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The simple answer is that most everything happens at least a little bit. The reason why is EQUILIBRIUM. You are correct---water is polar and oxygen is non-polar. The water molecules have great hydrogen bonding and dipole-dipole interactions with each other that the oxygen molecules cannot replace, and so it will take energy or ENTHALPY for oxygen to mix its way into the water. So the process is ENDOTHERMIC and hence unfavorable. However, when you dissolve oxygen in water, you get disorder---something that scientists quantify by talking about a solution's ENTROPY. It is favorable for entropy to increase, and in this case the entropy of the water solution would go up if you were to be able to squeeze some water molecules in there. So entropy and enthalpy are at odds for this reaction. Enthalpy is unfavorable, entropy is favorable. In situations like that systems will reach a state of equilibrium in which the reaction partially occurs. How much will depend on the relative sizes of the entropy and enthalpy changes.

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Q: If water H2O is polar and oxygen O2 non-polar how can there be dissolved oxygen in water?
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Because nonpolar oxygen is has a much greater electronegativity and oxygen and water go well.


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