For a dimerization reaction,$2 A_{(g)} \rightarrow A_{2(g)}$ at $298 \ K$,$\Delta U^{\ominus} = -20 \ kJ \ mol^{-1}$,$\Delta S^{\ominus} = -30 \ J \ K^{-1} \ mol^{-1}$,then the $\Delta G^{\ominus}$ will be........ $J$

For the reaction $\frac{1}{2}X_2 + \frac{3}{2}Y_2 \to XY_3$,$\Delta H = -30 \ kJ/mol$. Given $\Delta S_{X_2} = 60 \ J/mol \cdot K$,$\Delta S_{Y_2} = 40 \ J/mol \cdot K$,and $\Delta S_{XY_3} = 50 \ J/mol \cdot K$,calculate the temperature at equilibrium in $K$.

The temperature of $1 \ mol$ of an ideal gas is increased by $2 \ ^oC$ at constant pressure. The work done is:

For the reaction $X_2Y_{4(l)} \rightarrow 2XY_{2(g)}$ at $300 \ K$, the values of $\Delta U$ and $\Delta S$ are $2 \ kcal$ and $20 \ cal \ K^{-1}$ respectively. The value of $\Delta G$ for the reaction is (in $cal$)

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 $SO_{2(g)}$.

Match the List-$I$ with List-$II$

List-$I$ Thermodynamic Process	List-$II$ Magnitude in $kJ$
$A$. Work done in reversible, isothermal expansion of $2 \ mol$ of ideal gas from $2 \ dm^3$ to $20 \ dm^3$ at $300 \ K$.	$I$. $4$
$B$. Work done in irreversible isothermal expansion of $1 \ mol$ ideal gas from $1 \ m^3$ to $3 \ m^3$ at $300 \ K$ against a constant pressure of $3 \ kPa$.	$II$. $11.5$
$C$. Change in internal energy for adiabatic expansion of a $1 \ mol$ ideal gas with change of temperature $= 320 \ K$ and $\overline{C}_V = \frac{3}{2} R$.	$III$. $6$
$D$. Change in enthalpy at constant pressure of $1 \ mole$ ideal gas with change of temperature $= 337 \ K$ and $\overline{C}_P = \frac{5}{2} R$.	$IV$. $7$

Choose the correct answer from the option given below: