This question involves identifying an organic acid 'X' based on its sodium salt's reactions. Let's analyze the clues step by step:

Step 1: Effervescence with Conc. H₂SO₄

Sodium salts of organic acids produce CO₂ gas (effervescence) when treated with concentrated H₂SO₄ due to decomposition. This is a general test for carboxylate salts, but it doesn't distinguish between them.

Step 2: Reaction with Acidified CaCl₂

'X' forms a white precipitate with acidified CaCl₂ solution. This indicates the formation of an insoluble calcium salt. Common organic acids that form insoluble calcium salts include oxalic acid (calcium oxalate) and formic acid (calcium formate is somewhat soluble, but can precipitate under certain conditions). However, calcium oxalate (CaC₂O₄) is highly insoluble and a characteristic precipitate.

Step 3: Precipitate Decolorizes Acidic KMnO₄

The white precipitate decolorizes acidic potassium permanganate (KMnO₄) solution. This is a crucial test. Acidic KMnO₄ is decolorized by reducing agents. Oxalate ion (C₂O₄^2-) is a strong reducing agent and reduces MnO₄^- to Mn²⁺, decolorizing the purple solution. The reaction is:

$2{\mathrm{MnO}}_4{}^{-}+5C_2{O}_4{}^{2-}+16H^{+}\to 2{\mathrm{Mn}}^{2+}+10\mathrm{CO}2+8H_{2}O$

Formate ion (HCOO^-) also reduces acidic KMnO₄, but it does not form a highly characteristic white precipitate with CaCl₂ (calcium formate is moderately soluble). Acetate and benzoate ions do not reduce KMnO₄ and their calcium salts are soluble.

Conclusion

Combining all clues:

• Effervescence with H₂SO₄: Confirms it is a carboxylate salt.
• White precipitate with CaCl₂: Points towards oxalate.
• Decolorization of KMnO₄: Confirms strong reducing nature, characteristic of oxalate.

Therefore, 'X' is oxalic acid, and its sodium salt is Na₂C₂O₄ (Sodium oxalate).

Related Topics & Formulae

Tests for Carboxylic Acids and Their Salts:

• Reaction with NaHCO₃ produces CO₂ effervescence.
• Formation of insoluble salts with certain cations (e.g., Ag⁺, Ca²⁺, Fe³⁺) can help identify specific acids.

Oxidizing Agents:

• Acidic KMnO₄ is used to test for unsaturation and reducing agents.
• The deep purple color of MnO₄^- is discharged when reduced to Mn²⁺.

Important Reaction:
The oxidation of oxalate ion by permanganate is a classic volumetric reaction used to standardize KMnO₄ solutions.