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An organic compound contains 71.7% carbon, 6.7% hydrogen, 10.4% nitrogen and 11.8% oxygen by mass. Given that its vapour density is 67.5, determine its empirical formula and molecular formula.

From the mass percentages, I have found out that the empirical formula is $\ce{C8H9NO}$. However, to find the molecular formula we usually require the molecular mass.

What does "vapour density" mean, and how can I use it to calculate the molecular mass of the compound?

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According to Wikipedia, the vapour density of a molecule is "the density of a vapour in relation to that of hydrogen". The density of a gas, $\rho$, is proportional to its molecular mass, $M$:

$$\rho = \frac{m}{V} \propto \frac{m}{n} = M$$

where $m$ is the mass of the gas, $V$ is the volume, and $n$ the amount of gas. Therefore, if we denote your compound by $\ce{X}$:

$$\begin{align} 67.5 &= \frac{\rho(\ce{X})}{\rho(\ce{H2})} \\ &= \frac{M(\ce{X})}{M(\ce{H2)}} \\ M(\ce{X}) &= 67.5 \cdot M(\ce{H2}) \\ &= 67.5 \cdot \pu{2 g mol-1} \\ &= \pu{135 g mol-1} \end{align}$$

Finally, you can use this piece of information to find that the molecular formula is $\ce{C8H9NO}$ as well.

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