Question

If one mole of caffeine has a mass of 194.19 g and you drink an average of two servings of this drink a day, how many caffeine molecules do you ingest in one year

Answer 1

To calculate the number of caffeine molecules ingested in one year, you need to know the number of moles of caffeine in two servings and then convert that to the number of molecules. In two servings, you would ingest approximately 1.2044 × 10^24 caffeine molecules.

Step-by-step explanation:

To calculate the number of caffeine molecules ingested in one year, we need to know the number of moles of caffeine in two servings of the drink and then convert that to the number of molecules.

First, let's calculate the number of moles of caffeine in two servings. One serving contains 194.19 g, so two servings would be 388.38 g. Since the molar mass of caffeine is 194.19 g/mol, the number of moles in two servings would be:

388.38 g / 194.19 g/mol = 2 mol

Now, to calculate the number of molecules, we can use Avogadro's number, which states that there are 6.022 × 10^23 molecules in one mole of a substance. Therefore, in two servings, you would ingest:

2 mol × 6.022 × 10^23 molecules/mol = 1.2044 × 10^24 molecules

Answer 2

The standard cup of coffee sold in coffee shops have a serving size of 6 ounces. Since there are 28.3495 g in 1 oz, that is equivalent to 170.097 grams. Since you drink two servings, the total mass is 170.097×2 = 340.194 g. Using the molar mass (194.19 g/mol) and the Avogadro's number (6.022×10²³ molecules/mol):

340.194 g caffeine(1 mol/194.19 g)(6.022×10²³ molecules/mol) = 1.055×10²⁴ molecules