# 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?

Dec 23, 2015

$1 \times {10}^{22} \text{atoms C}$ are in a 1.00 carat diamond.

#### Explanation:

Convert 200 mg to g.

$\text{1000 mg=1 g}$

$200 \cancel{\text{mg"xx(1"g")/(1000cancel"mg")="0.2 g}}$

Convert carats to grams to moles.

$\text{1.00 ct=0.2 g}$
$1 \text{mol C=12.0107 g C}$

$1.00 \cancel{\text{ct C"xx(0.2cancel"g C")/(1cancel"ct C")xx(1"mol C")/(12.0107cancel"g C")="0.02 mol C}}$

Convert moles C to atoms C.

$1 \text{mol C"=6.022xx10^23 "atoms C}$

$0.02 \cancel{\text{mol C"xx(6.022xx10^23"atoms C")/(1cancel"mol C")=1xx10^22" atoms C}}$ (rounded to one significant figure)