A student takes 2 mL acetic acid in a dry test tube and adds a pinch of sodium hydrogen carbonate to it. He makes the following observations: I. A colourless and odourless gas evolves with a brisk effervescence. II. The gas turns lime water milky when passed through it. III. The gas burns with an explosion when a burning splinter is brought near it. IV. The gas extinguishes the burning splinter that is brought near it. The correct observations are:

When acetic acid ($CH_3COOH$) reacts with sodium hydrogen carbonate ($NaHCO_3$), a chemical reaction takes place yielding sodium acetate, water, and carbon dioxide gas:

$$CH_3COOH(aq) + NaHCO_3(s) \rightarrow CH_3COONa(aq) + H_2O(l) + CO_2(g)$$

Let us evaluate the observations for the evolved carbon dioxide ($CO_2$) gas:

• Observation I: Carbon dioxide is a colourless and odourless gas that is evolved with brisk effervescence. (Correct)
• Observation II: When passed through lime water, carbon dioxide reacts to form insoluble calcium carbonate ($CaCO_3$), turning the lime water milky. (Correct)
• Observation III: Carbon dioxide does not burn with an explosion. Hydrogen gas ($H_2$) is the gas that burns with a pop sound/explosion. (Incorrect)
• Observation IV: Carbon dioxide is a non-supporter of combustion, so it extinguishes a burning splinter. (Correct)

Thus, observations I, II, and IV are correct, which corresponds to Option D.