Question

A 13.736-gram sample of capsaicin, the compound that gives the hot taste to chili peppers, was analyzed. It has a molecular mass of 305.4 amu. It contained 9.72 grams of carbon, 1.225 grams of hydrogen, and .631 grams of nitrogen. The rest was oxygen. What is the molecular formula for capsaicin?

Answer 1

`\begin{equation*} C_(18)H_(27)NO_3 \end{equation*}`

Explanations:

Given the following mass of the elements

Mass of Carbon = 9.72 grams

Mass of Hydrogen = 1.225grams

Mass of nitrogen = 0.631 grams

Mass of oxygen = 13.736 - (9.72+1.225+0.631)

Mass of oxygen = 13.736 - 11.576 = 2.16grams

Convert the mass to moles

Moles of Carbon = 9.72/12 = 0.81moles

Moles of Hydrogen = 1.225/1 = 1.225moles

Moles of Nitrogen = 0.631/14 = 0.0451moles

Moles of Oxygen = 2.16/16 = 0.135moles

Divide by the lowest moles

For Carbon = 0.81/0.0451 = 17.96 = 18

For Hydrogen: 1.225/0.0451 = 27.16 = 27

For Nitrogen: 0.0451/0.0451 = 1

For Oxygen: 0.135/0.0451 = 3

Determine the empirical formula

`Empirical\text{ }formula=C_(18)H_(27)NO_3`

Determine the molecular formula

`\begin{gathered} (C_(18)H_(27)NO_3)n=305.4 \\ (18(12)+27(1)+14+3(16))n=305.4 \\ (216+27+14+48)n=305.4 \\ 305n=305.4 \\ n=(305.4)/(305) \\ n\approx1 \\ (C_(18)H_(27)NO_3)_1=C_(18)H_(27)NO_3 \end{gathered}`

Hence the molecular formula for capsacin is C18H27NO3