Is it permissible to fast from speaking, and what is the reward for doing so?

"Silence from speaking for a full day without need is disliked, due to the Hadith of Ali ibn Abi Talib (may Allah be pleased with him): 'There is no orphanhood after puberty, nor silence of a day until night.' And due to the saying of Abu Bakr Al-Siddiq (may Allah be pleased with him) to a woman who performed Hajj in silence: 'Speak, for this is not permissible; this is from the deeds of the Days of Ignorance (Jahiliyyah).'"