Question

what is the volume of a face centred cubic unit cell when its density is 2 gram cm -3 and the molar mass of 60.0 mole-1​

Answer 1

Answer:

Given =>

1. It is a FCC Unit Cell.

2. Density => 2 g cm⁻³

3. Mass of substance => 60.0 g mol⁻¹

Now, we know that for FCC ,

Z = 4 and Z is the no. of atoms present per unit cell or formula units.

Molar Mass = 60.0 gram

Volume of unit cell, a³ = ( Molar Mass * Z ) / ( Density * Nₐ )

a³ = ( 60.0 * 4 ) / ( 2 * 6.022 * 10²³ )

a³ = ( 60.0 * 2 ) / ( 6.022 * 10²³ )

a³ = ( 9.963 * 2 ) / 10²³

a³ = 19.926 * 10⁻²³ cm³

a³ = 19.926 * 10⁻²³ cm³

Here,

Nₐ = Avogadro Number = 6.022 * 10²³

The volume of a Face Centred Cubic(FCC) unit cell is 19.926 * 10⁻²³ cm³

Answer 2

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1. It is a FCC Unit Cell.

2. Density => 2 g cm⁻³

3. Mass of substance => 60.0 g mol⁻¹

Now, we know that for FCC ,

Z = 4 and Z is the no. of atoms present per unit cell or formula units.

Molar Mass = 60.0 gram

Volume of unit cell, a³ = ( Molar Mass * Z ) / ( Density * Nₐ )

➦a³ = ( 60.0 * 4 ) / ( 2 * 6.022 * 10²³ )

➦a³ = ( 60.0 * 2 ) / ( 6.022 * 10²³ )

➦a³ = ( 9.963 * 2 ) / 10²³

➦a³ = 19.926 * 10⁻²³ cm³

➦a³ = 19.926 * 10⁻²³ cm³

Here,

Nₐ = Avogadro Number = 6.022 * 10²³

The volume of a Face Centred Cubic(FCC) unit cell is 19.926 * 10⁻²³ cm³