The weight of a diamond is given in carats. One carat is equivalent to 200 mg. A pure diamond is made up entirely of carbon atoms. How many carbon atoms make up a 1.00 carat diamond?

##1xx10^22″atoms C”## are in a 1.00 carat diamond.
Convert 200 mg to g.
##”1000 mg=1 g”##
##200cancel”mg”xx(1″g”)/(1000cancel”mg”)=”0.2 g”##
Convert carats to grams to moles.
##”1.00 ct=0.2 g”##
##1″mol C=12.0107 g C”##
##1.00cancel”ct C”xx(0.2cancel”g C”)/(1cancel”ct C”)xx(1″mol C”)/(12.0107cancel”g C”)=”0.02 mol C”##
Convert moles C to atoms C.
##1 “mol C”=6.022xx10^23 “atoms C”##
##0.02cancel”mol C”xx(6.022xx10^23″atoms C”)/(1cancel”mol C”)=1xx10^22″ atoms C”## (rounded to one significant figure)