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Is there a way to figure out the acid/base properties of a compound just by looking at the chemical formula?

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Consider the two compounds above. Both have the formula $\ce{C5H10O2}$, yet one is about 20 orders of magnitude stronger an acid than the other. Without knowing the general structure of a molecule (what functional groups it is comprised of), suffice it to say no, you cannot know how acidic the molecule is.

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It depends on the type of formula you are talking about. You need to know the structure before you can start assessing acid/base behavior, and not all formulas are equal when doing so.

A structural formula can be useful, as they are textural representations of the chemical structure. It is possible to determine the acidity difference between $\ce{CH3CH2CH2OH}$ and $\ce{(CH3)2CHOH}$, even when both have a molecular formula of $\ce{C3H8O}$.

An empirical or molecular formula, however, tells you very little, unless you can identify the compound based on it, or work out the molecular structure from the formula. It is generally easier to do so for smaller molecules. An empirical is even less useful as it tells you even less about the molecule itself; you cannot even determine the size of the molecule with certainty, which makes determining the structure nearly impossible.

You might be able to make educated guesses about the compound given its empirical formula, but they will be just that, guesses. For example, seeing sodium or potassium can imply a base (or something more basic, at least), while halogens are equally associated with acids.

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