Finding the formula of an alcohol with a given molecular mass


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




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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$\ce{C\_nH\_{2n+1}OH}$ 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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