Question

Question 5 Tungsten is a solid phase of tungsten still unknown to science. The only difference between it and ordinary tungsten is that Tungsten forms a crystal with an fcc unit cell and a lattice constant . Calculate the density of Tungsten .

Answer 1

Complete Question

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Answer:

The density is
`\rho = 21.1 \ g/cm^3`

Step-by-step explanation:

From the question we are told that

The lattice constant is
`a = 0.387 nm = 0.387 *10^(-9) \ m`

Generally the volume of the unit cell is
`V = a^3`

=>
`V = [0.387 *10^(-9)]^2`

`V = 5.796 *10^(-29) \ m^3`

Converting to
`cm^3` We have
`5.796 *10^(-29) * 1000000 = 5.796 *10^(-23) cm^3`

The molar mass of Tungsten is constant with a value
`Z = 184 g/mol`

One mole of Tungsten contains
`6.022*10^(23)` unit cells

Where
`6.022*10^(23)` is a constant for the number of atom in one mole of a substance(Tungsten) which is known as Avogadro's constant

Now for FCC distance the number of atom per unit cell is n = 4

Mass of Tungsten (M) =
`= (Z * n )/(1 \ mole \ of \ Tungsten)`

=> Mass of Tungsten (M) =
`= (184 * 4 )/(6.023*10^(23))`

=> Mass of Tungsten (M) =
`= 1.222*10^(-21) \ g`

Now

The density of Tungsten is

`\rho = (M)/(V)`

substituting values

`\rho = (1.222*10^(-21))/(5.796*10^(-23))`

`\rho = 21.1 \ g/cm^3`