Aqueous sodium bicarbonate ($ NaHCO_3 $) solution is a weak base. Carboxylic acids react with $ NaHCO_3 $ to produce carbon dioxide ($ CO_2 $). Phenols are generally weaker acids than carboxylic acids and do not react with $ NaHCO_3 $ unless they are substituted with strong electron-withdrawing groups.
A. Benzoic acid ($ C_6H_5COOH $): Carboxylic acids react with $ NaHCO_3 $ to produce $ CO_2 $.
This compound produces $ CO_2 $.
B. Phenol ($ C_6H_5OH $): Phenols are generally weaker acids than carbonic acid and do not react with $ NaHCO_3 $.
This compound does NOT produce $ CO_2 $.
C. Picric acid (2,4,6-trinitrophenol): This is a strongly acidic phenol due to the presence of three nitro groups. It can react with $ NaHCO_3 $ to produce $ CO_2 $.
This compound produces $ CO_2 $.
D. Cyclohexanecarboxylic acid ($ C_6H_{11}COOH $): Carboxylic acids react with $ NaHCO_3 $ to produce $ CO_2 $.
This compound produces $ CO_2 $.
E. 4-Methoxyphenol: It is a very weak phenol and does not react with $ NaHCO_3 $, even slightly.
This compound does NOT produce $ CO_2 $.
Therefore, the compounds that produce $ CO_2 $ when reacted with aqueous $ NaHCO_3 $ are A, C, and D.
Final Answer:
The final answer is $ (3)\ A,\ C\ \text{and}\ D\ \text{only} $.
Let \( T_r \) be the \( r^{\text{th}} \) term of an A.P. If for some \( m \), \( T_m = \dfrac{1}{25} \), \( T_{25} = \dfrac{1}{20} \), and \( \displaystyle\sum_{r=1}^{25} T_r = 13 \), then \( 5m \displaystyle\sum_{r=m}^{2m} T_r \) is equal to: