The compound, among the following, that will not be soluble in sodium hydrogen carbonate is:

Sodium hydrogen carbonate ($NaHCO_3$) is a weak base. It reacts with acids that are stronger than carbonic acid ($H_2CO_3$) to release $CO_2$ and form soluble sodium salts.

1. Benzenesulphonic acid and Benzoic acid are much stronger acids than carbonic acid, so they dissolve in $NaHCO_3$.
2. 2, 4, 6-Trinitrophenol (Picric acid): Although it is a phenol, the presence of three strong electron-withdrawing nitro groups ($-NO_2$) makes it more acidic than carbonic acid. Thus, it is soluble.
3. o-Nitrophenol: Phenols are generally weaker acids than carbonic acid. While the nitro group increases acidity, a single $-NO_2$ group (especially with intramolecular hydrogen bonding in the ortho isomer) does not make it acidic enough to displace $CO_2$ from $NaHCO_3$. Therefore, it remains insoluble.