The difference between heats of reaction at constant pressure and at constant volume for the reaction $2C_6H_{6(l)} + 15O_{2(g)} \to 12CO_{2(g)} + 6H_2O_{(l)}$ at $25\,^{\circ}C$ in $kJ$ is

Standard entropies of $X_2$,$Y_2$ and $XY_3$ are $60$,$40$ and $50 \ J \ K^{-1} \ mol^{-1}$ respectively. For the reaction $\frac{1}{2} X_2 + \frac{3}{2} Y_2 \rightarrow XY_3$,the enthalpy change is $\Delta H = -30 \ kJ \ mol^{-1}$. At what temperature will the reaction be at equilibrium (in $K$)?

Identify the incorrect statements among the following:
$(a)$ All enthalpies of fusion are positive.
$(b)$ The magnitude of enthalpy change does not depend on the strength of the intermolecular interactions in the substance undergoing phase transformations.
$(c)$ When a chemical reaction is reversed,the value of $\Delta_r H^{\circ}$ is reversed in sign.
$(d)$ The change in enthalpy is dependent on the path between the initial state (reactants) and final state (products).
$(e)$ For most of the ionic compounds,$\Delta_{\text{sol}} H^{\circ}$ is negative.

At $300 \ K$,which of the following reactions with the given thermodynamic parameters occur spontaneously?

The heat evolved in the combustion of methane is given by the following equation: $CH_{4(g)} + 2O_{2(g)} \to CO_{2(g)} + 2H_2O_{(l)}$; $\Delta H = -890.3 \ kJ$. How many grams of methane would be required to produce $445.15 \ kJ$ of heat of combustion?

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

List-$I$	List-$II$
$A$. Spontaneous process	$I$. $\Delta H < 0$
$B$. Process with $\Delta P = 0; \Delta T = 0$	$II$. $\Delta G_{T, P} < 0$
$C$. $\Delta H_{reaction}$	$III$. Isothermal and isobaric process
$D$. Exothermic process	$IV$. [Bond energies of molecules in reactants] - [Bond energies of product molecules]

Choose the correct answer from the options given below: