Question

An man in Arkansas recently found a 9 carat diamond at Crater of Diamonds State Park. Five carats are equivalent to one gram, so this diamond weighs 1.8 g. Diamond is a crystalline form of the element carbon. How many atoms of carbon are in this 1.8 g diamond

Answer 1

The answer is "1.8 g diamond includes 9.03e22 atoms".

Step-by-step explanation:

Given:

Weight of 9-carat diamond = 1.8 g

`\therefore\\\\`

weight of 1-mole carbon =12 g

`\because`

calculating the moles which are available into 18 g carbon weight:

x= Carbon moles weight in 1.8 g

`1 - mol\ C = 12 g\\\\x - mol\ C = 1.8 g\\\\\to x = ((1.8 \ g * 1\ mol\ C))/( 12 \ g)\\\\\to x = 0.15\ moles`

In 1 mole element associated with Avogadro's number that is
`6.02 * 10^(23)\\\\`

Carbon includes in 1 mol
`=6.02 * 10^(23)\ atoms\\\\`

0.15 mol of carbon includes:

`= 0.15 * 6.02 * 10^(23) = 9.03 * 10^(22)\ atoms.`

Using the scientific notation:

0.15 mol of carbon includes: 9.03e22 atoms. So, 1.8 g diamond includes 9.03e22 atoms.