Answer : The volume of pure diamond is [tex]0.493inch^3[/tex]
Explanation : Given,
Density of pure carbon in diamond = [tex]3.52g/cm^3[/tex]
Moles of pure diamond = 23.7 moles
Molar mass of carbon = 12 g/mol
First we have to calculate the mass of carbon or pure diamond.
[tex]\text{ Mass of carbon}=\text{ Moles of carbon}\times \text{ Molar mass of carbon}[/tex]
Molar mass of carbon = 12 g/mol
[tex]\text{ Mass of carbon}=(23.7moles)\times (12g/mole)=284.4g[/tex]
Now we have to calculate the volume of carbon or pure diamond.
Formula used:
[tex]Density=\frac{Mass}{Volume}[/tex]
Now putting all the given values in this formula, we get:
[tex]3.52g/cm^3=\frac{284.4g}{Volume}[/tex]
Volume = [tex]80.8cm^3[/tex]
As we know that:
[tex]1cm^3=0.061inch^3[/tex]
So,
Volume = [tex]0.061\times 80.8inch^3[/tex]
Volume = [tex]0.493inch^3[/tex]
Therefore, the volume of pure diamond is [tex]0.493inch^3[/tex]
