I'm sure it's possible, and that someone has sat down and done the mathematics, and figured out that it's just not worthwhile. The most efficient way to do it

I'm sure it's possible, and that someone has sat down and done the mathematics, and figured out that it's just not worthwhile. The most efficient way to do it is to use solar thermal, not solar electric, power -- build a huge array of mirrors to focus on heaters which boil your water and distill it out. But it's not really "free" -- you need a lot of land, a lot of mirrors, and a staff of people who keep the mirrors clean and replace the broken ones. Oh, what the hell, I'll do the maths myself. To heat up and boil one litre of water from 20 degrees C takes 2.6 million joules. Sunlight, on a sunny day, is one kilowatt per square metre; let's generously assume we can get 50% efficiency over the eight hours of the day when the sun is high in the sky [don't forget, this is solar thermal power, it's more efficient than photovoltaics]. So each square metre of collecting area in our plant can boil 5.5 litres of water per day. The desal plant in this article produces 27.5 million gallons per day so to replace it with solar we'd need nineteen million square metres, or nineteen square km, of mirrors. That's a lot of mirrors, and a lot of squeegee men. If you wanted a solar-powered desal plant I'm sure you could do it cheaper using photovoltaics plus reverse osmosis.