A hypothetical AX type of ceramic material is known to have a density of 3.55 g/cm3 and a unit cell of cubic symmetry with a cell edge length of 0.39 nm. The atomic weights of the A and X elements are 90.5 and 37.3 g/mol, respectively. On the basis of this information, which one of the following crystal structures is possible for this material?a) fluoriteb) zinc blendc) cesium chloride

Explanation:

For AX type ceramic material, the number of formula per unit cells is as follows.

or,    

where,   n' = no. of formula units per cell

            = molecular weight of cation = 90.5 g/mol

            = molecular weight of anion = 37.3 g/mol

          = volume of cubic cell = 3.55

           a = edge length of unit cell =

        = Avogadro's number =

          = density = 3.55

Now, putting the given values into the above formula as follows.

                      =

                     = 0.9

                    = 1 (approx)

Therefore, we can conclude that out of the given options crystal structure of cesium chloride is possible for this material.

answer : (a) volume of the gas = 8.67 ×   l

                (b) second virial coefficient b = -1.21226 l/mole

solution :   given,     t = 300k

                                p = 20atm

                                z = 0.86

                                n = 8.2 mmoles = 8.2 × moles

                                r =   0.082 l atm/k/mol

        find,     (a) volume of gas   and (b) second virial coefficient b at 300k.

formula used :            

                          and            

(a)            

                    = \times 0.082\times 300}{20}[/tex]

                    = 8.67 ×   l

(b)      

                    = (0.00867-1) × 8.659

                    = - 8.5839 l/mole