Answer to Question #163603 in Organic Chemistry for fofo

Question

The Drug Enforcement Agency (DEA) confiscated a hallucinogenic substance during a drug raid. When the DEA chemists subjected the unknown hallucinogen to chemical analysis, they found that the substance had a molecular mass of 314. Elemental analysis revealed the presence of carbon and hydrogen only. Using the Rule of Thirteen, determine a molecular formula and an index of hydrogen deficiency for this substance. (Hint: The molecular formula of the unknown also contains two oxygen atoms. The unknown is tetrahydrocannabinol, the active constituent of marijuana. Look up the structure of tetrahydrocannabinol in The Merck Index and confirm its molecular formula.)

Answer 1

The rule of 13 states that the formula of a compound is a multiple n of 13 (the molar mass of CH) plus a remainder r. From here:

314 / 13 = 24r2

The predicted formula is C₂₄H₂₄₊₂ or C₂₄H₂₆.

As the substance has two oxygen atoms, the corresponding number of carbon and hydrogen atoms (2 × CH₄) must be subtracted. As a result, the predicted formula is C₂₂H₁₈O₂. However, the number of hydrogen atoms in the formula is higher than the number of carbon atoms. In this case, the modified formula is C₂₁H₃₀O₂.

The index of hydrogen deficiency can be calculated using the following formula:

index = (2C + 2 - H) / 2 = (2 × 21 + 2 - 30) / 2 = 7

Answer: C₂₁H₃₀O₂ ; index 7.