Question

A drug marguana owes its activity to tetrahydrocannabinol, which contains 70% as many carbon atoms as hydrogen atoms and 15 times as many hydrogen atoms as oxygen atoms. The number of mole in a gram of tetrahydrocannabinol is 0.00318. Determine the molecular formula.

• A. $C_{20}{H}_{30}{O}_2$
• B. $C_{21}{H}_{30}{O}_2$
• C. $C_{12}{H}_{20}{O}_2$
• D. $C_{12}{H}_{20}{O}_3$

Answer 1

Answer: (B)

$C_{21}{H}_{30}{O}_2$

Let the molecular weight of tetrahydrocannabinol be $W$

$⟹0.00318=\frac{1}{W}$

$⟹W=314.46$ $gm$

Let the formula be $CxHyOz$

Given, $x=0.7y,z=\frac{y}{15}$

$\Rightarrow C_{0.7}yHy{O}_{y/15}$

$⟹12\times 0.7y+y+\frac{16y}{15}=314.46$

$⟹10.466y=314.46$

$y=30,x=21,z=2$

Formula: $C_{21}{H}_{30}{O}_2$

Hence, the correct option is $\left(C\right)$