Why is potassium chloride is soluble in water?

It happens because of the bonding in the two compounds. Potassium chloride is an ionic compound, meaning it has polar bonds which, in water, causes it to be dissolved, as the stronger polar bonds in water pull them apart. Potassium has metallic bonding, so it can't be pulled apart by the water. Instead they react (explanation for this is long, so I advise looking it up if you need more in-depth information). Basically it's the difference in bonds that makes potassium chloride soluble. (Not in my own words, I found this)