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Deduce the molecular formula of the alcohol that has molecular mass 158.

I tried dividing this molecular mass (158) by the molecular mass of ethanol (46) to get a ratio, and then multiply the formula of ethanol $\ce{C2H5OH}$ by this ratio, but I didn't get a whole number.

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    $\begingroup$ The general formula of alcohol is CnH2n+2O. If you know the individual atomic masses of C, H and O, you can do some simple math to get your answer. $\endgroup$
    – Arishta
    Mar 26, 2017 at 10:09
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    $\begingroup$ Hardly a well posed question :( $\endgroup$ Mar 11, 2019 at 19:12
  • $\begingroup$ Why dividing by 46 ? Nobody says the your alcohol is a polymer of ethanol. Better follow Arishta's suggestion. $\endgroup$
    – Maurice
    May 9, 2020 at 11:49
  • $\begingroup$ As I commented 2 years ago, there is no information to show that the alcohol is saturated, to which the formula CnH2n+2O applies. $\endgroup$
    – user55119
    May 9, 2020 at 14:38

2 Answers 2

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We know that the general formula for the representation of an alcohol is $$\ce{C_nH_{2n+2}O}$$. Where $n$ refers to the number of carbon atoms in the chain. Lets put down the values of molecular masses of $\ce{C}$, $\ce{H}$ and $\ce{O}$.
We get, $$12n + (2n+2) + 16$$ which can be rewritten as, $$14n + 18$$ Thus the molecular mass given to us should satisfy a value of $n$ since it is an alcohol. $$14n + 18=158$$ Solve and you will get $$n=10$$ and the formula is $\ce{C10H22O}$. Note that this formula does not uniquely specify one particular alcohol, as there are multiple isomers with the same molecular mass.

Let's see where you went wrong. You divided the value of molecular mass given with the mass of ethanol, which could have been correct had alcohols been made up of repeating units of the same group$$\ce{C2H5OH}$$.

But that is not the case. The molecular masses of different alcohols are not multiples of any integer. For example, methanol, ethanol, and propanol have masses of 32, 46 and 60 respectively.

Thus the only way to get your answer would be to equate the molecular mass with the general molecular mass for an alcohol having $n$ carbon atoms.

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  • $\begingroup$ While the proof is correct, there is no statement that the alcohol is saturated. If n is not a whole number, then the alcohol must have a degree of unsaturation greater than zero. $\endgroup$
    – user55119
    Mar 25, 2018 at 15:02
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$\ce{C_nH_{2n+1}OH}$ is the general formula.

$\ce{C}$, $\ce{H}$, and $\ce{O}$ have relative atomic masses of 12, 1, and 16.

To solve: $$12n+2n+1+16+1=158$$ is the same as $$\begin{align}14n+18&=158\\158-18&=14n\\(158-18)/14&=n\\10&=n\end{align}$$

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