For the reaction $\mathrm{CH}_{4(\mathrm{~g})}+\mathrm{H}_{2(\mathrm{~g})} \longrightarrow \mathrm{C}_2 \mathrm{H}_{6(\mathrm{~g})}$ $\mathrm{K}_{\mathrm{p}}=3.356 \times 10^{17}$, calculate $\Delta \mathrm{G}^{\circ}$ for the reaction at 298 K .

Rate of a first order reaction is $1.5 \times 10^{-2} \mathrm{~mol} \mathrm{~L}^{-1}$ minute ${ }^{-1}$ at 0.5 M concentration of reactant, calculate half life of reaction.

Calculate the density of a metal molar mass $197 \mathrm{~g} \mathrm{~mol}^{-1}$ if it forms fcc structure. $\left[\mathrm{a}^3 \times \mathrm{N}_{\mathrm{A}}=40 \mathrm{~cm}^3 \mathrm{~mol}^{-1}\right]$

A gas expands isothermally against a constant external pressure of 1 bar from 10 dm$^3$ to 20 dm$^3$ by absorbing 800 J of heat from surrounding. Calculate value of $\Delta$U.