(Solved): The degree of polymerization of a certain oligomer sample is described by the distribution function ...

The degree of polymerization of a certain oligomer sample is described by the distribution function \[ w_{i}=K\left(i^{3}-i^{2}+5\right) \] where \( w_{i} \) is the weight fraction of polymer with degree of polymerization \( i \), and \( i \) is a continuous variable in the range \( 1 \leq i \leq 12 \). \( K \) is a numerical constant. (a) Calculate the number average degree of polymerization. (b) What is the standard deviation of the weight distribution? (Consider problem 3 above) (c) Calculate the \( z \) average degree of polymerization. (d) If the formula weight of the repeating unit \( M_{0} \) in this oligomer is \( 100 \mathrm{~g} / \mathrm{mol} \), what is \( M_{z} \) for the polymer?