Question

why soap solution appear cloudy?

Answer 1

Soap is mixed with water to form micelle which gives the solution a cloudy appearance when soap is added to the water the fatty acid ionizes. The polar water soluble gets attracted to water while the non-polar tails attract each other. Then the ions are attracted to each other and form the special clusters and sometimes in a form of emulsions which gives a cloudy look.

Answer 2

When soap is mixed in water a colloidal solution is formed. The soap solution has soap micelles which are an aggregate of soap molecules. These micelles are large and they scatter light. That is why the soap solution appears cloudy.