Question

How many carbon atoms are there in a diamond (pure carbon) with a mass of 47 mg ?

Answer 1

To find the number of carbon atoms in a 47 mg diamond, first convert the mass to grams, calculate the number of moles using the molar mass of carbon, and then multiply by Avogadro's number. The diamond contains approximately 2.35 × 10²± carbon atoms.

Step-by-step explanation:

To calculate the number of carbon atoms in a diamond with a mass of 47 mg, we need to use the concept of moles and the molar mass of carbon. First, we convert the mass of the diamond from milligrams to grams:

47 mg = 0.047 g

Next, we use the average molar mass of carbon, which is 12.011 g/mol, to find out how many moles of carbon are in 0.047 g:

Number of moles = Mass of diamond / Molar mass of carbon

Number of moles = 0.047 g / 12.011 g/mol ≈ 0.003912 moles

Now, since one mole of any substance contains 6.022 × 10²³ atoms (Avogadro's number), we can find the number of carbon atoms:

Number of carbon atoms = Number of moles × Avogadro's number

Number of carbon atoms = 0.003912 moles × 6.022 × 10²³ atoms/mole ≈ 2.35 × 10²± atoms

Therefore, a diamond with a mass of 47 mg contains approximately 2.35 × 10²± carbon atoms.

Answer 2

2.4 x 10^21 First, calculate the number of moles of carbon you have by dividing the mass (in grams) by the atomic weight of carbon. Atomic weight of Carbon = 12.0107 0.047 g / 12.0107 g/mol = 0.003913 mole Now multiply by avogadro's number 0.003913 * 6.0221409 x 10^23 = 2.35646 x 10^21 Since you only have 2 significant figures, round the result to 2 significant figures 2.4 x 10^21