Question
Unlike phenol, $2,4-$dinitrophenol is soluble in sodium carbonate solution in water because?

Answer

Presence of two electron withdrawing $\ce{−No_2​}$ groups in the ring makes $2,4-$dinitrophenol a stronger acid than phenol.
Hence it react with aqueous $\ce{Na_2​CO_3​}$ solution to form sodium salt thus making it soluble in $\ce{Na_2​CO_3}​.$

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