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How does an ion exchange method remove the hardness of water?

Answer
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Hint: Water from various natural sources contain different types of impurities in different amounts.
Depending on the behaviour of water with dissolved salts, the soap is categorized as hard water and soft water. Soft water produces lather with soap solution like distilled water, purified water, and rain water.
Hard water- water is not able to generate lather on treating with soap solution easily and is termed as hard water. Examples of hard water are sea water, drainage water, tap water etc.

Complete answer:
Hardness of water appears due to the presence of a number of ions such as chloride ions, sulphate ions, bicarbonate ions of calcium or magnesium metals.
These ions are introduced into water when it passes through any rocks or grounds.
Hard water is not capable of producing lather on reacting with soap solution because different ions in water react with soap and form precipitate which is insoluble in nature and get settled at the bottom of the soap solution.
Therefore the ion exchange method is used to remove the hardness of water. In this method, different ions which are responsible for causing hardness of water are substituted with less damaging ions with the help of ion exchangers.
Ion exchangers are of two type’s namely inorganic ion exchanger and organic ion exchanger.
In order to remove hardness of by water by inorganic ion exchanger hard water is poured into a tank which contain hydrated sodium aluminium silicate as exchanger which react with calcium ion of hard water to form calcium zeolite
$N{a_2}Z + C{a^{ + 2}} \to CaZ + 2N{a^ + }$
Ion exchanger which reacts with magnesium ions of hard water to form magnesium zeolite.
$N{a_2}Z + M{g^{ + 2}} \to MgZ + 2N{a^ + }$
Where $N{a_2}Z$ is sodium zeolite and $Z$ is $A{l_2}S{i_2}{O_8}.x{H_2}O$
The calcium ion and magnesium ion get attached to the zeolite and water becomes soft and produces lather with soap.
As the process continues, zeolite gets used which is further regenerated from the process by passing a $10\% $sodium chloride solution.
$CaZ + 2N{a^ + } \to N{a_2}Z + C{a^{ + 2}}$
Hardness of water is also removed by using organic ion exchangers which are large polymeric solid insoluble in water containing acidic as well as basic reactive groups. They are capable of removing any type of ion impurities in hard water.
Hard water in this process is first passed by cation ion exchange resin which causes substitution of all cations with ${H^ + }$ ions.
$2$Resin$ - {H^ + } + C{a^{ + 2}} + 2C{l^ - } \to Ca$(Resin)2 $ + 2{H^ + } + 2C{l^ - }$
2 Resin$ - {H^ + } + M{g^{ + 2}} + S{O_4}^{ - 2} \to Mg$(Resin)2 $ + 2{H^ + } + 2S{O_4}^{ - 2}$
Now the water after passing through this reaches at the bottom of tank where it treated with anionic resin which substitutes $O{H^ - }$ ions with $C{l^ - }$ions and $S{O_4}^{ - 2}$ ions.
Resin$ - N{H_3}^ + O{H^ - } + 2C{l^ - } \to $Resin$N{H_3}^ + C{l^ - } + O{H^ - }$
2 Resin$ - N{H_3}^ - O{H^ + } + S{O_4}^{ - 2} \to $(Resin$ - N{H_3}^ + {)_2}S{O_4}^{ - 2} + 2O{H^ - }$
Finally the remaining ions from the first tank and ions from the second tank combine to form deionized water (soft water).
${H^ + } + O{H^ - } \to {H_2}0$

Additional information:
Hardness of water is also removed by some other methods such as-
Clark’s method- $Ca{(HC{O_3})_2} + Ca{(OH)_2} \to 2CaC{O_3} \downarrow + 2{H_2}O$
Washing soda method- $CaC{l_2} + N{a_2}C{O_3} \to CaC{O_3} \downarrow + 2NaCl$
Boiling method- $Ca{(HC{O_3})_2} \to CaC{O_3} \downarrow + C{O_2} \uparrow + {H_2}O$

Note:
Inorganic ion exchanger method is also known as Permutit method. Hydrated sodium aluminium silicate used in this method is known as zeolite and can be naturally occurring or synthetic.
Water obtained after organic ion exchange resin method is known as demineralized water or deionized water. This method is more useful for removing the hardness of water.