Question

Diamond is one of several naturally occurring forms of carbon. one carat is defined to be exactly 0.200 grams. how many atoms of carbon are in a 0.75 carat diamond? use "e" for scientific notation

Answer 1

7.52E21 (or) 7.52 × 10²¹ C atoms

Solution:

Data Given:

Mass of Diamond = 0.2 × 0.75 = 0.15 g

M.Mass of Diamond = 12.01 g.mol⁻¹ (as it is purely Carbon)

Step 1: Calculate Moles of Diamond as,

Moles = Mass ÷ M.Mass

Putting values,

Moles = 0.15 g ÷ 12.01 g.mol⁻¹

Moles = 0.0125 mol

Step 2: Calculate number of Carbon atoms,

As 1 mole of any substance contains 6.022 × 10²³ particles (Avogadro's Number) then the relation for Moles and Number of Carbon atoms can be written as,

Moles = Number of C Atoms ÷ 6.022 × 10²³ Atoms.mol⁻¹

Solving for Number of C atoms,

Number of C atoms = Moles × 6.022 × 10²³ Atoms.mol⁻¹

Putting value of moles,

Number of C atoms = 0.0125 mol × 6.022 × 10²³ Atoms.mol⁻¹

Number of C atoms = 7.52 × 10²¹ C atoms