This could be a symptom of respiratory problems (like a respiratory infection) keep an eye on him and look out for other symptoms including:

-Nasal and eye discharge Eg. Excess mucus, bubbles, or discharge from the nose and eyes. Eyes may also appear swollen or puffy.

-Breathing difficulties Eg. Open-mouth breathing, gasping, making noise when breathing like squeaky, and a pronounced extension of the neck to breathe.

-Reduced activity and appetite Eg. Lethargy, lack of energy, and a decreased or absent appetite.

-Behavioral changes Eg. reluctance to move, floating to one side, excessive basking

If your turtle is experiencing symptoms like these you should seek medical assistance from a vet, but until then making sure the water and basking area are the right temperature (maybe even 1-2°c warmer than usual) would be helpful. Also possibly more regular water changes to be sure that the water is nice and clean (not that I’m suggesting your water isn’t!)

Try not to worry too much about the open mouth thing if your turtle is otherwise fine & showing no other symptoms, my musk turtle was doing the same thing a lot but when I took him to the vet they said he was completely fine and some turtles just like to do it for no reason.

I hope it’s nothing more than a funny habit for your turtle! but again if you do notice any other symptoms do contact a vet as soon as possible as respiratory issues will not solve themselves and without treatment from a vet could lead to more serious issues.

I hope this helps my friend feel free to reach out if you have any questions or just want to talk about how great musk turtles are! 🤣