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Methane crystallises in a cubic unit cel...

Methane crystallises in a cubic unit cell with a = 0.598 nm. Calculate the theoretical density of methane assuming Z = 1, 2 and 4. If the density of liquid methane is `0.466"g cm"^(-3)` and assume that density of solid is the same as that of the liquid at a given temperature, predict which type of unit cell result?

Text Solution

Verified by Experts

We know that `rho=(ZxxM)/(a^(3)xxN_(0))`
`a=0.589nm=0.589xx10^(-7)cm,M=16gmol^(-1),N_(0)=6.022xx10^(23)mol^(-1)`
`rho(z=1)=(1xx(16gmol^(-1)))/((0.589xx10^(-7)cm)xx(6.022xx10^(23)mol^(-1)))=0.130"g cm"^(-3)`
`rho(z=2)=(2xx(16gmol^(-1)))/((0.589xx10^(-7)cm)xx(6.022xx10^(23)mol^(-1)))=0.260"g cm"^(-3)`
`rho(z=4)=(4xx(32gmol^(-1)))/((0.589xx10^(-7)cm)xx(6.022xx10^(23)mol^(-1)))=0.5203"g cm"^(-3)`
The experimenatl value of density `(0.466"g cm"^(-3))` nearly agrees with the theoretical value of density with Z = 4. i.e., it has fcc structure.
Thus, methane (solid) crystallises as 'fcc' structure.
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