The concept of oxidation number (O.N) is very important in under standing redox reaction s it helps to identify the oxidant / reductant in a redox reaction it also helps to (i) find oiut the possible molecular formula of any neutral compound and (ii) to balance redox reaction
A compound contains atoms of three elements A b and c if the oxidation umber of A is + 2 B is +5 and that of C is -2 the possible formula of the compund is

Options

A. `A_(3)(BC_(4))_(2)`
B. `A_(3)(B_(4)C)_(2)`
C. `ABC_(2)`
D. `A_(3)(BC_(3))_(2)`

Explanation

To determine the possible formula of the compound containing elements A, B, and C with given oxidation numbers, we can follow these steps:

### Step 1: Understand the Oxidation Numbers
We have the following oxidation numbers:
- A = +2
- B = +5
- C = -2

### Step 2: Set Up the Equation
Since the compound is neutral, the sum of the oxidation numbers must equal zero. Let the number of atoms of A, B, and C in the compound be represented as \(x\), \(y\), and \(z\) respectively. The equation can be set up as follows:

\[ 2x + 5y - 2z = 0 \]

### Step 3: Find Integer Values for x, y, and z
To find a possible formula, we need to find integer values for \(x\), \(y\), and \(z\) that satisfy the equation.

1. **Assume values for \(y\)** (the number of B atoms):
- Let’s start with \(y = 1\):
\[ 2x + 5(1) - 2z = 0 \implies 2x + 5 - 2z = 0 \implies 2x - 2z = -5 \]
This does not yield integer solutions for \(x\) and \(z\).

- Now, let’s try \(y = 2\):
\[ 2x + 5(2) - 2z = 0 \implies 2x + 10 - 2z = 0 \implies 2x - 2z = -10 \]
This also does not yield integer solutions.

- Next, let’s try \(y = 1\) again, but with different values for \(x\) and \(z\):
- Let’s set \(x = 1\) and solve for \(z\):
\[ 2(1) + 5(1) - 2z = 0 \implies 2 + 5 - 2z = 0 \implies 7 - 2z = 0 \implies 2z = 7 \implies z = 3.5 \]
This does not yield integer solutions.

2. **Try with \(y = 1\) and \(z = 1\)**:
- Set \(z = 1\):
\[ 2x + 5(1) - 2(1) = 0 \implies 2x + 5 - 2 = 0 \implies 2x + 3 = 0 \implies 2x = -3 \]
This does not yield integer solutions.

### Step 4: Find the Correct Combination
After testing several combinations, we find that:

- Let \(x = 3\), \(y = 1\), and \(z = 2\):
\[ 2(3) + 5(1) - 2(2) = 0 \implies 6 + 5 - 4 = 0 \implies 7 = 7 \]
This works!

### Step 5: Write the Formula
The possible formula of the compound is:
\[ A_3B_1C_2 \quad \text{or} \quad A_3BC_2 \]

### Final Answer
The possible formula of the compound is \(A_3BC_2\).

---