PLEASE ANSWER $5$ QUESTIONS CAREFULLY AND IN DETAILED SOLUTION. I NEED FOR MY HOMEWORK. GOD BLESS.

Question $3(2$ pt$,$ L$.$O$\mathrm{.}2)$ Consider the electrochemical cell

$0\mathrm{.}100.$ Given that ${}_{Cd2\frac{+}{C}d}=-0\mathrm{.}403V,{}_{\text{A}\text{g}\text{C}\frac{l}{A}g}=+0\mathrm{.}222V$

a$)$ Determine the half$-$cell reactions and the overall cell reaction.

b$)$ Calculate the electromotive force $($V$)$ at $298K.$

c$)$ Determine the equilibrium constant $K$ at $298K.$

d$)$ Is the cell reaction spontaneous as written? Explain.

Question $4$ : From a single one polystyrene sample, polystyrene$/$toluene solutions with different concentrations were prepared and their viscosities measured at temperature $298K,$ resulting the following data:

Given the relative viscosity of these polystyrene$/$toluene solutions is directly proportional to their concentrations and the intrinsic viscosity depends on the polystyrene mole mass as followed $[]=3\mathrm{.}7{10}^{-5}{M}_{\text{p}\text{o}\text{l}\text{y}\text{s}\text{t}\text{y}\text{r}\text{e}\text{n}\text{e}}^{0\mathrm{.}62}d{m}^3*g^{-1}.$

Calculate the mole mass of this polystyrene sample and comment on the result obtained.

Question $5$ :

The adsorption equilibrium of gas CO onto $1g$ of an activated carbon sample at temperature $273K$ obeys the Langmuir isotherm. Based on the experimental data given below,

The values for adsorbed volumes are already corrected to $273K,1\mathrm{.}0$atm.

a$.$ Find the corresponding Langmuir isotherm

b$.$ Find the specific surface area of this adsorbent, given the effective cross section of $CO$ molecule is $0\mathrm{.}36n{m}^2.$

Question $6(0\mathrm{.}75$ pt$,$ L$.$O$\mathrm{.}3)$ Calculate the surface energy in a system consisting of $1$ liter $(1d{m}^3)$ liquid water distributed as spherical droplets with radius $100nm$ in a gaseous phase, given the surface tension "gaseous phase $/$ liquid water" under these circumstances is $7\mathrm{.}275{10}^{-4}\frac{J}{d}{m}^2.$

Question $7(0\mathrm{.}75$ pt$,$ L$.$O$\mathrm{.}3)$

Given a polymer sample consisting of $3($monodisperse$)$ molar mass fractions $62kgmo{l}^{-1},78kgmo{l}^{-1}$ and $95kgmo{l}^{-1}$ with their mole ratio $3$:$2$:$1,$ respectively. Calculate the number$-$average$-$ and weight$-$average mole mass of this polymer sample.