the weight of a diamond is given in carats . one carat is equivalent to 200mg . a pure diamond is made up entirely of carbon atoms .how many carbon atoms make up a 1.00 carat diamond?
The molar mass of carbon is 12.01 g/mol.
From here, we can calculate the number of carbon atoms in a 200 mg (0.2 g) diamond as:
0.2 g / 12.01 g/mol = 0.0167 mol of carbon
To find the number of carbon atoms, we need to multiply by Avogadro's number:
0.0167 mol * 6.02 x 10^23 atoms/mol = 1.00 x 10^22 carbon atoms
Therefore, a 1.00 carat diamond is made up of 1.00 x 10^22 carbon atoms.
To determine the number of carbon atoms in a 1.00 carat diamond, we need to convert the weight of the diamond into grams.
Given:
1 carat = 200 mg
Converting to grams:
200 mg = 200/1000 g = 0.2 g
Next, we need to calculate the number of moles of carbon in the diamond by using its molar mass.
The molar mass of carbon (C) is approximately 12.01 g/mol.
Using the equation: Moles = Mass / Molar mass
Moles = 0.2 g / 12.01 g/mol ≈ 0.016 moles
To find the number of carbon atoms, we can use Avogadro's number, which states that there are approximately 6.022 × 10^23 atoms in one mole of a substance.
Number of Carbon atoms = Moles × Avogadro's number
Number of Carbon atoms = 0.016 moles × 6.022 × 10^23 atoms/mol
Calculating this:
Number of Carbon atoms = 0.016 × 6.022 × 10^23 ≈ 9.6352 × 10^21
Therefore, a 1.00 carat diamond made up entirely of carbon atoms would contain approximately 9.6352 × 10^21 carbon atoms.