$(30$ pts$)$

An unknown polymer material is tested for molecular weight. The following molecular weight data is tabulated. Complete the columns of the table, including the "Total:" row and calculate and label the numberfraction molecular weight $(Mn)$ and the weight$-$fraction molecular weight $(Mw).$ The degree of polymerization $($DP$)$ for this polymer is $736.$ Calculate the repeat unit molecular weight and identify the unknown polymer $($Table $14\mathrm{.}3).$ What is the polydispersity $($PD$)$ of the polymer?

This polymer material has a density of $0\mathrm{.}95\frac{g}{m}l$ and a crystallinity of $37\mathrm{.}5\%.$ It is known that the material formed in its minimum crystalline state has a density of $0\mathrm{.}89\frac{g}{m}l.$ What is the maximum density that this polymer material can be formed?

$\backslash$table$[[$weight range,Mi$,$wi$,$xi$],[6000-24000,,0\mathrm{.}04,],[24000-42000,,0\mathrm{.}07,150],[42000-60000,,0\mathrm{.}16,990],[60000-78000,,0\mathrm{.}26,5610],[78000-96000,,0\mathrm{.}24,15870],[96000-114000,,0\mathrm{.}12,23490],[114000-132000,,0\mathrm{.}08,17850],[132000-150000,,0\mathrm{.}03,15990],[\frac{g}{m}ol,,,7050]]$