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How does soap work?
Soap molecules are long and stringy just like oil molecules are. They have two very distinct ends. The head of this soap molecule string loves water and will attach to other water molecules. Its tail on the other hand loves oil and will search out and attach to other oil molecules. This gives us a very interesting situation where the head of the soap molecule will attach to other water molecules and the tail will find and attach to other oil molecules. The effect is that the soap molecule will latch onto the oil with its tail and be flushed away with other water molecules attached with its head. To make matters even better, soap molecules disrupt the surface tension of water by crowding around the water surface with their water loving heads which disrupts the waters ability to stay tightly coupled together in a sphere like a rain drop. So in a way it flattens waters ability to remain in this sphere configuration and makes the water molecules flatter thus wetting everything even the smallest crevices.
Actually when soap is dissolved in water, it forms a colloidal suspension in which the soap molecules cluster together to form micelles. The micelles remain suspended in water because the similar negative charges at the end of each soap molecule repel each other. In a micelle the soap molecules are arranged radially, with the hydrocarbon end directed towards the centre and the ionic end directed outwards. Now when the dirty clothes are put in this soap solution, then the soap micelle entraps the dirt particles by attaching the hydrocarbon part of the soap molecule to the greasy or oily particles. Since the ionic part of the soap molecules remains attached to water molecules, therefore the greasy dirty particles get dispersed in water and the cloth gets cleaned.