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Free chlorine has no odor in the recommended concentrations of 3 - 5 ppm. The smell that most people associate with chlorine comes from combined chlorine. This is chlorine that has reacted with the bugs and it must be burned off periodically by shocking the tub with a dose that is 5 - 7 times greater than the daily dose.
Anne,First of all, don't sniff your dichlor bottle. :-)Seriously, though, chlorine (and bromine too) is a very nasty and powerful chemical. In it's bottle and when you are adding it to the tub, you should try very hard not to inhale it as concentrations this high would cause all kinds of health problems. Once you have added you teaspoon or two and let it dissolve and thoroughly mix with all of the water in your tub, there will be no odor. Regards,Bill