All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
It is desirable to rinse one's mouth when performing ablution with the right hand. Ibn Qudaamah said: 'It is desirable to rinse one's mouth and nose with the right hand and then uses his left hand when blowing out the water from his nose. The evidence is that it is reported that ‘Uthmaan asked for water to perform ablution, so he washed his hands three times, then he took water with his right hand and he rinsed his mouth and nose with the same handful of water and then he blew out the water from his nose with his left hand, and he did this three times.'
Al-Kaasaani when mentioning some recommended acts of ablution, said: 'Among which is rinsing the mouth and nose with the right hand, and some scholars said: “Rinsing the mouth should be with the right hand and rinsing the nose should be with the left hand because the mouth is pure whereas the nose contains mucus, so the right hand is to be used for pure things while the left hand is to be used for dirty things.'
Allaah Knows best.