Final answer:
The melting temperature (Tm) of poly(decamethylene adipate) increases with the degree of polymerization (Xn), and based on the provided data, the equilibrium melting temperature would be higher than the given 75°C for Xn=10.
Step-by-step explanation:
The question pertains to the melting temperature (Tm) of a polymeric material and how it changes with the degree of polymerization (Xn). To estimate the equilibrium melting temperature of poly(decamethylene adipate), one must understand the relationship between molecular weight (or degree of polymerization) and the melting temperature. The question provides two data points: Tm = 65°C for Xn = 3 and Tm = 75°C for Xn = 10.
In polymers, the melting temperature increases with higher degrees of polymerization due to more significant intermolecular forces and reduced chain ends, which typically depress the melting temperature. Assuming the relationship between Tm and Xn is linear over the range of interest, one could extrapolate to estimate the equilibrium melting temperature (the melting temperature of an infinitely long polymer chain). However, without more data points, an accurate prediction is challenging. Therefore, consider the provided data as limiting case scenarios and that the equilibrium melting temperature would be higher than 75°C.