Dishwashers and the Indoor Air
The biggest indoor air problem associated with dishwashers is air contaminated with volatile organic compounds (VOCs). This is because the hot steam during the dishwashing cycle is very effective in stripping the VOCs from VOC-contaminated water so that these chemicals may become airborne if the dishwasher is opened immediately after the final cycle.1 Examples of VOCs that have been measured include toluene, chloroform and methyl tert-butyl ether (MTBE).
The way to minimize one's risk from inhaling the VOCs that become airborne after the dishwashing cycle is to not open the dishwasher until the air in the dishwasher has had time to cool. That decreases the chance of VOC-contaminated steam getting into kitchen's air.
References
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Howard-Reed C, Corsi RI. Mass transfer of volatile organic compounds from drinking water to indoor air: The role of residential dishwashers. Environmental Science and Technology. 1999;33(13):2266-2272.