What is the number of moles of ethane obtained from $2n$ moles of bromomethane using $2n$ moles of sodium atoms in dry ether medium?

The amount of energy required to break a bond is the same as the amount of energy released when the same bond is formed. In the gaseous state,the energy required for homolytic cleavage of a bond is called Bond Dissociation Energy $(BDE)$ or Bond Strength. $BDE$ is affected by the $s$-character of the bond and the stability of the radicals formed. Shorter bonds are typically stronger bonds. $BDEs$ for some bonds are given below:
$Cl-Cl_{(g)} \rightarrow Cl^{\bullet}_{(g)} + Cl^{\bullet}_{(g)} \quad \Delta H^{\circ} = 58 \text{ kcal mol}^{-1}$
$CH_3-Cl_{\text{(g)}} \rightarrow CH_3^{\bullet}{_{\text{(g)}}} + Cl^{\bullet}{_{\text{(g)}}} \quad \Delta H^{\circ} = 85 \text{ kcal mol}^{-1}$ $H-Cl_{(g)} \rightarrow H^{\bullet}_{(g)} + Cl^{\bullet}_{(g)} \quad \Delta H^{\circ} = 103 \text{ kcal mol}^{-1}$
$(1)$ The correct match of the $C-H$ bonds (shown in bold) in Column $J$ with their $BDE$ in Column $K$ is:

Column $J$ Molecule	Column $K$ $BDE \text{ (kcal mol}^{-1})$
$(P)$ $H-CH(CH_3)_2$	$(i)$ $132$
$(Q)$ $H-CH_2Ph$	$(ii)$ $110$
$(R)$ $H-CH=CH_2$	$(iii)$ $95$
$(S)$ $H-C \equiv CH$	$(iv)$ $88$

$(A)$ $P-iii, Q-iv, R-ii, S-i$
$(B)$ $P-i, Q-ii, R-iii, S-iv$
$(C)$ $P-iii, Q-ii, R-i, S-iv$
$(D)$ $P-ii, Q-i, R-iv, S-iii$
$(2)$ For the following reaction:
$CH_{4(g)} + Cl_{2(g)} \xrightarrow{\text{light}} CH_3Cl_{(g)} + HCl_{(g)}$
the correct statement is:
$(A)$ Initiation step is exothermic with $\Delta H^{\circ} = -58 \text{ kcal mol}^{-1}$.
$(B)$ Propagation step involving $CH_3^{\bullet}$ formation is exothermic with $\Delta H^{\circ} = -2 \text{ kcal mol}^{-1}$.
$(C)$ Propagation step involving $CH_3Cl$ formation is endothermic with $\Delta H^{\circ} = +27 \text{ kcal mol}^{-1}$.
$(D)$ The reaction is exothermic with $\Delta H^{\circ} = -25 \text{ kcal mol}^{-1}$.

What is the minimum number of carbon atoms required for an alkane to contain a quaternary carbon atom?

Identify the reagent $(A)$ used in the following reaction.

The Fischer-Tropsch process is used for the manufacture of

Give the methods of preparation of alkanes. Write the general reactions.