Question

A hydrocarbon contains 85.7% carbon. If 42 mg of the compound contains 3.018 $\times$ ${10}^{20}$ molecules, what is the molecular formula of the compound?

Answer 1

$85.7$ % carbon $\Rightarrow 100-85.7=14.3$ % Hydrogen

gram molecular weight= $6.023\times {10}^{23}$

$\Rightarrow 42mg=3.018\times {10}^{20}$

$\Rightarrow 84mg=6.02\times {10}^{20}$

& $84g=6.02\times {10}^{23}$

$\therefore 85.7$ %=$\frac{85.7}{100}\times 84=72g$

$1$ mole of $C=12g$

$6$ moles of $C=12\times 6=72g$

$\therefore$ There are $6$ carbons in each molecule

$84-72=12g$ of $H=12H$ atoms in each molecule

$\therefore$ Molecular formula= $C_6{H}_{12}$