# What is the molecular formula of a substance that decomposes into 1.33 g of H and 21.3 g of O, and was found to have a molar mass of 34.1 gmol^-1?

May 21, 2017

The molecular formula of the substance is ${H}_{2} {O}_{2}$.

#### Explanation:

$H$ has a molar mass of $1$ $g m o {l}^{-} 1$, so $1.33$ $g$ = $1.33$ mol.

(I have assumed that we are talking about individual $H$ atoms, not ${H}_{2}$ molecules, and similarly for $O$ versus ${O}_{2}$.

Oxygen has a molar mass of $16$ $g m o {l}^{-} 1$, so using $n = \frac{m}{M}$, $n = \frac{21.3}{16} = 1.33$ $g m o {l}^{-} 1$.

We see that there are the same number of moles of each element in the substance, so we can think of the molecular formula as ${H}_{x} {O}_{x}$. We need to find the value of $x$.

If $x$ was equal to $1$, the molar mass would be $1 + 16 = 17$ $g m o {l}^{-} 1$.

Since the given molar mass is almost exactly 2x that, at $34.1$ $g m o {l}^{-} 1$, the value of $x$ must be $2$, and the molecular formula must be ${H}_{2} {O}_{2}$.

(incidentally, this is the formula of the chemical substance hydrogen peroxide)