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Arrange the following:
In increasing order of solubility in water:
 $ {C_6}{H_5}N{H_2},{({C_2}{H_5})_2}NH,{C_2}{H_5}N{H_2}. $

Answer
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Hint :The solubility of a compound in a solution depends on the presence of the same bonds or the same polarity between the substance and the solution. A substance is soluble in water if it has hydrogen bonding and a place for water to form hydrogen bond with the lone pair or any negative charge residue on the compound due to polarity.

Complete Step By Step Answer:
The solubility of a compound in water depends on the following factors: -
The availability of an already present hydrogen bond – now the presence of hydrogen bond ensures there is already a hydrogen bond present there and that means there is polarity I the compound and that too with hydrogen only.
Hinderance – the compound having lone pair or hydrogen should not have too much hindrance on that particular element of that compound so that there are less problems for the hydrogen to form hydrogen bonds and make the compound soluble in it.
The number of hydrogen bonds – the greater the number of hydrogen bonds greater will be the solubility of the compound in water, as more hydrogen bonding and less hindrance due to small hydrogen atoms.
Electronegativity of the element having hydrogen bond in the compound - the higher the electronegativity the higher the polarity, the higher will be the solubility
Now we have phenyl amine, now phenylamine is a hindered compound due to the presence of the benzene ring therefore it is the least soluble.
Another we have $ {({C_2}{H_5})_2}NH $ , in this compound we have two ethyl group attached to the nitrogen atom, while the third atom is hydrogen, so there is only one hydrogen bond present while the ethylamine has greater number of hydrogen and less hindrance than two methyl groups.
In ethyl amine there are two hydrogen bonds already and also there is very less hindrance on the lone pair for the hydrogen bond to happen due to two small hydrogen atoms and higher polarity.
 $ {C_6}{H_5}N{H_2}\langle \,\,{({C_2}{H_5})_2}NH\,\,\langle {C_2}{H_5}N{H_2}. $ .

Note :
Hydrogen bonding also depends on the element in the compound, the higher the electronegativity of the compound the higher would be the solubility of the compound in a solution of water.