Chapter 16, Problem 16.11P

Interpretation Introduction

Interpretation:

The number of chains in the given PVC pipe is to be determined.

Concept Introduction:

The molecular weight of a polymer is not fixed. It has a certain range under which its molecular weight falls. For a linear polymer, degree of polymerization represents the average length of the polymer. Degree of polymerization is defined as:

  $\begin{array}{c}\text{Degree of polymerization}=\frac{\text{average molecular weight of polymer}}{\text{molecular weight of repeating unit}}\\ n=\frac{{\left(\text{MW}\right)}_{\text{av}\text{.}}}{{\left(\text{MW}\right)}_{\text{repeating unit}}}\end{array}$   ....... (1)

Volume $\left(V\right)$ of a hollow cylinder with height $\left(h\right)$, inner diameter $\left(d_i\right)$, and outer diameter $\left(d_o\right)$ is:

  $V=\frac{\pi h\left(d_o^2-d_i^2\right)}{4}$   ....... (2)

Density $\left(\rho \right)$ of a substance is defined as:

  $\rho =\frac{m}{V}$   ....... (3)

Here, $m$ is the mass of the substance and $V$ is the volume of the substance.

The formula to calculate number of chains in the given mass of polymer is:

  $\text{Number of chains}=\frac{m\times N_A}{{\left(\text{MW}\right)}_{\text{av}\text{.}}}$   ....... (4)

Here, $m$ is the mass of the polymer, $N_A$ is the Avogadro's number, and ${\left(\text{MW}\right)}_{\text{av}\text{.}}$ is the average molecular mass of the polymer.