Answer to Question #163609 in Organic Chemistry for fofo

Question

An alkaloid was isolated from a common household beverage. The unknown alkaloid proved to have a molecular mass of 194. Using the Rule of Thirteen, determine a molecular formula and an index of hydrogen deficiency for the unknown. Alkaloids are naturally occurring organic substances that contain nitrogen. (Hint: There are four nitrogen atoms and two oxygen atoms in the molecular formula. The unknown is caffeine. Look up the structure of this substance 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:

194 / 13 = 14r12

The predicted formula is C₁₄H₁₄₊₁₂ or C₁₄H₂₆.

However, as the molecule contains four nitrogen atoms and two oxygen atoms, we need to substract the corresponding values:

1. 4 × [N - 15] = 4 × [N - (CH + H)] = 4 × [N - CH₂].

This gives a formula C₁₀H₁₈N₄.

2. 2 × [O - 16] = 2 × [O - CH₄].

This gives a final formula C₈H₁₀N₄O₂.

Index of hydrogen deficiency can be calculated using the following formula:

Index = (2C + 2 + N - H) / 2 = (2 × 8 + 2 + 4 - 10) / 2 = 6.

Answer:C₈H₁₀N₄O₂; index 6.