Potassium bromide ( ) and rubidium bromide ( ) each adopt the rock-salt structure

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

Problem

Potassium bromide (

KBr

) and rubidium bromide (

RbBr

) each adopt the rock-salt structure. The two salts form an ideal binary solid solution

K_{1-x}Rb_xBr

over the full composition range

0 \le x \le 1

. Six-coordinate ionic radii: •

K^+

1.38\,\text{\AA}

•

Rb^+

1.52\,\text{\AA}

•

Br^-

1.96\,\text{\AA}

Assume that the lattice parameter

a

of the rock-salt unit cell is twice the average nearest-neighbor cation–anion distance. (a) Derive an expression for the lattice parameter

a(x)

of the solid solution as a function of composition

x

, treating the cation–anion distance as the arithmetic mean of the radii of

Br^-

and the average cation present. (b) Using your expression from part (a), calculate

a(0.40)

and

a(0.85)

in ångströms to two significant figures. (c) Explain how the variation in

a(x)

you obtained would influence the magnitude of the lattice energy across the composition range. Include explicit reference to Coulombic considerations. (d) Predict which composition,

x \approx 0

x \approx 1

, is likely to exhibit the higher hardness. Provide a justification that integrates your results from parts (a)–(c).

Related theory

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