Question

How many atoms of carbon has a young man has given to his bride to be if the engagement ring contains 0.5 carat diamond? There are 200mg in a cara.

Answer 1

`5.02xx10^21 " atoms"`

Explanation:

First, we'll work out the mass of the diamond.

`"mass"=200xx10^-3xx0.5`

`=0.1"g"`

Now, we can find the number of moles of carbon in 0.1g.

`"mass"=M_rxx"moles"`

`"moles"="mass"/M_r`

`=0.1/12`

`=1/120=8.33xx10^-3 "mol"`

To find the number of carbon atoms, we multiply this by Avogadro's number, `6.02xx10^23`

`"number of atoms"=1/120xx6.02xx10^23`

`=5.02xx10^21 " atoms"` (3sf)

Answer 2

#n = .5 \ "carat" times {200 \ "mg"}/{"carat"} times {1\ "gram"}/{1000\ "mg"} times {1\ "mole"}/{12.01\ "gram"} times { 6.02 times 10^{23} \ "atoms"}/{"mole"} = 5.01 times 10^21 \ "atoms"#

Explanation:

I haven't done a chemistry question in forty years. I used `12.01` as the atomic weight of carbon, assuming it's a mixture of isotopes. `6.02 times 10^23` is of course Avogadro's constant giving molecules per mole.