Calculate the theoretical density of iron, and then determine the number of vacancies per cm3 needed for a BCC iron crystal to have a density of 7.874 g/cm3 . The lattice parameter of iron is 2.866 * 10-8 cm.

In this exercise we have to use the density knowledge to calculate the number of vacancies, in this way we can find that:

Density is

Number of vacancy is

So from the information given in the text we find that:

Knowing that the density formula is given by:

Now substituting the values in the given formula we find that:

Now we have to find out the number of unit cell of iron crystal having density, we have:

Therefore the vacancy of atom per cell :

That will be:

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Therefore the theoretical density of iron is 7.877 g/cm³ .

Therefore the number of vacancy per cm³ is

Explanation:

BCC structure contains 2 atoms per cell.

BCC : Body centered cubic.

Atomic mass of iron = 55.845 gram/mole.

Atomic mass of a chemical element is the mass of 1 mole of the chemical element.

Density: Density of a matter is the ratio of mass of the matter and volume of the matter.

Avogrdro Number is number of atoms per 1 mole.

Avogrdro Number= 6.023×10²³

Lattice parameter of iron = 2.866×10⁻⁸ cm

The theoretical density:

    g/cm³      [x= 2,Since it is BCC structure]

=7.877 g/cm³

Therefore the theoretical density of iron is 7.877 g/cm³ .

Now we have to find out the number of unit cell of iron crystal having density  7.874 g/cm³.

⇒ x =1.9923 atom/cell

Therefore the vacancy of atom per cell = (2- 1.9923)=0.0077

Therefore the number of vacancy per cm³ is

fe 55.85 g/mol and h2o 18.02 g/mol.

a gas, having a molecular weight of 13 kg/kmol and a kinematic viscosity of 0.25 cm2/s, flows through a pipe 0.25 m internal diameter and 5 km long at the rate of 0.4 m3/s and is delivered at atmospheric pressure.