A salt which gives `CO_2` with hot `H_2 SO_4` and also decolourizes acidified `KMnO_4` on warming is

Options

A. `HCO_(3)^(-)`
B. `CO_(3)^(2-)`
C. Oxalate ion
D. Acetate ion

Answer

To solve the question, we need to identify a salt that meets two criteria:

1. It produces carbon dioxide (CO2) when reacted with hot sulfuric acid (H2SO4).
2. It decolorizes acidified potassium permanganate (KMnO4) upon warming.

Let's analyze the options provided: bicarbonate ion, carbonate ion, oxalate ion, and acetate ion.

### Step 1: Reaction with Hot H2SO4
- **Bicarbonate Ion (HCO3-)**: When bicarbonate reacts with hot H2SO4, it produces CO2 gas.

\[ \text{HCO}_3^- + \text{H}_2\text{SO}_4 \rightarrow \text{CO}_2 + \text{H}_2\text{O} + \text{SO}_4^{2-} \]

- **Carbonate Ion (CO3^2-)**: Similarly, carbonate reacts with hot H2SO4 to produce CO2 gas.

\[ \text{CO}_3^{2-} + \text{H}_2\text{SO}_4 \rightarrow \text{CO}_2 + \text{H}_2\text{O} + \text{SO}_4^{2-} \]

- **Oxalate Ion (C2O4^2-)**: Oxalate also produces CO2 when reacted with hot H2SO4.

\[ \text{C}_2\text{O}_4^{2-} + \text{H}_2\text{SO}_4 \rightarrow 2\text{CO}_2 + \text{H}_2\text{O} + \text{SO}_4^{2-} \]

- **Acetate Ion (CH3COO-)**: Acetate does not produce CO2 with hot H2SO4.

### Step 2: Reaction with Acidified KMnO4
- **Bicarbonate Ion**: Does not reduce KMnO4; therefore, it does not decolorize it.

- **Carbonate Ion**: Similar to bicarbonate, it does not reduce KMnO4.

- **Oxalate Ion**: Oxalate can reduce KMnO4. The oxidation state of carbon in oxalate is +3, and when it is oxidized to CO2 (where the oxidation state is +4), it reduces KMnO4 from Mn(VII) to Mn(II), leading to decolorization.

\[ \text{C}_2\text{O}_4^{2-} + 2\text{KMnO}_4 + 3\text{H}_2\text{SO}_4 \rightarrow 2\text{CO}_2 + 2\text{MnSO}_4 + 3\text{H}_2\text{O} + K_2\text{SO}_4 \]

- **Acetate Ion**: Acetate does not reduce KMnO4 either.

### Conclusion
Based on the analysis:
- The bicarbonate and carbonate ions produce CO2 with hot H2SO4 but do not decolorize KMnO4.
- The acetate ion does not produce CO2 with hot H2SO4 and does not decolorize KMnO4.
- The oxalate ion meets both criteria: it produces CO2 with hot H2SO4 and decolorizes KMnO4.

Thus, the correct answer is **oxalate ion (C2O4^2-)**.