Final answer:
The calculation using Avogadro's number and the molar mass of caffeine for 7.70×1020 molecules results in a mass that does not exactly match any of the provided options, with the calculated mass being 2.4832×10-4 kg.
Step-by-step explanation:
The mass of 7.70×1020 molecules of caffeine can be calculated using Avogadro's number and the molar mass of caffeine. To find the answer, we first determine the number of moles from the given number of molecules, and then we convert moles to mass using the molar mass of caffeine which is 194 g/mol.
Firstly, we use Avogadro's number (6.022×1023 molecules/mol) to find the number of moles:
Number of moles = 7.70×1020 molecules / 6.022×1023 molecules/mol = 1.28×10-3 mol
Next, we convert moles to mass:
Mass = Number of moles × Molar mass of caffeine = 1.28×10-3 mol × 194 g/mol = 0.24832 g
Finally, converting grams to kilograms:
Mass in kg = 0.24832 g × 10-3 kg/g = 2.4832×10-4 kg
However, none of the options provided (a) 1kg, (b) 7.7×10-2 kg, (c) 7.7×102 kg, (d) 7.7×10-20kg corresponds exactly to this calculated mass. Therefore, the closest match to the calculated mass, without rounding, is not listed among the provided options.