please answer in paper Using the data given in Table 12.3 below, answer the foll

Question

please answer in paper

Using the data given in Table 12.3 below, answer the following: Give two cations that combine with the oxide ion (O2-) in octahedral geometry and two cations in cubic geometry; Which cation(s) can have tetrahedral, octahedral geometries or eventually both. Justify mathematically your answers Magnesium oxide has the rock salt crystal structure and a density of 3.58 g/cm3. Determine the unit cell edge length. How does this result compare with the edge length as determined from the radii in Table 12.3, assuming that the Mg2* and O2- ions just touch each other along the edges? )

Explanation / Answer

(a) Check the ratio for the geometry.

r- = 0.14 nm; so, r+ can be in the range = 0.14(0.414 to 0.732) = 0.057 to 0.102 nm. (for octahedral)

So, matching cations are nine. Let's choose the approximate middle ones for surety. So, answer is: Mg2+ and Fe2+

r- = 0.14 nm; so, r+ can be in the range = 0.14(0.732 to 1) = 0.102 to 0.14 nm. (for cubic)

So, matching cations are three. So, answer is: Ba2+ and K+

(b)

r- = 0.14 nm; so, r+ can be in the range = 0.14(0.414 to 0.732) = 0.057 to 0.102 nm. (for octahedral)

r- = 0.14 nm; so, r+ can be in the range = 0.14(0.225 to 0.414) = 0.031 to 0.057 nm. (for tetrahedral)

So, cations which can exist as tetrahedral = Ca2+, Fe2+, Fe3+, Mg2+, Mn2+, Na+ (borderline), Ni2+, Ti4+ (borderline), Al3+ (borderline)

So, cations which can exist as tetrahedral = Si4+, Al3+ (borderline), Ti4+ (borderline)

So, cations which can exist as both = Al3+, Ti4+ (possibly)

(c) d=3.58, Zeff = 4 (for Rock salt structure)

so, d=(Zeff*M)/(a^3 * N)

a=edge length

N=Avogadro's number = 6 x 10^23

M=molar mass of MgO = 24+16 = 40 g

so, on calculating, a = 0.4202 nm

whereas, 2(Mg2+ + O2-) = 2(0.072+0.14) = 0.424 nm

Hence, they are almost equal.

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