A,B and C are three elements forming a compound in which their oxidation state are +2,+5, and -2 respectively. Which could not be the formula of compound?

Options

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

Answer

To determine which formula could not be the compound formed by elements A, B, and C with oxidation states of +2, +5, and -2 respectively, we need to ensure that the overall charge of the compound is neutral (i.e., the sum of the oxidation states equals zero). Let's analyze the possible combinations step by step.

### Step 1: Understanding Oxidation States
- Element A has an oxidation state of +2.
- Element B has an oxidation state of +5.
- Element C has an oxidation state of -2.

### Step 2: Setting Up the General Formula
Let’s denote:
- The number of A atoms as \( x \)
- The number of B atoms as \( y \)
- The number of C atoms as \( z \)

The total charge contributed by each element can be expressed as:
- Charge from A: \( 2x \)
- Charge from B: \( 5y \)
- Charge from C: \( -2z \)

### Step 3: Writing the Charge Balance Equation
For the compound to be neutral, the sum of the charges must equal zero:
\[ 2x + 5y - 2z = 0 \]

### Step 4: Analyzing Possible Formulas
Let’s consider various combinations of \( x \), \( y \), and \( z \) to find which combinations do not satisfy the charge balance equation.

1. **Formula 1: \( A_2B_5C_2 \)**
- Charge: \( 2(2) + 5(5) - 2(2) = 4 + 25 - 4 = 25 \) (not neutral)

2. **Formula 2: \( AB_3C_4 \)**
- Charge: \( 1(2) + 3(5) - 4(2) = 2 + 15 - 8 = 9 \) (not neutral)

3. **Formula 3: \( A_3B_2C_8 \)**
- Charge: \( 3(2) + 2(5) - 8(2) = 6 + 10 - 16 = 0 \) (neutral)

4. **Formula 4: \( A_2B_5C \)**
- Charge: \( 2(2) + 5(5) - 1(2) = 4 + 25 - 2 = 27 \) (not neutral)

### Step 5: Conclusion
From the analysis, the formulas that could not be the compound are:
- Formula 1: \( A_2B_5C_2 \)
- Formula 2: \( AB_3C_4 \)
- Formula 4: \( A_2B_5C \)

Thus, the answer to the question is that the formulas \( A_2B_5C_2 \), \( AB_3C_4 \), and \( A_2B_5C \) cannot be valid formulas for the compound.