Given the following thermochemical equations:
$(i) S_{(s)} + \frac{3}{2} O_{2(g)} \rightarrow SO_{3(g)} + 2x \, kcal$
$(ii) SO_{2(g)} + \frac{1}{2} O_{2(g)} \rightarrow SO_{3(g)} + y \, kcal$
Find the heat of formation of $SO_{2(g)}$.

For which of the following thermodynamic processes is $\Delta U = 0$?

For the reaction $2X_{(s)} + 2Y_{(s)} \to 2C_{(\ell)} + D_{(g)}$,the value of $q_p$ is $-28 \, \text{kcal mol}^{-1}$ at $2700 \, ^\circ\text{C}$. Calculate the value of $q_v$ in $\text{kcal mol}^{-1}$.

For the reaction $2X_{(g)} + Y_{(g)} \to 2Z_{(g)}$ at $298 \ K$,$\Delta U = -10.5 \ kJ$ and $\Delta S^o = -10.5 \ J/K$. Calculate $\Delta G^o$ for the reaction. Will the reaction be spontaneous or not? Explain.

The entropy change associated with the conversion of $1 \ kg$ of ice at $273 \ K$ to water vapours at $383 \ K$ is: (Specific heat of water liquid and water vapours are $4.2 \ kJ \ K^{-1} \ kg^{-1}$ and $2.0 \ kJ \ K^{-1} \ kg^{-1},$ heat of fusion and vaporisation of water are $334 \ kJ \ kg^{-1}$ and $2491 \ kJ \ kg^{-1},$ respectively) $(\ln \ 273 = 5.61, \ln \ 373 = 5.92, \ln \ 383 = 5.95)$

Consider a reaction $2H_2O_{(l)} \to 2H_{2(g)} + O_{2(g)}$. Calculate the work done at $25\, ^oC$ for the decomposition of $36\, mL$ of water. (in $, KCal$)