Suppose you throw two lumps of sugar into a 200-mL mug, and then fill it up with

Question

Suppose you throw two lumps of sugar into a 200-mL mug, and then fill it up with tea. A 500-g box of sugar contains 250 lumps. The molecular mass of sucrose is 342 Da. (a) What will be the sugar concentration in the tea? (b) The well-known sweetener aspartam is the methyl ester derivative of the aspartyl-phenylalanine dipeptide. One weight unit of aspartam is 180 times as sweet as one weight unit of sugar. What is the mM concentration of aspartam with a sweetness identical to that of the sugar concentration of the tea described above? (The molecular mass of aspartam is 294 Da.)

Explanation / Answer

(a) Mass of two lumps of sucrose = (500 g/250 lumps) x 2 lumps = 4 g

moles of sucrose = grams/molar mass = 4 g/342 Da = 0.0117 mol

sugar concentration in tea = moles/volume (L) = 0.0117 mol/0.200 L = 0.06 M

(b) mass of aspartam in solution = 4 g/180 = 0.022 g

moles aspartam = 0.022 g/294 Da = 7.56 x 10^-5 mol

concentration of aspartam in tea = 7.56 x 10^-5/0.200 = 3.78 x 10^-4 M

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