It is not permissible to sell, buy or drink intoxicating beer. Scholars have ruled that non-intoxicating beer is permissible because it is completely free of alcohol, or because it contains a minuscule amount of alcohol.

There are many authentic Hadiths concerning the punishment for one who drinks alcohol which say that his prayers will not be accepted for forty days. The fact that his prayers are not accepted does not mean that they are not valid, or that he should give up praying, rather it means that he will not be rewarded for them.

If the alcohol which this mouthwash contains is not intoxicating, then it is OK to use it, so long as it is not harmful, because what is prohibited is only that which is intoxicating.

Alcohol is haram because it is intoxicating and contains a substance that makes people lose their minds. Allah has forbidden everything that harms the body and mind. For more, see the detailed answer.