Riddles and Trivia

Chaim loves writing down his chiddushei Torah on Chol HaMoed. This Pesach, Chaim’s younger brother Akiva noticed that on Chaim’s table there were two jars of ink. Akiva also noticed that Chaim never used one of those jars to write his chiddushim. When he inquired about it, Chaim answered: “I am not allowed to use that jar of ink on Pesach!”

Akiva asked back: “Is it because the ink is Chometzdik?”

Chaim answered: “Of course not! A dog would never eat this ink. And by the way, the ink jar that I am using on Pesach has absolutely the same type of ink as this one.”

Why is Chaim not allowed to use the first jar of ink on Pesach?