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Why do soaps not work in hard water?

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Answer
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Hint: Hard water has salts of the elements which belong to the s-block, especially group 2 elements. When the soap and the salts combine a precipitate is formed rather than mixing up.

Complete step by step answer:
Natural water contains dissolved salts. Depending on the behavior towards soap solution water is classified as soft and hard water:
Soft water: Water that produces lather with soap readily is called soft water. Examples of soft water are rainwater, distilled water, and demineralized water.
Hard water: Water that does not form lather easily with water is called hard water. Some examples of hard water are river water, seawater, spring water, etc.
Cause of hardness of water: It has been established that hardness of water is due to the presence of bicarbonates, chlorides, and sulphonates of magnesium and calcium in it. Hard water does not form lather easily with soap or soap does not work in hard water. This is because:
Soap is sodium or potassium salt of certain higher fatty acids such as stearic acid, palmitic acid, etc. When hard water is treated with soap solution, \[C{{a}^{2+}}\] and \[M{{g}^{2+}}\] ions present in hard water react with the anions of fatty acids present in soap to form scum or curdy white precipitates. As a result, hard water does not produce lather with soap immediately.
\[2{{C}_{17}}{{H}_{35}}CO{{O}^{-}}N{{a}^{+}}+CaC{{l}_{2}}\to {{({{C}_{17}}{{H}_{35}}COO)}_{2}}Ca\downarrow +2NaCl\]
\[2{{C}_{17}}{{H}_{35}}CO{{O}^{-}}N{{a}^{+}}+MgS{{O}_{4}}\to {{({{C}_{17}}{{H}_{35}}COO)}_{2}}Mg\downarrow +N{{a}_{2}}S{{O}_{4}}\]
Thus, hard water is not suitable for washing purposes since a lot of soap is wasted in precipitating out and ions present in hard water.

Note:
However, when all the \[C{{a}^{2+}}\] and \[M{{g}^{2+}}\] ions present in hard water have been precipitated by addition of sufficient amount of soap, resulting water becomes soft and readily produce lather with soap. Instead, we can use detergent in the hard water because it forms lather with detergent.