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Question
An element with density 2.8 g cm–3 forms a f.c.c. unit cell with edge length 4 x 10–8 cm. Calculate the molar mass of the element.
(Given : NA = 6.022 x 1023 mol –1)
Solution
Density of f.c.c. unit cell = 2.8 g cm-3
Edge length of f.c.c unit cell = 4 x 10-8 cm
NA = 6.022 x 1023 mol-1
Molar mass of the element = ?
For f.c.c. unit cell, Z = 4
Substituting the values in the equation:
`rho=(ZxxM)/(a^3xxN_0)`
`d = (z xx M ) /(N_A xx a^3)`
m =`(N_A xx a^3 xx d)/Z`
`(2.8 "g cm"^3 xx (4 xx 10^(-8)"cm")^3 xx 6.022 xx10^23)/4`
⇒ M = 2.8 x 16 x 10-1 x 6.022
=26.98g mol-1 ≅ 27 g mol-1
Therefore, the molar mass of the element is 26.98 gmol-1 .
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