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

Options

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

Explanation

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: Identify the oxidation states
- A has an oxidation state of +2
- B has an oxidation state of +5
- C has an oxidation state of -2

### Step 2: Set up the charge balance equation
In an ionic compound, the total positive charge must equal the total negative charge. We can express this mathematically as:
\[ \text{Total positive charge} = \text{Total negative charge} \]

### Step 3: Analyze the given options
We will check each option to see if the total positive charge equals the total negative charge.

#### Option 1: \( A_3B_4C_2 \)
- Contribution from A: \( 3 \times (+2) = +6 \)
- Contribution from B: \( 4 \times (+5) = +20 \)
- Contribution from C: \( 2 \times (-2) = -4 \)

Total positive charge = \( +6 + 20 = +26 \)
Total negative charge = \( -4 \)
**Not equal, so this option is incorrect.**

#### Option 2: \( A_3BC_4 \)
- Contribution from A: \( 3 \times (+2) = +6 \)
- Contribution from B: \( 1 \times (+5) = +5 \)
- Contribution from C: \( 4 \times (-2) = -8 \)

Total positive charge = \( +6 + 5 = +11 \)
Total negative charge = \( -8 \)
**Not equal, so this option is incorrect.**

#### Option 3: \( A_2BC_3 \)
- Contribution from A: \( 2 \times (+2) = +4 \)
- Contribution from B: \( 1 \times (+5) = +5 \)
- Contribution from C: \( 3 \times (-2) = -6 \)

Total positive charge = \( +4 + 5 = +9 \)
Total negative charge = \( -6 \)
**Not equal, so this option is incorrect.**

#### Option 4: \( ABC_2 \)
- Contribution from A: \( 1 \times (+2) = +2 \)
- Contribution from B: \( 1 \times (+5) = +5 \)
- Contribution from C: \( 2 \times (-2) = -4 \)

Total positive charge = \( +2 + 5 = +7 \)
Total negative charge = \( -4 \)
**Not equal, so this option is incorrect.**

### Step 4: Conclusion
After analyzing all the options, we find that only **Option 2: \( A_3BC_4 \)** satisfies the condition where the total positive charge equals the total negative charge.

### Final Answer
The possible formula of the compound is \( A_3BC_4 \).

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