Oxidation numbers of A, B, C are +2, +5 and -2 respectively. Possible formula of compound is

Options

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

Answer

To determine the possible formula of a compound formed by elements A, B, and C with oxidation numbers +2, +5, and -2 respectively, we need to ensure that the overall charge of the compound is neutral (i.e., the total positive charge equals the total negative charge).

### Step-by-Step Solution:

1. **Identify Oxidation States:**
- A has an oxidation number of +2.
- B has an oxidation number of +5.
- C has an oxidation number of -2.

2. **Set Up the Charge Balance Equation:**
- Let the number of atoms of A be \( x \), the number of atoms of B be \( y \), and the number of atoms of C be \( z \).
- The total positive charge from A and B must equal the total negative charge from C for the compound to be neutral.
- The equation can be written as:
\[ 2x + 5y - 2z = 0 \]

3. **Choose Values for x, y, and z:**
- We need to find integer values for \( x \), \( y \), and \( z \) that satisfy the charge balance equation.
- Let's try \( x = 1 \), \( y = 1 \), and \( z = 2 \):
\[ 2(1) + 5(1) - 2(2) = 2 + 5 - 4 = 3 \quad (\text{not neutral}) \]
- Now, let's try \( x = 2 \), \( y = 1 \), and \( z = 2 \):
\[ 2(2) + 5(1) - 2(2) = 4 + 5 - 4 = 5 \quad (\text{not neutral}) \]
- Next, let's try \( x = 2 \), \( y = 1 \), and \( z = 5 \):
\[ 2(2) + 5(1) - 2(5) = 4 + 5 - 10 = -1 \quad (\text{not neutral}) \]
- Finally, let's try \( x = 2 \), \( y = 1 \), and \( z = 3 \):
\[ 2(2) + 5(1) - 2(3) = 4 + 5 - 6 = 3 \quad (\text{not neutral}) \]
- After several trials, we find that \( x = 3 \), \( y = 2 \), and \( z = 8 \):
\[ 2(3) + 5(2) - 2(8) = 6 + 10 - 16 = 0 \quad (\text{neutral}) \]

4. **Write the Formula:**
- The formula based on the coefficients we found is \( A_3B_2C_8 \).

### Final Answer:
The possible formula of the compound is \( A_3B_2C_8 \).