At $1 \ atm$ pressure,$\Delta S = 75 \ J/K \cdot mol$ and $\Delta H = 30 \ kJ/mol$. The temperature of the reaction at equilibrium is $....... \ K$.

Identify the incorrect statements from the following.
$I$. For adiabatic process,$\Delta U = w_{ad}$
$II$. Enthalpy is an intensive property
$III$. For the process,$H_2O_{(l)} \rightarrow H_2O_{(s)}$,the entropy increases

For the reaction,$X_2O_{4(l)} \to 2XO_{2(g)}$,$\Delta U = 2.1 \ kcal$ and $\Delta S = 20 \ cal \ K^{-1}$ at $300 \ K$. Calculate $\Delta G$ in $kcal$.

$X \, g$ of ice at $0^{\circ} C$ is added to $340 \, g$ of water at $20^{\circ} C$. The final temperature of the resultant mixture is $5^{\circ} C$. The value of $X$ (in $g$) is closest to:
[Heat of fusion of ice $= 333 \, J / g$; specific heat of water $= 4.184 \, J / g \cdot K$]

Consider the following reaction :
$2A (g) + B (g) \rightarrow 2D(g)$
$\Delta U^{\circ} = -10 \text{ kJ mol}^{-1}$ and $\Delta S^{\circ} = -44 \text{ J K}^{-1} \text{ mol}^{-1}$ at $298 \text{ K}$.
Identify the correct option with $\Delta G^{\circ}$ for the reaction and spontaneity of the reaction at $298 \text{ K}$.
(Given : $R = 8.31 \text{ J mol}^{-1} \text{ K}^{-1}$)

From the following data,the enthalpy of dilution of $KCl$ will be ............ $kJ$.
$KCl_{(s)} + 20H_2O \to KCl(20H_2O); \Delta H = + 15.90 \ kJ$
$KCl_{(s)} + 200H_2O \to KCl(200H_2O); \Delta H = + 18.58 \ kJ$