`AB_(4)^(-) + C^(+2) rarr C^(+3) + A^(+2)`
It the O.N. of B is -2 . Choose the true statement for the above change -

Options

A. O.N. of A decreases by -5
B. O.N. of C decreases by `+1`
C. O.N. of A decreases by `+ 5` and that of C increases by `+1`
D. O.N. of A decreases by `+5` and that of C decreases by `+1`

Answer

To solve the problem, we need to analyze the given reaction and determine the oxidation states of the elements involved. Let's break it down step by step.

### Step 1: Identify the oxidation states
The reaction is:
\[ AB_4^{-} + C^{+2} \rightarrow C^{+3} + A^{+2} \]

We are given that the oxidation number of B is -2.

### Step 2: Determine the oxidation state of A
Let the oxidation state of A be \( x \). In the compound \( AB_4^{-} \):
- The contribution from 4 atoms of B (each with an oxidation state of -2) is \( 4 \times (-2) = -8 \).
- The overall charge of the species is -1.

Using the equation:
\[ x - 8 = -1 \]
Solving for \( x \):
\[ x = -1 + 8 = +7 \]
Thus, the oxidation state of A is +7.

### Step 3: Analyze the changes in oxidation states
- A goes from +7 in \( AB_4^{-} \) to +2 in the products. This is a decrease of 5, indicating that A is reduced.
- C goes from +2 to +3, which is an increase of 1, indicating that C is oxidized.

### Step 4: Summarize the changes
- A is reduced (oxidation state decreases from +7 to +2).
- C is oxidized (oxidation state increases from +2 to +3).

### Step 5: Choose the correct statement
Now, let's analyze the statements given in the question:
1. Oxidation number of A decreases by -5 (correct, as it goes from +7 to +2).
2. Oxidation number of C decreases by +1 (incorrect, as it increases from +2 to +3).
3. Oxidation number of A decreases by +5 (correct).
4. Oxidation number of C decreases by +1 (incorrect).

### Conclusion
The true statement for the above change is that the oxidation number of A decreases by +5.