Cellulose in wood has a monoclinic crystal structure. The unti cell consists of

Question

Cellulose in wood has a monoclinic crystal structure. The unti cell consists of five(5) cellulose chains, one each at the corners and one in the center of the monoclinic crystal structure. The crystal is held together by hydrogen bonding between oxygen and hydrogen atoms on adjacent cellulose molecules. The unit cell has dimensions a=8.35 Angstroms, b= 10.3 Angstroms and c=7.9 Angstroms. Calculate the density of cell wall substance under the assumption that the cell wall substance of wood is made up of all crystaline cellulose and the molecular weight of the repeating anhydrous glucose unit (C_6H_10O_5) in the cellulose is 162 grams per mole?

Explanation / Answer

clearly it is BCC structure . number of molecular units in BCC = 2

Z = 2

N = 6.023 x 10^23

V = volume = a x b x c = 8.35 x 10.3 x 7.9 = 679.4 Ao^3 = 679 . 4 x (10^-8)3

V = 6.79 x 10^-22 cm^3

M = 162 g/mol

density = d = Z M / N V

d = 2 x 162 / (6.023 x 10^23 ) (6.79 x 10^-22 )

d = 0.792 g / cm^3

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