Question

The mass of diamond is 3.25 carats (1 carat = 0.200 g). Assume diamonds are pure carbon, use dimensional analysis to determine how many atoms of carbon are in the diamond.

a) 1.625 x 10^22 atoms of carbon
b) 3.25 x 10^22 atoms of carbon
c) 6.5 x 10^22 atoms of carbon
d) 3.26 x 10ˆ22 atoms C

Answer 1

To find the number of carbon atoms in a 3.25 carat diamond, we convert carats to grams, grams to moles, and then use Avogadro's number to find the atoms. The calculations yield approximately 3.26 x 10^22 carbon atoms, which is option (d).

Step-by-step explanation:

The mass of the diamond is given as 3.25 carats, and we are asked to determine how many atoms of carbon are present in the diamond using dimensional analysis. To solve this problem, we first convert carats to grams, using the fact that 1 carat equals 0.200 grams. Next, we convert grams to moles of carbon using the average molar mass of carbon, which is 12.011 grams/mol. Finally, we use Avogadro's number to convert moles of carbon to atoms of carbon.

Here's the calculation step by step:

1. Convert carats to grams: 3.25 carats × (0.200 grams/carat) = 0.65 grams of carbon.
2. Convert grams to moles: 0.65 grams × (1 mol/12.011 grams) = 0.054151 mol of carbon.
3. Convert moles to atoms: 0.054151 mol × (6.022 × 1023 atoms/mol) = 3.26 × 1022 atoms of carbon.

Therefore, the number of atoms of carbon in the diamond is approximately 3.26 × 1022 atoms, which corresponds to option (d).