Tub cleaning with chlorhexadine?

I'm wondering what the proper way to clean the tub is with chlorhexadine?

http://www.reptilebasics.com/chlorhexadine-16oz

I diluted the solution to about 2 tablespoons to half a gallon of water.

I just soaked a paper towel in it and wiped down the inside of the tub and items in the tub with it... and then soaked another paper towel with water, and wiped it down again. I'm just making it up as I go though. Is the solution harmful if it's not thoroughly washed out in the tub? Can I clean the snake itself with the diluted solution?

I mix up a batch of it at the start of every month in a large spray bottle (the one Reptile Basics sells actually) once the tub is emptied out I spray it down and let it sit for a minute or two then wipe it down with paper towels until it dries out. I don't bother to rinse as chlorhexadine is really mild, supposedly you could use it as mouth wash if you wanted though I haven't bothered to try that one out yet.

My husband had oral surgery 2 months ago and he was prescribed chlorhexadine mouthwash. His mouthwash is 0.12% chlorhexadine. Math (I may be wrong, it is math and I am often wrong with it) tells me that diluting the 2% chlorhexadine at 1 oz per gallon of water dilutes the amount of chlorhexadine to 0.015% for disinfecting reptile tanks.

So math tells me don't worry about rinsing the diluted solution. However, there are 2 tablespoons to an ounce. You are making your solution twice as strong as it needs to be. I think you will still be fine if you don't rinse but you are probably just wasting it.

You don't need to clean your snake with it either. It would be one thing to clean his wounds with it but not as a bathing. If at all, use luke warm water and paper towels to wipe your snake down. Use your temp gun to check the temperature of the water so it isn't too warm. :)