Answer:
3.86 x 10^24 carbon atoms in a 77 gram diamond
Step-by-step explanation:
A key tool for chemistry and physics is the concept of the mole. The definition of a mole is actually quite simple. One mole is 6.02 x 10^23 of something. Anything. One can say " I have 1 mole of paperclips(PPC) in my closet.". That simply says that there are 6.02 x 10^23 paperclips(PPC) in your closet. It does suggest, however, that you may be demented. One mole of PPC, placed end-to-end, would stretch a LONG way.
Average PPC Length = 4.45 cm
! mole of PPC would stretch (6.02 x 10^23)*(4.45 cm) = 2.68 x 10^24 cm
That is 2.68 x 10^19 km
The distance to the moon is 3.84x10^5 km. So 1 mole of PPC will stretch to the moon and back 6.97 x 10^13 times.
This mental diversion does not answer the question, but it does explain what comes next for calculating the number of carbon atoms in 77 mg of diamond. The brilliant connection that allows this calculation is how 1 mole (Avogadro's Number) ties in with the atomic masses of the elements. The atomic mass of an element, as shown on a periodic table, is also the mass of that element that contain Avogadro's Number of atoms. The atomic mass, written in AMU (atomic mass units) can ALSO be written as the molar mass, in units of grams/mole. That is, the number of grams of that element that would amount to 6.02 x 10^23 (1 mole) of tat element's atoms.
Carbon, with an atomic mass of 12, can be said to have a Molar Mass of 12 grams/mole.
Use the units to guide the calculation needed to find the number of carbon atoms (in this case divide the grams carbon by the molar mass):
(77 grams Carbon)/(12 grams/mole Carbon)
The grams unit cancels and the moles unit moves to the top, leaving a number that is simply moles of carbon.
(77 grams Carbon)/(12 grams/mole Carbon) = 6.42 moles carbon
By definition, 1 mole equals 6.02 x 10^23 carbon atoms.
(6.42 moles carbon)*((6.02 x 10^23 carbon atoms)/mole)
Moles cancel, leaving carbon atoms
= 3.86 x 10^24 carbon atoms in a 77 gram diamond