$6.$ In free$-$radical polymerization,

$($a$)$ Calculate a number$-$average molar mass of polystyrene prepared by bulk radical polymerization.

$($b$)$ If the light lamp is suddenly broken in the middle of initiation stage, explain briefly possible variations in the

rate of polymerization and degree of polymerization. No need to use equations.

Assumptions: $(1)$ The initial concentration of the benzophenone as an initiator is $3\mathrm{.}3{10}^{-3}mo\frac{l}{d}{m}^3$; $(2)$ Quantum

yield of benzophenone is $0\mathrm{.}8$ ; $(3)$ Molar absorptivity of the initiator is $4\mathrm{.}34{10}^3\frac{L}{m}ol-cm$; $(4)$

Intensity of incident light is $1200mo\frac{l}{m^2}-s$; $(5)$ The rate coefficients for propagation and termination

are $341$ and $4{10}^{7}d\frac{m^3}{m}ol-s,$ respectively; $(6)$ The density of styrene at the polymerization

temperature is $0\mathrm{.}88\frac{g}{c}{m}^3$; $(7)$ Termination by disproportionation is negligible; $(8)$ Chain transfer is

negligible; $(9)$ Neglect contributions from end groups; $(10)$ The ultraviolet light lamp $(365nm$ in

wavelength$)$ is used in this experiment; $(11)$ Steady state condition.

Hint: $1L=1d{m}^3.$

$7.$ In conventional free$-$radical polymerization, explain about size evolution of

oligomer and polymer particles

through

polymerization steps which are prepared by

$($a$)$ suspension polymerization and provide reason$($s$)$ for your answer.

$($b$)$ emulsion polymerization and provide reason$($s$)$ for your answer.

Assumptions: $(1)$ Consider initiation$-$propagation$-$termination steps and I$-$II$-$III

steps $($in the following Figure$)$ for suspension and emulsion

polymerizations, respectively; $(2)$ Assume that particle size of propagating oligomers in suspension

and emulsion polymerizations are same as the size of droplet and micelle, respectively.