Final answer:
The densities of totally crystalline and totally amorphous PET can be found by solving a set of equations based on the rule of mixtures for the provided sample densities and crystallinities. The unit cell volume is determined by PET's molecular weight and the density of the crystalline form. The degree of crystallinity of a third sample can be found using a linear equation derived from the crystalline and amorphous densities.
Step-by-step explanation:
To compute the densities of totally crystalline and totally amorphous poly(ethylene terephthalate) (PET), we can use the rule of mixtures for the two provided samples with their respective density and crystallinity percentages:
- For sample 1 (density = 1.41 g/cm3, crystallinity = 74%), we can write the equation: 1.41 = Pc·74% + Pa·26%, where Pc is the density of the crystalline form and Pa is the density of the amorphous form.
- For sample 2 (density = 1.34 g/cm3, crystallinity = 31%), we write: 1.34 = Pc·31% + Pa·69%.
Solving these two equations simultaneously, we get Pc (density of totally crystalline PET) and Pa (density of totally amorphous PET).
For the unit cell volume, if one repeat unit of PET (which has a mass based on its molecular weight) fit into each unit cell, the density of totally crystalline PET could help us find the volume using the formula:
Density = Mass/Volume, or Volume = Mass/Density.
To find the degree of crystallinity for a third sample with a density of 1.38 g/cm3, we use the equation derived from the line equation between the crystalline and amorphous points: 1.38 = Pc·Xc + Pa·(1-Xc), where Xc is the crystalline fraction we need to find.