The unit cell for cr2o3 has hexagonal symmetry with lattice parameters a = 0.4961 nm and c = 1.360 nm. if the density of this material is 5.22 g/cm3, calculate its atomic packing factor. the atomic weights of cr

To calculate the packing factor, first calculate the area and volume of unit cell.

Area is calculated as:

Here, R is radius and is related to a as follows:

Putting the value in expression for area,

The value of a is 0.4961 nm

Since,

Thus,

Putting the value,

Now, volume can be calculated as follows:

The value of c is 1.360 nm or

Putting the value,

now, number of atom in unit cell can be calculated by using the following formula:

Here, A is atomic mass of is 151.99 g/mol.

Putting all the values,

Thus, there will be 18 units in 1 unit cell.

Since, there are 2 Cr atoms and 3 oxygen atoms thus, units of chromium and oxygen will be 2×18=36 and 3×18=54 respectively.

The atomic radii of and is 62 pm and 140 pm respectively.

Converting them into cm:

Thus,

and,

Volume of sphere will be sum of volume of total number of cations and anions thus,

Since, volume of sphere is ,

Putting the values,

The atomic packing factor is ratio of volume of sphere and volume of crystal, thus,

Thus, atomic packing factor is 0.758.

the enthalpy of formation of water is given as -285.8kj/mol, which states that the enthalpy of formation is negative.

negative enthalpy of formation indicates that the heat is released during the reaction process. the heat is released from reaction to the surroundings the enthalpy is expressed with a negative sign with the energy given out in the reaction process.

the formation of water takes place by giving out heat which is -285.8 kj/mol.