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

Answer:

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

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

$1 - mol\ C = 12 g\\\\x - mol\ C = 1.8 g\\\\\to x = \frac{(1.8 \ g \times 1\ mol\ C)}{ 12 \ g}\\\\\to x = 0.15\ moles$

In 1 mole element associated with Avogadro's number that is $6.02 \times 10^{23}$

 Carbon includes in 1 mol$=6.02 \times 10^{23}\ atoms$

0.15 mol of carbon includes:

$= 0.15 \times 6.02 \times 10^{23} = 9.03 \times 10^{22}\ atoms.$

Using the scientific notation:

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