Vinyl items such as shower curtains often have a strong characteristic odor for days or even weeks after you take them out of their original packaging. Reduce the odor by allowing the vinyl to "breathe" outdoors or in a well-ventilated area for several hours -- or even several days, if possible. Cleaning the surface helps a bit as well.
The Source of the Smell
That odor you smell is numerous chemicals "off-gassing" into the air -- converting back into chemical form and wafting around in the air you breathe. Some of these chemicals are considered toxins, so it's best to wait a while before using brand-new, fresh-out-of-the-package vinyl items.
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Getting Rid of the Odors
Step 1: Remove the packaging.
Remove the vinyl product from its packaging, if any, to allow it to air out.
Step 2: Air out the vinyl.
Place the vinyl outdoors for several hours or longer, so it can off-gas a bit. Unfold items such as shower curtains or inflatable pool floats and boats; the more surface area it has, the more the vinyl can off-gas. If the odor is strong, leave the item outside for several days, if possible.
Step 3: Wash it off.
Wash the vinyl off with a mild dish soap and warm water. Add a splash of white vinegar to help remove some of the odor from the surface of the vinyl. Allow the vinyl to air dry in a well-ventilated area.
Step 4: Remove more of the odor.
Remove more of the lingering odor by sprinkling baking soda over the surface of the vinyl, allowing it to sit for several hours or overnight. Dump the baking soda into the trash afterward, and then wipe the vinyl down with a damp cloth. Spritz equal parts vinegar and water over the vinyl to help remove even more of the odor from the outside of the vinyl product.