The Solid State

The Solid State

Question

An element with density 2.8 g cm−3 forms of the f.c.c. unit cell with edge length 4 X10−8 cm. Calculate the molar mass of the element.
(Given: NA = 6.022 X 1023 mol −1)

Answer

Edge length, a = 4 x 10-8 cm

Density, d = 2.8 g cm-3

As the lattice is fcc type, the number of atoms per unit cell, z is 4.

Avogadro's number, NA = 6.022 x 1023 mol-1

Molar mass can be calculated with the help of given relation:
straight d space equals space fraction numerator straight Z space straight x space straight M over denominator straight N subscript straight A space straight x space straight a cubed end fraction

straight m equals space fraction numerator straight N subscript straight A space space straight x space straight a cubed space straight x space straight d over denominator straight Z end fraction

fraction numerator 2.8 space straight x space left parenthesis 4 space straight x space 10 to the power of negative 8 end exponent right parenthesis cubed space straight x space 6.022 space straight x space 10 to the power of 23 over denominator 4 end fraction space equals space 26.98 space straight g space mol to the power of negative 1 end exponent approximately equal to space 27 space straight g space mol to the power of negative 1 end exponent

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