Question

In terms of diamonds, a paragon is a flawless stone of at least 100 carats.

One carat is equal to 200 mg. A pure diamond is made up entirely of carbon
atoms. How many atoms are in a 100-carat, paragon diamond?
A) 2 x 10^23 atoms
B) 2 x 10^24 atoms
C) 2 x 10^25 atoms
D) 2 x 10^26 atoms

Answer 1

A 100-carat paragon diamond weighs 20 grams, which corresponds to about 1.666 moles or approximately 1.003 x 10²´ carbon atoms. The closest answer to the number of carbon atoms in such a diamond is option B) 2 x 10²´ atoms.

Step-by-step explanation:

To determine how many atoms are in a 100-carat, paragon diamond, we first convert the carat weight into grams. Given that 1 carat equals 200 mg, a 100-carat diamond would be 100 x 200 mg, which equals 20,000 mg or 20 grams. Next, we need to find the number of moles of carbon in 20 grams of diamond. Since the molar mass of carbon (C) is about 12.01 g/mol, we divide the total mass of the diamond by the molar mass of carbon:

20 g ÷ 12.01 g/mol ≈ 1.666 moles of carbon

Now, we use Avogadro's number (which is approximately 6.022 x 10²³ atoms per mole) to find the total number of atoms:

1.666 moles x 6.022 x 10²³ atoms/mol ≈ 1.003 x 10²´ atoms

Therefore, a 100-carat diamond contains approximately 1.003 x 10²´ carbon atoms. The closest answer would be option B) 2 x 10²´ atoms.