a$)$ A high$-$molecular$-$weight polyethylene has an average molecular weight of $410000$

$\frac{g}{m}ol.$ What is its average degree of polymerization? $($Atomic mass of $C=12\frac{g}{m}ol$ and $H=1$

$\frac{g}{m}ol)(10$ points$)$

b$)$ Three monodisperse poly$(1,10$ decanediol adipate$)$ polymer were mixed as shown

below

$10g$ was taken from A which has molecular weight of $40000gmo{l}^{-1}$

$5g$ was taken from B which has molecular weight of $100000gmo{l}^{-1}$

$3g$ was taken from $C$ which has molecular weight of $200000gmo{l}^{-1}$

Calculate the number$-$average, $($:$M_n$:$),$ and weight$-$average, $($:$M_w$:$),$ molar mass and

polydispersity index of the mixture. $(15$ Points$)$

I$)$ What is red shift? $(2\mathrm{.}5$ points$)$

a$)$ The shifting of an absorption to shorter wavelength

b$)$ The shifting of an absorption to lower energy.

c$)$ The shifting of an absorption to lower energy.

d$)$ The shifting of an absorption towards the blue end of the spectrum.

II$)$ A solution of $x$ of concentration $0\mathrm{.}010mold{m}^{-3}$ gives an absorbance of $0\mathrm{.}5.$ What

concentration is a solution of $x$ which gives an absorbance reading of $0\mathrm{.}25?$ Assume that the

same optical cell is used for both readings. $(7\mathrm{.}5$ points$)$

III$)$ How do values of ${}_{\text{m}\text{a}\text{x}}$ for the $**larr$ transitions vary among a series of conjugated

polyenes? $(5$ Points$)$

a$)$ Values shift to longer wavelength as the number of $C=C$ double bond increases.

b$)$ Values shift to shorter wavelength as the number of $C=C$ double bond increases.

c$)$ Values vary but in no particular manner.

d$)$ Values vary very little.

What is an universal calibration curve and what is the advantage of using it in GPC

analysis? $(15$ points$)$