No, a solar stil can't get benzene and some other stuff out of the water (see below) but you won't be using tap water: You'll be distilling the water that you condense out of the air, so benzene won't be a problem.
In other words, with a few hours and $150-$200 (depending on your family's drinking needs), you can build your own solar water still and become independent of the city water supply for your drinking water! A solar water still relies on the moisture in the air.
And sorry about all those links. Many are just minor variations on a basic solar still....
The info below on benzene and other VOCs is from the page
http://www.solarsolutions.info/faq/faqright.htmlbut it redirects, so hit STOP to see it!
Q: Are There Any Contaminants Distillation Will Not Remove?
A: Yes, distillation cannot remove a class of chemicals known as Volatile Organic Compounds (VOC), which evaporate and condense at similar and lower temperatures than water. VOCs include toxic chemicals like crude oil and its derivatives (gasoline, kerosene, diesel, fuel oil, motor oil, etc.); solvents like turpentine and benzene; and other substances like antifreeze (glycol), alcohols, and paint. Many plant poisons (poison oak and ivy for instance) are also VOC. In practice, if source water smells like chemicals or paint, has a shimmery, rainbow-colored substance floating on it, or is a strange color, distillation may not remove the contaminants. In fact, no purification method should be trusted. If the area of contamination is widespread, appropriate authorities should be contacted. Clean up and removal of these kinds of toxic chemicals is not within the range of any consumer-oriented water purification device, but rather serious remediation efforts are required. Also note that care should be exercised if plants are used as a source of fluid for distillation, because if toxic plants are used, the distilled water could be contaminated. Even non-toxic plants may impart a taste to the water, as most substances that we can smell and taste are also (non-toxic) VOC.
Finally, you should be aware that in many instructions for building box-type water stills, the use of silicone sealants is advised. However, there is concern that many of these sealants release VOC over their lifetime that could contaminate the distilled water.
http://www.solarsolutions.info/faq/faqright.html