OK to reach a conclusion I'll start at the beginning.
In an accident at a factory, some nitric acid was split.
Which substance then, when added in excess, would be the best chemical to neutralise the acid without leaving an alkaline solution?
Calcium carbonate or sodium carbonate?
When I first read this I thought that this had been a real accident at a factory the OP worked at. Now I wonder if it is really an academic exercise?
Anyway I should observe something obvious viz that to neutralise something is to render it neutral ie neither acid nor alkaline.
Now nitric acid is an acid liquid, whilst calcium and sodium carbonates are white neutral solids, usually powders. Only the sodium carbonate is soluble in water.
So if we consider our puddle of spilt nitric acid and shovel on some white powder until it turns from acid to neutral.
The reaction is
metal carbonate (solid) + nitric acid \rightarrow metal nitrate (solution) + water + carbon dioxide (gas)
Since both nitrates are soluble, either powder dissolves in the liquid, and the reaction gives off carbon dioxide as a gas.
The liquid turns from acid to neutral.
At this point the action is the same whichever carbonate is used.
However once the acid is neutralised no further powder will dissolve if calcium carbonate is used. That white powder will simply settle to the bottom of the puddle.
Since there are no further chemical changes the liquid never becomes alkaline, meeting the condition of the question.
If, however, sodium carbonate is added to the neutral liquid this dissolves adding sodium and carbonate ions to the liquid.
Some carbonate ions now react with water to form bicarbonate and hydroxyl ions. The hydroxyl ions turning the liquid alkaline, since the matching proton is now part of the bicarbonate ion and so does not form a hydroxonium ion that would maintain the liquid neutrality.
The more excess sodium carbonate is added the more alkaline the liquid becomes.
Kyoma, are you able to write symbolic chemical reactions for this?