Question

A pure diamond is made only of carbon atoms. (a) How many moles of carbon are there in a0.60g (3.0 carat) diamond? Show your work with calculation steps.

Answer 1

To find the number of moles of carbon in a 0.60g diamond, divide the mass by the molar mass of carbon, resulting in 0.050 moles. For 4.72 × 1024 carbon atoms, divide by Avogadro's number, yielding 7.84 moles of carbon.

Step-by-step explanation:

To calculate how many moles of carbon are there in a 0.60g diamond, we first need to know that one mole of carbon has a mass of 12.0 g, and since a diamond is pure carbon, we can use this information directly. Here are the calculation steps:

1. 
   
3. Determine the molar mass of carbon, which is 12.0 g/mol.
4. 
   
6. Using the mass of the diamond (0.60g), divide it by the molar mass of carbon to find the number of moles:

Number of moles = mass of diamond / molar mass of carbon

= 0.60g / 12.0 g/mol

= 0.050 moles

Therefore, a 0.60g diamond contains 0.050 moles of carbon atoms.

Similarly, to find how many moles of carbon atoms is 4.72 × 1024 atoms of carbon, we use Avogadro's number, which is 6.022× 1023 atoms per mole:

Number of moles = number of atoms / Avogadro's number

= 4.72 × 1024 atoms / 6.022× 1023 atoms/mol

= 7.84 moles of carbon atoms