$1$ M KNO$3$ solution containing $5-10$ drops of phenolphthalein was poured into the U$-$shaped electrolyte vessel, then the cleaned carbon electrodes $($connected to the battery poles$)$ were inserted into the U$-$tube outlets. The solution was electrolyzed for about $30$ minutes and the appearance of a pink color of phenolphthalein was observed near the negative pole of the battery. a$)$ Please write electrode reactions at the anode and cathode as well as total reaction b$)$ Please explain why did the pink phenolphthalein color occur near the negative pole