Caffeine (C8H10N4O2) can kiil you if you consume as much as 1.55x1022 molucules (60 gallons of Mcdonalds coffee). How many grams is this?

1 Answer
Feb 21, 2018

#5 \ "g of" \ C_8H_10N_4O_2#

Explanation:

Well, if there are #1.55*10^22# molecules of caffeine, we need to convert that amount into moles of caffeine.

We know that

#1 \ "mol"=6.02*10^23# molecules

#:.1.55*10^22 \ "molecules"=(1.55*10^22color(red)cancelcolor(black)"molecules")/(6.02*10^23color(red)cancelcolor(black)"molecules""/mol")=0.0257475083 \ "mol"#

I will not round off the number yet, as we have not gotten the answer we need.

If we want to convert that amount into grams, we need to multiply this by the molar mass of caffeine.

Caffeine #(C_8H_10N_4O_2)# has a molar mass of #194.19 \ "g/mol"#.

So, the mass in grams of caffeine here is

#0.0257475083color(red)cancelcolor(black)"mol"*194.19 \ "g/"color(red)cancelcolor(black)cancel"mol"=4.99990863678 \ "g"~~ 5 \ "g"#

So, about #5 \ "g"# of caffeine would kill you.