Question

A PET sample with 40% crystallinity shows only a melting endotherm in the first heating cycle of DSC with a melting enthalpy of 50 J/g. The degree of crystallinity (%) of another PET sample which also shows only a melting endotherm but with a melting enthalpy of 80 J/g is (in integer) ____________________.

Hint:

- The degree of crystallinity is calculated by comparing the measured melting enthalpy to the expected melting enthalpy for a fully crystalline sample.

Answer 1

Correct Answer: 64

To calculate the degree of crystallinity of the second sample, we use the following relationship between the melting enthalpy and crystallinity: \[ % \text{ Crystallinity} = \left( \frac{\Delta H_{\text{sample}}}{\Delta H_{\text{melt}}} \right) \times 100 \] Where: - \( \Delta H_{\text{sample}} \) is the melting enthalpy of the sample. - \( \Delta H_{\text{melt}} \) is the melting enthalpy of the fully crystalline sample. Given that: - The first sample has 40% crystallinity and a melting enthalpy of 50 J/g, so the melting enthalpy of the fully crystalline PET \( \Delta H_{\text{melt}} = \frac{50}{0.4} = 125 \) J/g. - The second sample has a melting enthalpy of 80 J/g. We can now calculate the degree of crystallinity for the second sample: \[ % \text{ Crystallinity} = \left( \frac{80}{125} \right) \times 100 = 64 \] Thus, the degree of crystallinity for the second sample is \( \boxed{64} \).