How do we prove that alcohols are weaker acids than water?
My response will be somewhat lengthy because I want to give a thorough explanation of why this occurs.
Taking into account the fact that an alkyl group is actually an EDG, or electron donating group (sometimes referred to as an ERG, or electron releasing group), is crucial to demonstrating why alcohols are weaker acids than water.
Since oxygen is more electronegative than the other atom in the functional group, it will draw the bond electrons to itself, which will facilitate the proton's removal.
In the case of an alcohol, on the other hand, the alkyl group will "push" electrons towards the oxygen; this will cause the oxygen atom's electron density to increase and its pull on the two bonding electrons it shares with the acidic proton to decrease.
Because of the strengthened bond between hydrogen and oxygen, the hydrogen will be more difficult to remove as a direct result.
Regarding the conjugate bases, the variation in stability can be attributed to the identical alkyl group's positive inductive effect.
Conjugate base stability is directly related to acid strength; the more stable a conjugate base, the less reactive it is; the less reactive it is, the weaker it will be, which implies that the acid will be stronger. In other words, stronger acids have weaker conjugate bases and vice versa.
The oxygen can accommodate the negative charge in both scenarios; however, because of the alkyl group's previously mentioned positive inductive effect, oxygen in the case of an alkoxide ion has to accommodate an additional negative charge.
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Alcohols are weaker acids than water because their conjugate bases are more stable due to the electron-donating alkyl groups attached to the oxygen atom, which stabilize the negative charge. This can be shown through experiments comparing the acidity of alcohols and water using pH measurements or acid-base titrations.
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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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