The alkaline-earth oxide crystallizes in the same structure as NaCl

CHEMISTRY · Multi-part · AP · Chemistry · Compound Structure and Properties · Compound Structure and Properties

Problem

The alkaline-earth oxide

CaO

crystallizes in the same structure as NaCl. An engineer proposes replacing

Ca^{2+}

with the smaller

Mg^{2+}

ion to form

MgO

while keeping the

O^{2-}

lattice unchanged. Selected ionic radii (six-coordinate) are listed below. •

Ca^{2+}

1.00\,\text{\AA}

•

Mg^{2+}

0.86\,\text{\AA}

•

O^{2-}

1.40\,\text{\AA}

For a first-order estimate, treat the lattice energy

|U|

as being inversely proportional to the cation–anion distance

r

and directly proportional to the product of the ionic charges (

|U| \propto \frac{|q_{+}q_{-}|}{r}

). (1) Part 1: (a) Using the proportionality stated above and the radii provided, calculate the ratio

|U|_{MgO}/|U|_{CaO}

. Show your reasoning. (2) Part 2: (b) State whether the calculated ratio indicates that

MgO

is expected to be more or less thermally stable than

CaO

, and explain briefly. (3) Part 3: (c) If a 10 mol % solid solution

Ca_{0.90}Mg_{0.10}O

is synthesized, predict qualitatively (no calculation required) how its lattice energy per ion pair will compare with that of pure

CaO

. Support your prediction with reasoning based on part (a).