Why are some alcohols soluble in water?
Because to a first approximation, the smaller alcohols are half a water molecule.
Methanol and ethanol are infinitely miscible in water. This reflects the capacity of the alcohols to hydrogen bond, and also the shortness of the hydrocarbyl tail. Propanol and the higher alcohols have limited solubility in water, in that interaction between the hydrophobic tails becomes the important interaction.
Here is something else to consider. And this also reflects the influence of the phenomenon of hydrogen bonding. Ethanol and hexanes are infinitely miscible. Methanol and hexanes are IMMISCIBLE: i.e. methanol and hexanes would form 2 separate layers. Can you advance a rationalization?
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Some alcohols are soluble in water due to their ability to form hydrogen bonds with water molecules. Alcohols with one to three carbon atoms are generally soluble in water because they can form hydrogen bonds with the hydroxyl (-OH) group of the alcohol molecule and the polar water molecules. As the size of the alcohol molecule increases, its solubility in water decreases because the nonpolar hydrocarbon chain becomes more dominant and less compatible with the polar water molecules.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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