A 12-oz can of diet soda contains 180 mg of the artificial sweetener aspartame (

Question

A 12-oz can of diet soda contains 180 mg of the artificial sweetener aspartame (trade names NutraSweet and Equal). When aspartame is ingested, it is metabolized to phenylalanine, aspartic acid, and methanol, according to the balanced equation: H_18N_2O_5 + 2 H_2O rightarrow C_9H_11NO_2 + C_4H_7NO_4 + CH_3OH a. Using this equation, determine how much methanol (in mg) is formed on metabolism of the aspartame in each 12-oz can. The molar mass of aspartame is 294.2 g/mol, and the molar mass of methanol is 32.04 g/mol. b. Methanol is a toxic compound, with the average lethal dose in humans estimated at 428 mg/kg of body weight. How many cans of soda would a 52-kg individual have to ingest to obtain a lethal dose of methanol?

Explanation / Answer

a) According to the reaction, it's a 1:1 stechiometry relation, so, with the moles of aspartane we can assume that these will be the moles produced of methanol, and then, we can calculate the mass of methanol. Doing this:

moles aspartane = moles methanol = 0.180 g / 294.2 g/mol = 0.000612 moles
mass methanol = 0.000612 moles * 32.04 g/mol = 0.0196 g or simply 19.6 mg.

b) in this part, we can simply use conversion factor:
1 can -------> 19.6 mg methanol
#can = 52 kg * 428 mg/kg * 1 can/19.6 mg = 1135.51 can

Hope this helps

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