A,B and C are three elements forming part of a compound in oxidation states of `+2,+5` and -2 respectively. What could be the compound ?

Options

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

Answer

To determine the compound formed by elements A, B, and C with oxidation states of +2, +5, and -2 respectively, 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: Write the general formula for the compound
We can denote the compound as \( A_xB_yC_z \), where x, y, and z are the number of atoms of A, B, and C in the compound.

### Step 3: Analyze the charge balance
The total positive charge contributed by A and B must equal the total negative charge contributed by C.

1. The charge from A: \( +2x \)
2. The charge from B: \( +5y \)
3. The charge from C: \( -2z \)

The equation for charge balance is:
\[ +2x + 5y = 2z \]

### Step 4: Test possible combinations
We will test various combinations of x, y, and z to find a valid compound.

#### Option 1: \( A_2B C_2 \)
- Here, \( x = 2, y = 1, z = 2 \)
- Charge balance: \( +2(2) + 5(1) = 2(2) \)
- Calculation: \( 4 + 5 = 4 \) (Not balanced)

#### Option 2: \( A_2B C_4 \)
- Here, \( x = 2, y = 1, z = 4 \)
- Charge balance: \( +2(2) + 5(1) = 2(4) \)
- Calculation: \( 4 + 5 = 8 \) (Not balanced)

#### Option 3: \( A_3B C_4 \)
- Here, \( x = 3, y = 1, z = 4 \)
- Charge balance: \( +2(3) + 5(1) = 2(4) \)
- Calculation: \( 6 + 5 = 8 \) and \( 2(4) = 8 \) (Balanced)

### Step 5: Conclusion
The compound that satisfies the oxidation states is \( A_3B C_4 \).

### Final Answer
The compound is \( A_3B C_4 \).

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