3. In sodium chloride, the distance between the center of a sodium ion and the c

Question

3. In sodium chloride, the distance between the center of a sodium ion and the center of an adjacent chloride ion is 0.2819 nm. Calculate the density (g/cm^(3)) of an ideal sodium chloride crystal, and compare your value with that listed in the CRC Handbook of chemistry and Physics.

4. Consider hard spheres of radius t arranged in contact in the form of a simple cubic unit cell. Calculate, in terms of r, the radius of the largest sphere that can fit in the hole (called an interstitial site) in the very center of this unit cell. HINT: Calculate the cube diagonal in terms of r.

Explanation / Answer

3)

p(rho) = (Z X M)/(a^3 X No)

where p(rho) is density of crystal in g/cm^3
Z = number of particles present per unit cell ,,for fcc it is = 4
M = mass of NaCl = 23 + 35.5 = 58.5 g/mole
No is Avogadro's number = 6.022 X 10^23
a = edge of unit cell..
as distance between Na+ and Cl- is given as 281.9 pm
so edge length a will = 281.9 X 2 = pm = 563.8 X 10^-12 metre or 563.8 X 10^-10 cm

putting the values...
p(rho) = (4 X 58.5)/ [ (563.8 X 10^-10)^3 X 6.022 X 10^23 ]
= 2.134g/cm^3

4)

cube diagonal =sqrt(3)*2r

= 2*sqrt(3)r

and 2t+2r =3.464r

t =1.464/2*r =0.732r

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