Question

Aspartame, otherwise known as the artificial sweetener Nutrasweet, has a molecular mass of 294 amu. It contains 57.14% carbon, 6.12% hydrogen, 9.52% nitrogen, and 27.2% oxygen. What is its molecular formula?

Answer 1

`\begin{equation*} C_(14)H_(18)N_2O_5 \end{equation*}`

Explanations:

Given the following parameters

Carbon = 57.14%

Hydrogen = 6.12%

Nitrogen = 9.52%

Oxygen = 27.2%

Convert the percentages to grams

Carbon = 57.14g

Hydrogen = 6.12g

Nitrogen = 9.52g

Oxygen = 27.2g

Convert the mass to moles

Mole of carbon = 57.14g/12 = 4.76moles

Mole of hydrogen = 6.12g/1= 6.12moles

Mole of nitrogen = 9.52/14 = 0.68 moles

Mole of oxygen = 27.2/16 = 1.7moles

Divide by the lowest number of moles

For Carbon: 4.76/0.68 = 7(2) = 14

For hydrogen: 6.12/0.68 = 9(2) = 18

For nitrogen: 0.68/0.68 = 1(2) = 2

For oxygen: 1.7/0.68 = 2.5(2) = 5

Determine the empirical formula

Empirical formula = C14H18N2O5

Determine the molecular formula

`\begin{gathered} (C_(14)H_(18)N_2O_5)n=294 \\ (14(12)+18(1)+2(14)+5(16))n=294 \\ (168+18+28+80)n=294 \\ 294n=294 \\ n=(294)/(294) \\ n=1 \end{gathered}`
`(C_(14)H_(18)N_2O_5)_1=C_(14)H_(18)N_2O_5`

Hence the molecular formula of aspartame is C14H18N2O5