Can sperm live in water?

Yes, I am a clumsy boy who masturbates almost everyday in the shower. The thing is, I let the d sperm sit in the water and the sadder thing is, the tub is shared with my sister. So, the question is; can HIGH-CONCENTRATION sperm survive in the purified water with ABSOLUTELY no contaminants, acids, salts, or any type of chemicals and somehow fertilize an egg of my sister's when she takes a bath?