Hard water [local] contains dissolved salts. The cations of some salts (Ca2+, Mg2+) form precipitates with soap (soap scum). In general, cleaning is easier with water that has these ions removed (soft water).
The composition of cleaning agents [local] (soaps and detergents) are explained and how and why each works [local]. Three linked pages from Soap and Detergent Manufacturers.
Sample home experiments [local] with hard/soft water.
Common water problems.
Salt Based Water Softeners [local]. We love them and we hate them.
For every grain of hardness in water, 7.5 mg of sodium will be added to each quart of water by the ion-exchange method. Water with 10 grains per gallon hard; you will add 75.0 mg of sodium per quart of water softened by ion-exchange.