Explain the formation of scum when hard water is treated with soap.

Hard water contains salts of calcium and magnesium. When soap molecule comes in contact with these salts it forms a curdy white precipitate (compound insoluble in water) called scum. 

Soap + Hard water ⎯→ scum 

Soap does not work properly when the water is hard. A soap is a sodium or potassium salt of long chain fatty acids. Hard water contains salts of calcium and magnesium. When soap is added to hard water, calcium and magnesium ions present in water displace sodium or potassium ions from the soap molecules forming an insoluble substance called scum. A lot of soap is wasted in the process.

When soap reacts with water, calcium and magnesium salts are formed which causes hardness for water. Ionic ends of soap interacts with water while the carbon chain interacts with oil. The soap molecules, thus form structures called micelles where one end of the molecules is towards the oil droplet while the ionic-end faces outside. This forms an emulsion in water.