Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 12
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Sum: 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. - Chemistry

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Sum

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)

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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 .

Concept: Calculations Involving Unit Cell Dimensions
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