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)