A 194-g sample of caffeine (C3H10 N4O2) contains 6.02 x 10^23 molecules of caffeine. If some energy drink contains 210. mg of caffeine, how many molecules of caffeine are present in the drink?

6.52×10²⁰ molecules.

Explanation:

We'll begin by converting 210 mg of caffeine to grams (g). This can be obtained as follow:

Recall:

1 mg = 1×10¯³ g

Therefore,

210 mg = 210 mg / 1 mg × 1×10¯³ g

210 mg = 0.21 g

Therefore, 210 mg of caffeine is equivalent to 0.21 g of caffeine.

Finally, we shall determine the number of molecules in 0.21 g of caffeine as follow:

194 g of caffeine contains 602×10²³ molecules.

Therefore, 0.21 g of caffeine will contain = (0.21 × 602×10²³)/194 = 6.52×10²⁰ molecules.

Therefore 0.21 g contains 6.52×10²⁰ molecules.

Thus, we can say that 210 mg (i.e 0.21g) of caffeine contains 6.52×10²⁰ molecules.