Does the oath become binding with the formula: "O Allah, I swear to You that I will not do such and such" when there are voices around the swearer and he cannot hear his own voice?

The statement "I swear to you" (أُقسِم لك) is considered an oath by many scholars, even if the intention to make an oath was not present. The Shafi'is hold that it is not considered an oath at all. The Malikis, however, differentiate: if a person intended to swear by Allah after saying "I swear" (أُقسِمُ), then the oath is binding; otherwise, it is not. The safer approach is to consider it an oath, so if you break it, an expiation for an oath becomes incumbent upon you. The inability to hear the sound of the oath's utterance does not prevent it from being binding.