Question

The Density of pure carbon in Diamond form is 3.52 g/cm^3. How many cubic inches would 23.7 moles of pure diamond occupy?

Answer 1

Answer : The volume of pure diamond is
`0.493inch^3`

Explanation : Given,

Density of pure carbon in diamond =
`3.52g/cm^3`

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.

`\text{ Mass of carbon}=\text{ Moles of carbon}* \text{ Molar mass of carbon}`

Molar mass of carbon = 12 g/mol

`\text{ Mass of carbon}=(23.7moles)* (12g/mole)=284.4g`

Now we have to calculate the volume of carbon or pure diamond.

Formula used:

`Density=(Mass)/(Volume)`

Now putting all the given values in this formula, we get:

`3.52g/cm^3=(284.4g)/(Volume)`

Volume =
`80.8cm^3`

As we know that:

`1cm^3=0.061inch^3`

So,

Volume =
`0.061* 80.8inch^3`

Volume =
`0.493inch^3`

Therefore, the volume of pure diamond is
`0.493inch^3`