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?

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Answer 1 · 2015-12-23T04:17:55

#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)