Question #44670

The question tests the dimensional analysis of the ideal gas law combined with organic structural elucidation.

The core trap lies in the unit of density ($\text{kg m}^{-3}$).

When using strictly SI units ($P$ in Pa, $d$ in $\text{kg m}^{-3}$, $R = 8.314\text{ J K}^{-1}\text{ mol}^{-1}$), the molar mass $M$ is calculated in $\text{kg mol}^{-1}$.

Students frequently miss this and assume the result is in $\text{g mol}^{-1}$, leading to a massive error, or they incorrectly convert $\text{kg m}^{-3}$ to $\text{g L}^{-1}$ by multiplying by 1000 instead of 1 (since $1\text{ kg m}^{-3} = 1\text{ g L}^{-1}$).

Bypassing this yields $M = 84\text{ g mol}^{-1}$.

The subsequent chemical trap requires identifying a symmetrical alkene capable of geometrical isomerism (hex-3-ene) and correctly counting the $\alpha$-hydrogens in its ozonolysis product (propanal), avoiding confusion with acetaldehyde which would result from a miscalculated mass of $56\text{ g mol}^{-1}$.