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I'm not a chemist, and nor do I study chemistry so please try to be gentle.

Glucose has the molecular formula $\mathrm{C}_6\mathrm{H}_{12}\mathrm{O}_6$ and the empirical formula $\mathrm{C}\mathrm{H}_{2}\mathrm{O}$.

Starting from the empirical formula and working the other way, am I guaranteed that $\mathrm{C}_n\mathrm{H}_{2n}\mathrm{O}_n$, where $n$ is a positive whole number, are all going to be well-define molecular formulae?

Some examples are Formaldehyde ($n=1$), Acetic Acid ($n=2$) and Ribose ($n=5$). As a starting point, does $n=3$ and $n=4$ make sense, i.e. $\mathrm{C}_3\mathrm{H}_{6}\mathrm{O}_3$ and $\mathrm{C}_4\mathrm{H}_{8}\mathrm{O}_4$ respectively?

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Yes they make sense but the same molecular formula can represent different compounds, for the first case $\ce{C3H6O3}$ may rappresent:

Glyceraldehyde:enter image description here

or lactic acid (and its optical isomers):enter image description here

$\ce{C4H8O4}$ leads to even more possibilities see the three different tetrose enter image description here

Generally these compounds may be created when the sum of the formal charges of each atom in the molecular formula is equal to zero. Oxygen, hydrogen normally have formal charge of -2 and -1 carbon +4 so:

$$-2\times n + (-1 \times n \times 2) + (+4 \times n)=-4\times n +4\times n=0$$

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  • $\begingroup$ Thank you for your answer. I really do appreciate your help. If we have an empirical formula, say $\mathrm{X}_m\mathrm{Y}_n$, then does $\mathrm{X}_{km}\mathrm{Y}_{kn}$ always exist? (Here $X$ and $Y$ are elements and $k,m,n$ are positive integers.) $\endgroup$ – Fly by Night Jun 9 '14 at 18:39
  • $\begingroup$ @FlybyNight You are welcome. Not always, it depends on different factors I think you can find useful this question about criss-cross method. $\endgroup$ – G M Jun 9 '14 at 18:45
  • $\begingroup$ Hmmm... This is beyond me. I'm sorry. I have the following empirical formulae: $\mathrm{Li}_2\mathrm{O}$, $\mathrm{NH}_3$, $\mathrm{Al}_2\mathrm{O}_3$ and $\mathrm{H_3}\mathrm{PO}_4$. Which multiples of the subscripts are possible? $\endgroup$ – Fly by Night Jun 9 '14 at 19:01
  • $\begingroup$ No in not applicable to these compounds. $LiO_2$ and $Al_2O_3$ are ionic compounds so you have a lattice not a molecules hence there's no need to choose a larger unit LiO2 can describe all the compounds: Li2O4 etc etc. I know that exist $\ce{N2H6^{++}}$ but I don't know about N2H6. \ce{H6P2O8} doesn't exit up to my knowledge. Have a look at [Homologous series](en.wikipedia.org/wiki/Homologous_series ) for an example of the behavior you showed in your question . $\endgroup$ – G M Jun 9 '14 at 20:39

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