The sodium salt of an organic acid X produces effervescence with concentrated H$$_{2}$$SO$$_{4}$$. X reacts with the acidified aqueous CaCl$$_{2}$$ solution to give a white precipitate which decolourises acidic solution of KMnO$$_{4}$$. X is

First, we note that the sodium salt in each option is the sodium salt of a particular organic acid. We have to match all the observations given in the question with the behaviour of the salt.

Observation 1: “produces effervescence with concentrated $$H_2SO_4$$.” To trigger effervescence, a gas must be evolved. With sodium salts of carboxylic acids, concentrated sulphuric acid generally liberates the free acid, and if that free acid is unstable it decomposes to a gas. Let us write the general idea for the oxalate candidate because oxalic acid is known to decompose thermally:

We would have

$$Na_2C_2O_4 + H_2SO_4 \;(\text{conc.}) \rightarrow H_2C_2O_4 + Na_2SO_4$$

and then

$$H_2C_2O_4 \rightarrow CO + CO_2 + H_2O$$

The mixture of $$CO$$ and $$CO_2$$ comes out as brisk effervescence. By contrast, the free acids obtained from $$HCOONa$$, $$CH_3COONa$$ or $$C_6H_5COONa$$ do not give such noticeable effervescence under the same conditions. Thus, sodium oxalate already fits the first clue well.

Observation 2: “reacts with the acidified aqueous $$CaCl_2$$ solution to give a white precipitate.” We write the reaction of sodium oxalate with calcium chloride in the presence of dilute hydrochloric acid (to keep the medium acidic):

$$Na_2C_2O_4 + CaCl_2 \rightarrow CaC_2O_4 \downarrow + 2\,NaCl$$

The substance $$CaC_2O_4$$ is calcium oxalate, and it is well known to be an insoluble white precipitate. So the second observation is also fully satisfied by sodium oxalate.

Observation 3: “the precipitate decolourises acidic $$KMnO_4$$ solution.” In acidic solution the purple permanganate ion $$MnO_4^-$$ is reduced to the nearly colourless $$Mn^{2+}$$ ion. For that reduction, some species must be oxidised. Oxalate ion $$C_2O_4^{2-}$$ is a classic reducing agent under acidic conditions and is oxidised to carbon dioxide. The net ionic redox change is usually written as

$$5\,C_2O_4^{2-} + 2\,MnO_4^- + 16\,H^+ \rightarrow 2\,Mn^{2+} + 10\,CO_2 + 8\,H_2O$$

Because oxalate reduces the permanganate, the purple colour disappears; therefore calcium oxalate precipitate indeed shows the described behaviour. None of the other possible precipitates (calcium formate, calcium acetate, calcium benzoate) possesses this strong reducing power toward acidic permanganate.

All three observations fit perfectly and uniquely with the salt $$Na_2C_2O_4$$, i.e., sodium oxalate. The option list shows this as option C.

Hence, the correct answer is Option C.