It is important to note that while the molecular formula provides these details, it doesn't directly indicate how atoms are arranged in space, which is described by the structural formula instead.

What is a Neutral Compound?

A neutral compound is one in which the net charge is zero. This means that the sum of all oxidation numbers of the atoms in the molecular formula must cancel each other out to equal zero.
Each element in a compound has a designated oxidation state, which is essentially a hypothetical charge assigned according to certain rules. When forming a neutral compound, these charges must combine in a way such that they balance perfectly, resulting in a compound with no overall charge.
In our exercise, we have specific oxidation states for A, B, and C, being +6, -2, and -1 respectively. Thus, when forming a compound, the combination of atoms (as indicated by the molecular formula) has to be such that their sum equals zero. This is key to maintaining stability and neutrality in the chemical structure.

Oxidation Number Sum and Its Significance

The oxidation number sum is a crucial concept for ensuring the neutrality of a compound. The sum of the individual oxidation numbers in a molecule should be zero if the compound is neutral.
Let's break it down:

• The oxidation number is an indication of how many electrons an atom gains or loses when forming a compound.
• For our elements: A has an oxidation state of +6, B is -2, and C is -1.
• When determining the total oxidation number sum for a molecular formula, multiply the oxidation state of each element by the number of times it appears in the formula, then add them together.

The goal is to balance this sum to zero. So, only the option where these numbers come together to result in zero, like in choice (b) in the exercise, will qualify as the right molecular composition of a neutral compound. This balance is vital in chemical reactions and for understanding compound stability.