The polymerization of ethylene to linear polyethylene is represented by the reaction,

${\mathrm{nCH}}_2={\mathrm{CH}}_2\to {\left(-{\mathrm{CH}}_2-{\mathrm{CH}}_2-\right)}_{\mathrm{n}}$, where $\mathrm{n}$ has a large integral value. Given that the average enthalpies of bond dissociation for $\mathrm{C}=\mathrm{C}$ and $\mathrm{C}-\mathrm{C}$ at $298 \mathrm{K}$ are $+590$ and $+331 \mathrm{kJ}$ ${\mathrm{mole}}^{-1}$, respectively, calculate the enthalpy of polymerization per mole of ethylene at $298 \mathrm{K}$.

A hydrocarbon $\left(\mathrm{A}\right)$ $\text{[}\mathrm{C}-90.56\%$, Vapour density $53\text{]}$ was subjected to vigorous oxidation to give a dibasic acid $\left(\mathrm{B}\right)$. $0.1 \mathrm{g}$ of $\left(\mathrm{B}\right)$ required $24.1$$\mathrm{mL}$ of $0.05 \mathrm{N} \mathrm{NaOH}$ for the complete neutralization. The nitration of $\left(\mathrm{B}\right)$ gave a single mononitro derivative. When $\left(\mathrm{B}\right)$ was heated strongly with soda lime, it gave benzene. Identify $\left(\mathrm{A}\right)$ and $\left(\mathrm{B}\right)$.

A chloro compound $\left(\mathrm{A}\right)$ showed the following properties:

$\left(\mathrm{i}\right)$ Decolourised bromine in ${\mathrm{CCl}}_4$

$\left(\mathrm{ii}\right)$ Absorbed hydrogen catalytically

$\left(\mathrm{iii}\right)$ Gave a precipitate with ammonium cuprous chloride

$\left(\mathrm{iv}\right)$ When vapourised, $1.49 \mathrm{g}$ of $\left(\mathrm{A}\right)$ gave $448 \mathrm{mL}$ of vapour at $\mathrm{STP}$.

Identify $\left(\mathrm{A}\right)$.

How many grams of ${\mathrm{CaF}}_2$ must be dissolved in $100 \mathrm{mL}$ of water at $25°\mathrm{C}$ to make the solution saturated? ${\mathrm{K}}_{\mathrm{sp}}\left({\mathrm{CaF}}_2\right)=3.9\times {10}^{-11}{\mathrm{M}}^3$

(Molar mass of ${\mathrm{CaF}}_2=78 \mathrm{g} \mathrm{per} \mathrm{mole}$)

Answer after rounding-off the answer up to four digits after decimal.

A solution which is $0.1 \mathrm{M}$ in $\mathrm{NaI}$ and $0.1 \mathrm{M}$ in ${\mathrm{Na}}_2\left({\mathrm{SO}}_4\right)$, is treated with solid $\mathrm{Pb}{\left({\mathrm{NO}}_3\right)}_2$. Which compound, ${\mathrm{PbI}}_2$ or ${\mathrm{PbSO}}_4$, will precipitate first? What is the concentration of the anion of the least soluble compound, when the more soluble one starts precipitating?

Given: ${\mathrm{K}}_{\mathrm{sp}}\left({\mathrm{PbI}}_2\right)=8.7\times {10}^{-9}, {\mathrm{K}}_{\mathrm{sp}}\left({\mathrm{PbSO}}_4\right)=1.8\times {10}^{-8}$