The Solid State

Chemistry I

Chemistry

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An element E crystallizes in body centred cubic structure. If the edge length of the cell is 1.469 x 10^{–10} m and the density is 19.3 g cm^{–3}, calculate the atomic mass of this element. Also calculate the radius of this element.

Solution:

We have given that

Z= 2 since it is bcc structure

edge length, a = 1.469 x 10

Density, d= 19.3 g cm

$\mathrm{d}=\frac{2\times 3}{{\mathrm{a}}^{3}\times {\mathrm{N}}_{\mathrm{A}}}\phantom{\rule{0ex}{0ex}}19.3=\frac{2\times \mathrm{M}}{(1.469\times {10}^{-8}{)}^{3}\times 6.023\times {10}^{23}}\phantom{\rule{0ex}{0ex}}\mathrm{or}\mathrm{M}=\frac{19.3\times 3.17\times {10}^{-34}\times 6.023\times {10}^{23}}{2}\phantom{\rule{0ex}{0ex}}=\frac{19.3\times 3.17\times 6.023\times 10}{2}\phantom{\rule{0ex}{0ex}}=18.4\mathrm{g}{\mathrm{mol}}^{-1}.$

mass of element is 18.4g mol

(ii) Cell edge,

$\mathrm{a}=1.469\times {10}^{-10}\mathrm{m}$

Body diagonal = 4R

Then 4R = $\sqrt{39}$

$=\sqrt{3}\times 1.469\times {10}^{-10}\mathrm{m}$

or $\mathrm{R}=\frac{\sqrt{3}\times 1.469\times {10}^{-10}}{4}\mathrm{m}\phantom{\rule{0ex}{0ex}}=0.64\times {10}^{-10}\mathrm{m}\phantom{\rule{0ex}{0ex}}=6.4\times {10}^{-11}\mathrm{m}.$

Radius of element is 6.4 x 10^{-11}m.

or $\mathrm{R}=\frac{\sqrt{3}\times 1.469\times {10}^{-10}}{4}\mathrm{m}\phantom{\rule{0ex}{0ex}}=0.64\times {10}^{-10}\mathrm{m}\phantom{\rule{0ex}{0ex}}=6.4\times {10}^{-11}\mathrm{m}.$

Radius of element is 6.4 x 10

Why do solids have a definite volume?

A solid have a definite volume because the inter molecular distance between its molecules are fixed.

Refractive index of a solid is observed to have the same value along all directions. Comment on the nature of this solid. Would it show clevage property?

Refractive index of a solid which have the same value along all directions are isotropic in nature. It would not show cleavage property.

Classify the following as amorphous or crystalline solids: Polyurethane, naphthalene, benzoic acid, teflon, potassium nitrate, cellophane, polyvinyl chloride, fibre glass, copper.

Amorphous solids: Polyurethane, teflon, cellophane, polyvinyal chloride, fibre glass.

Crystalline solids: naphthlene, benzoic acid, potassium nitrate, copper.

Why is glass considred a super-cooled liquid?

Glass is amorphous solids and have a tendency to flow, though very slowly. Therefore, these are called pseudo solids or super cooled liquids .

Why are solids rigid?

Solids are rigid because the internuclear distance between the molecules of a solid are very less and closely packed and their positions are fixed due to the strong forces of attraction between them.