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Soap is usually made from one or more fatty acids. Fatty acids are relatively long chain organic molecules that have both a hydrophobic (water repelling/fat loving) part and a hydrophillic (water loving/fat repelling) part which is the carboxylic acid end group. When the acid group is neutralized by combination with a group one metal ion, the resulting ion will dissolve in water.
The way that the soap works is that the hydrophilic end will interact with the oils and greases that you are trying to remove from your hands/clothes/etc. and dissolve them. At the same time the hydrophilic end makes the molecule water soluble so when you rinse your hands the soap molecule and the dirt are washed down the drain.
Soaps when added to water also reduce the surface tension of water, allowing the formation of the lather that you referred to. There is a certain minimum amount of soap - the critical micelle concentration - that is necessary for the lather to form. That is why if you use soap with really dirty dishes the initial lather disappears, even in soft water.
Now, in hard water there are relatively large amounts of calcium and magnesium ions. Each of these ions can react with two soap molecules, forming an insoluble precipitate. Since the soap has been effectively removed from solution there is not enough molecules left to form the soap lather. The common way hard water is noticed is the ring that is left around the bathtub when bathing in water that is hard.
Soap is formed by performing a reaction between natural fatty acids like palm oil, coconut oil which are a few among hundreds others and an alkali like sodium hydroxide. This leads to the formation of a mixture of different sodium salts formed with the fats.
When used in hard water that contains a lot of calcium and magnesium ions they cause the soap to precipitate and it is unable to form lather. This can be minimized by the addition of chemicals like sodium trimetaphosphate, borax, sodium silicate etc. These prevent the calcium and magnesium ions from reacting with the soap and allow it to form lather.
soaps are the potassium or calcium salt of fatti acids having high molecular weight (such as :pamitic acid ,stearic acid etc.) .
and hard water consists sulphate, bicarbonate, and chloride salts
of ferrus ,calcium or magnesium.
so they react with each other and sodium sulphate or chloride along with magnesium or calcium stearate or etc. is produced and they are sedimented under the water. when all the salts of the hard water completes the reaction , a little lather is produced.
such as :
2Na-Stearate + CaCl2 = Ca(stearate)2 + 2 NaCl.
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