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Why is ethyl acetate insoluble in water?

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Answer
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Hint: Solubility is the relative ability of a solute to dissolve in a solvent and to predict whether a compound (solute) will be soluble in a given solvent, we always follow a rule which states that, “Like dissolves like”. That means the polar compounds will be readily dissolved or are soluble in polar molecules whereas the non-polar compounds are soluble in non-polar solvents.

Complete answer:
As both ethyl acetate and water both are polar molecules, so before discussing the solubility of ethyl acetate in water, let us discuss the basic concept involving polar solvents.
Polar Protic solvents: These are capable of hydrogen bonding because they contain at least one hydrogen atom which is directly bonded to an electronegative element like $ O-H $ or $ N-H $ bond.
Polar aprotic solvents: These solvents contain no hydrogen atoms directly bonded to an electronegative element and thus, are not capable of hydrogen bonding.
Now, ethyl acetate is an organic compound with molecular formula $ {{C}_{4}}{{H}_{8}}{{O}_{2}} $ and structurally can be represented as follows:
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It is clear from the structure that both the oxygen atoms (electronegative atoms) are covalently bonded to the carbon atom and no hydrogen atom is directly bonded to it. Thus, it is a polar aprotic molecule.
Water can structurally be represented as follows:
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As the oxygen atom is directly bonded to hydrogen atoms, so the molecule is polar protic.
That means, water is capable of hydrogen bonding while ethyl acetate is not and due to which the dielectric constant of water (78.5) is relatively higher as compared to the dielectric constant of ethyl acetate (6). Since ethyl acetate is incapable of effectively separating the coulombic forces of attraction acting between water molecules, these two liquids are immiscible.
Thus, we can conclude that due to strong hydrogen bonding in water molecules, the molecules of ethyl acetate do not polarise the water molecules easily. So, ethyl acetate is insoluble in water.

Note:
Remember that the dielectric constant for a molecule (specifically solvent) is a measure of its polarity and the higher the dielectric constant, the more polar the compound is. It is important to note that solubility of a compound does not depend on the size of the particle. If given enough time, even large particles will eventually dissolve in the solvent. The solubility of a compound is only affected by factors like temperature, pressure and polarity.