KBr crystallizes in a NaCl (B1) structure with a lattice constant of a=0.65966nm. Determine the bulk density...

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Chemistry

KBr crystallizes in a NaCl (B1) structure with a latticeconstant of a=0.65966nm.
Determine the bulk density of KBr and the distance between a K ionand a touching Br
ion in the structure. Rationalize your result with the sum of ionicradii for K and Br

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3.9 Ratings (539 Votes)

Volume of KBr unit cell = a^3

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = (0.65966 x 10^-9)^3

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = 2.87 x 10^-22 cm^3

mass of 4 atoms in a unit cell = 4 x 119 g/mol/6.023 x 10^23

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = 7.90 x 10^-22 g

Bulk density = mass/volme

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = 7.90 x 10^-22/2.87 x 10^-22

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = 2.75 g/cm^3

ionic radii for K ion and a touching Br atom = a/2sq.rt.(2)

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = 6.5966 x 10^-8 cm/2 x sq.rt.(2)

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = 2.33 x 10^-8 cm

Result from ionic radii of K and Br = (1.52 + 182) pm

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = 3.34 x 10^-8 cm

So the radii calculated and the theoretical radii are close to one another.

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