Aspartame is the methyl ester of the dipeptide of aspartic acid ( $C X_{4} H X_{7} NO X_{4}$ ) and phenylalanine ( $C X_{9} H X_{11} NO X_{2}$ ). Take aspartame to be 100 times sweeter than sucrose on a mass-for-mass basis, and atomic masses C 12, H 1, N 14, O 16. How many micromoles of aspartame give the same sweetness as 2.45 g of sucrose? Give the answer to two decimal places.

Numerical answer type, answer in micromol, tolerance 0.01.

Answer: 83.33 micromol

The formula of aspartame is

C X_{14} H X_{18} N X_{2} O X_{5}

(amino acids joined with loss of one water, then methyl ester formation with loss of another), so M = 14(12) + 18(1) + 2(14) + 5(16) = 294 g/mol. Mass needed = 2.45 g / 100 = 24.5 mg. Amount = 24.5 mg / 294 g/mol = 83.33 micromol.

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Answer: 83.33 micromol

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