The Solid State

Chemistry I

Chemistry

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An element crystallizes in a structure having a fcc unit cell of an edge 200 pm. Calculate its density if 200 g of this element contains 24 x 10^{23} atoms.

Solution:

We have given that

Edge length of the unit cell

= 200 pm = 200 x 10^{–10} cm

Vol. of the unit cell

= (200 x 10^{–10} cm)^{3 }= 8 x 10^{–24} cm^{3}Therefore, volume of the substance

= Vol. of unit cell x Vol. of 1 unit cell.

Since the element has a fcc unit cell, number of atoms per unit cell = 4.

Total number of atoms = Atoms/unit cell x number of unit cells.

= 24 x 10^{23}atoms = 4

atoms/unit cell x No. of unit cells.

∴ No. of unit cells = $\frac{24\times {10}^{23}\mathrm{atoms}}{4\mathrm{atoms}/\mathrm{unit}\mathrm{cell}}$

$=6\times {10}^{23}\mathrm{unit}\mathrm{cells}.$

∴ Volume of the substance

$6\times {10}^{23}\mathrm{unit}\mathrm{cell}\times 8\times {10}^{-24}{\mathrm{cm}}^{3}/\mathrm{unit}\mathrm{cell}=4.8{\mathrm{cm}}^{3}$

Now, $\mathrm{Density}=\frac{\mathrm{Mass}}{\mathrm{Volume}}\phantom{\rule{0ex}{0ex}}=\frac{200\mathrm{g}}{4.8{\mathrm{cm}}^{3}}=4.17\mathrm{g}{\mathrm{cm}}^{-3}.$

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Why do solids have a definite volume?

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

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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.

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

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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 .

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