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 : N_{A} = 6.022 x 10^{23} 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 10^{23} 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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