A soap has two dissimilar ends. At one end is the hydrocarbon chain that is non-polar and hydrophobic (oil soluble). At the other end there is the carboxylate ion that is polar and hydrophilic (water soluble).
When soap is added to water, its molecules make a unimolecular film on the surface of water with their carboxyl groups dissolved in water and the hydrocarbon chains standing on end to form a hydrocarbon layer as shown in the figure below.
Example:
When a dirty cloth is soaked in soap solution, soap dissolves dirt (fat or oil with dust absorbed in it) by micelle formation. The oil or fat is at the centre of the sphere with fat-soluble hydrocarbon chains of soap dissolved in it. The water soluble carboxylate ions make a hydrophilic surface around this sphere and render the miscelles of oil or fat water-soluble. Thus the micelle is dissolved in water and is washed away.
Soap tends to concentrate on the solution surface and therefore lowers its surface tension, causing foaming. This helps it to penetrate the fabric. It emulsifies fat in dirt to form micelles render all the micelles water-soluble. Thus the water washes the dirt away.
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