A compound contains three elements `A,B` and `C`, if the oxidation number of `A=+2B=+5` and `C=-2` then possible formula of the compound is

Options

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

Answer

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

### Step 1: Write down the oxidation states
The oxidation states are given as follows:
- Oxidation number of A = +2
- Oxidation number of B = +5
- Oxidation number of C = -2

### Step 2: Set up the charge balance equation
Since the compound is neutral, the sum of the oxidation states multiplied by their respective number of atoms must equal zero. Let:
- x = number of atoms of A
- y = number of atoms of B
- z = number of atoms of C

The charge balance equation can be written as:
\[ 2x + 5y - 2z = 0 \]

### Step 3: Rearrange the equation
Rearranging the equation gives us:
\[ 2x + 5y = 2z \]

### Step 4: Find integer solutions
We can find integer solutions for x, y, and z. We can try different values for x and y and solve for z.

1. **Assume x = 1:**
\[ 2(1) + 5y = 2z \implies 2 + 5y = 2z \]
- If y = 1:
\[ 2 + 5(1) = 2z \implies 7 = 2z \implies z = 3.5 \quad \text{(not an integer)} \]
- If y = 2:
\[ 2 + 5(2) = 2z \implies 12 = 2z \implies z = 6 \quad \text{(integer)} \]
- So one possible solution is \( x = 1, y = 2, z = 6 \).

2. **Assume x = 3:**
\[ 2(3) + 5y = 2z \implies 6 + 5y = 2z \]
- If y = 2:
\[ 6 + 5(2) = 2z \implies 16 = 2z \implies z = 8 \quad \text{(integer)} \]
- So another possible solution is \( x = 3, y = 2, z = 8 \).

### Step 5: Write the formulas
From the solutions:
1. For \( x = 1, y = 2, z = 6 \): The formula is \( A_1B_2C_6 \) or simply \( AB_2C_6 \).
2. For \( x = 3, y = 2, z = 8 \): The formula is \( A_3B_2C_8 \).

### Step 6: Conclusion
The possible formulas for the compound are:
- \( AB_2C_6 \)
- \( A_3B_2C_8 \)