At room temperature the unit cell for this material is triclinic is 1 unit/cell.
In the problem statement we are given the following equation and information:
V = abc * sqrt(1 - cos^2 alpha - cos^2 beta - cos^2 gamma + 2cos alpha * cos beta * cos gamma)
= (0.497)(0.547)(1.729) √1 - cos2 48.4 - cos² 76.7 - cos² 62.5 + 2 cos 48.4 cos 76.7 cos 62.5
= 0.31n * m ^ 3
Next calculate the repeat unit weight for Nylon 6,6
m = 12A_{C} + 22A_{H} + 2A_{O} + 2A_{N}
= 12(12.01) + 22(1) + 2(16) + 2(14.01)
= 226.14g / m * ol
We can now calculate the number of repeat units per a unit cell. However we must convert V from n * m ^ 3 to c * m ^ 3 which results in V = 3.1 * 10 ^ - 22
n = (rho*VN)/m
= (1.213(3.1 * 10 ^ - 22)(6.02 * 10 ^ 23))/226.14
1 unit/cell.
The complete question is The density of totally crystalline nylon 6,6 at room temperature is 1.213g / c * m ^ 3 Also, at room temperature the unit cell for this material is triclinic with lattice parameters:
a = 0.497nm c = 48.4 deg
b = 0.547nm beta = 76.6 deg
c = 1.729nm y = 62.5 deg
If the volume of a triclinic unit cell, V tr i prime is a function of these lattice parameters as
V tri =abc sqrt 1-cos^ 2 a-cos^ 2 beta-cos^ 2 gamma+2 cos a cos beta cos gamma
determine the number of repeat units per unit cell.
Click on the link to access Table 4.3.
Atomic weights for several elements are included in the following table:
Carbon 12.01 g/mol
Chlorine 35.45 g/mol
Fluorine 19.00 g/mol
Hydrogen 1.008 g/mol
Oxygen 16.00 g/mol
Nitrogen 14.01 g/mol
To learn more about unit cell refer to:
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