chemistry molarity

Question

Each cup of coffee contains around 95 mg of caffeine. How many moles of caffeine are present in one cup of coffee? How many caffeine molecules are present? 

Answer 1

Hi Rosyy! I love this question, maybe because it has to do with caffeine (coffee!). We are asked to find out how many moles of caffeine are present in one cup of coffee. Lucky for us, we are able to find the number of moles of a substance using its molar mass. So all we need to do is figure out how many grams of caffeine are in one cup and then use molar mass to convert over to moles.

In one cup of coffee, there are 95 mg of caffeine. We can convert mg into grams by doing a unit conversion. We are going from mg to grams, so mg will be on the bottom of the conversion fraction.

95 mg (1 gram / 1000 mg) = 0.095 grams caffeine in one cup of coffee

Using the molar mass of caffeine, which we can find by using the periodic table and adding up the amu of all the elements in caffeine, we get 194.19 g/mol. Now let's use this to convert from grams to moles.

0.095 g (1 mol / 194.19 g) = 0.000489 mol or 4.89 x 10^-4 mol caffeine in one cup of coffee

The question also asks us to figure out the amount of molecules of caffeine. We can use Avogadro's number to figure this out (6.02 x 10²³ molecules/mole).

4.89 x 10^-4 mol (6.02 x 10²³ molecules / 1 mol) = 2.94 x 10²⁰ molecules of caffeine in one cup of coffee

Let me know if you have any questions!