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$A$ liquid confined inside an adiabatic container is taken from state $1$ to state $2$ by a single-stage process as shown in the $P-V$ diagram. Then,$\Delta H$ is:

For the reaction $2A_{(g)} + B_{(g)} \to 2D_{(g)}$,given $\Delta U^{\theta} = -10.5 \ kJ$ and $\Delta S^{\theta} = -44.1 \ J \ K^{-1}$. Calculate $\Delta G^{\theta}$ for the reaction at $298 \ K$ and predict whether the reaction may occur spontaneously.

Calculate $\Delta H^{\circ}$ for the reaction, $Na_2O_{(s)} + SO_{3(g)} \longrightarrow Na_2SO_{4(s)}$, given the following reactions:
$(A) \ Na_{(s)} + H_2O_{(l)} \longrightarrow NaOH_{(s)} + \frac{1}{2}H_{2(g)} \quad \Delta H^{\circ} = -146 \ kJ$
$(B) \ Na_2SO_{4(s)} + H_2O_{(l)} \longrightarrow 2NaOH_{(s)} + SO_{3(g)} \quad \Delta H^{\circ} = +418 \ kJ$
$(C) \ 2Na_2O_{(s)} + 2H_{2(g)} \longrightarrow 4Na_{(s)} + 2H_2O_{(l)} \quad \Delta H^{\circ} = +259 \ kJ$

Match the transformations in column $I$ with appropriate options in column $II$.
Column $I$ Column $II$
$A$. $CO_{2(s)} \rightarrow CO_{2(g)}$ $p$. phase transition
$B$. $CaCO_{3(s)} \rightarrow CaO_{(s)} + CO_{2(g)}$ $q$. allotropic change
$C$. $2H_{(g)} \rightarrow H_{2(g)}$ $r$. $\Delta H$ is positive
$D$. $P_{(\text{white, solid})} \rightarrow P_{(\text{red, solid})}$ $s$. $\Delta S$ is positive
$t$. $\Delta S$ is negative

$\Delta H_f^o$ of water is $-285.5\, kJ\, mol^{-1}$. If enthalpy of neutralisation of monoacidic strong base is $-57.3\, kJ\, mol^{-1}$,$\Delta H_f^o$ of $OH^{-}$ ion will be $.....\, kJ\, mol^{-1}$.

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