Identify from following, the relation between standard free energy change in a reaction and equilibrium constant $K_c$.

A gas absorbs $120$ J of heat and expands by $300 \times 10^{-6}\ \text{m}^3$ against a constant external pressure of $2 \times 10^5\ \text{Nm}^{-2}$. What will be the change in internal energy of the system ?

An ideal gas expands from initial volume $5\ \text{dm}^3$ to $15\ \text{dm}^3$ against a constant external pressure of $2$ atm. What is the work done by the gas ?

Calculate the work done in the oxidation of one mole $\mathrm{HCl}_{(\mathrm{g})}$ at $27^{\circ} \mathrm{C}$, according to reaction.

$$ \begin{aligned} & 4 \mathrm{HCl}_{(\mathrm{g})}+\mathrm{O}_{2(\mathrm{~g})} \longrightarrow 2 \mathrm{Cl}_{2(\mathrm{~g})}+2 \mathrm{H}_2 \mathrm{O}_{(\mathrm{g})} \\ & \left(\mathrm{R}=8.314 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\right) \end{aligned} $$