The reason hot water is best for dissolving salt (and other chemicals) has to do with the motion of the molecules making up the water. When the water gets hot, the molecular motion increases, running into more salt molecules and making the bonds easier to pull apart. [1] X Research source
When water reaches its saturation point, it no longer has any ability to dissolve salt at a molecular level — so much salt has dissolved that there is no longer any chemical potential for the water to pull apart new salt crystals. [2] X Research source
Don’t waste your leftover salt water — there are tons of things you can use it for. For instance, you can use it to poach an egg, boil potatoes, preserve spinach, and even help you peel nuts![3] X Research source
Feel free to scrape a little bit of salt from your paper to season your food — it should be perfectly safe to eat. Be careful not to get any paper shavings in your food, though!
As the saltwater boils, the water (minus the salt) will turn into steam and rise out of the pot. As it hits the lid, it will cool slightly and form liquid condensation (water) on the underside of the lid. This water doesn’t contain salt, so all we need to do is gather it to have salt-free water.
If you like, you can also run a long, skinny metal or glass object (like a stirring rod or thermometer) from the bowl up to the lowest point on the lid — the water should run down this object into the bowl.
Technically, this water should be safe to drink. However, unless you’re sure that both the lid for your pot and the bowl you collected the water in (and the skinny metal or glass rod, if you used one) are clean, you may not want to do this.
Reverse osmosis pumps are sometimes sold for residential use but are also often used for recreational purposes like camping. Pumps can be somewhat expensive, usually running several hundred dollars. [5] X Research source
Decanoic acid is available from chemical supply stores — usually around $30-$40 per bottle.
Note that this process does not necessarily remove bacteria or other contaminants from the water, so further treatment may be needed to get drinkable water from this method in the wild. Recent research has been promising, however, suggesting new techniques that do kill bacteria as part of the process.