Question

Both diamond and graphite (i.e. pencil lead) consist of carbon atoms. They are only different in their crystalline structures. One carat or 0.20 g, of a high-quality diamond costs up to $5000, while 25 g of pencil lead may only cost $2. Determine the numbers of C-atom in diamond vs. graphite which can be obtained with $1.

Answer 1

Answer:

Moles of carbon atoms  = 3.33  ×  $10^{-6}$ mol

No. of atoms of C in Diamond  = 2.007 ×   $10^{28}$ atom

Atoms of graphite = 6.27 × $10^{23}$ Atoms

Explanation:

given data

Cost of 0.2g of diamond = $5000

Cost of 25 g of graphite = $ 2

solution

we know cost of 0.2g of diamond is $ 5000 so that for 1$

if buy 1$ = $\frac{0.20}{5000}$

1$ = 4.0 × $10^{-5}$ g Carbon

and Moles of carbon atoms  is express as

Moles of carbon atoms = Given mass of Carbon ÷ atomic mass of C      .........1

Moles of carbon atoms  = 4.0  ×  $10^{-5}$    g/ 2.0g

Moles of carbon atoms  = 3.33  ×  $10^{-6}$ mol

and

No. of atoms of C in Diamond = No. of moles × Avogadro NO    ..............2

No. of atoms of C in Diamond  = 3.33 ×   $10^{-6}$ mol × 6.022 ×   $10^{28}$

No. of atoms of C in Diamond  = 2.007 ×   $10^{28}$ atom

Graphite

and wew have given Cost of 25 g of graphite is $2 so for but 1$ we get

for buy $1 = 25÷2  = 12.5 g Of graphite

Moles of graphite = 12.5÷12 = 1.04 mol

Atoms of graphite = 1.04 × 6.022 × 1023

Atoms of graphite = 6.27 × $10^{23}$ Atoms