Regarding the purity of alcohol, we would like to quote Dr. Muzammil Siddiqi, former president of the Islamic Society of North America (ISNA), who states:
There are many types of alcohol, actually there are hundreds of members in alcohol family. Among them ethyl is the best known and this alcohol is generally used in beverages. There are some types of alcohol that are denatured and are used in perfumes and other cleansing agents. The rubbing alcohol does not contain ethyl alcohol. It is dangerous for drinking and may cause blindness and death. The external use of such alcohol is not forbidden in Islam.
According to the Qur’an and Sunnah, it is haram to drink alcohol or alcoholic beverages. Even a small amount of alcohol is haram and it must be avoided. However, jurists have differed on the Najasah or the physical impurity of alcohol. Some of them consider it Najis (impure), meaning that if it touches the body and clothes then it must be washed. There are others who do not consider it Najis. There are many jurists who have allowed the use of rubbing alcohol and the use of perfumes that contain alcohol.
As far as toothpaste or mouthwash that contain alcohol is concerned, it is better to avoid them, because they go inside the mouth.