The $\Delta E^o$ of combustion of $2-$methylpropene is $-X \ kJ \ mol^{-1}$. The value of $\Delta H^o$ is

Assuming the water vapour to be a perfect gas,calculate the internal energy change when $1 \ mol$ of water at $100^{\circ} C$ and $1 \ bar$ pressure is converted to ice at $0^{\circ} C$. Given the enthalpy of fusion of ice is $6.00 \ kJ \ mol^{-1}$ and heat capacity of water is $4.2 \ J \ g^{-1} {\circ} C^{-1}$.

Calculate $\Delta H$ when $2 \ moles$ of solid benzoic acid undergo complete combustion at $300 \ K$ if $C_6H_5COOH_{(s)} + \frac{15}{2} O_{2(g)} \rightarrow 7CO_{2(g)} + 3H_2O_{(l)}$,$\Delta U_{reaction} = -750 \ kJ/mole$ [$R = 8 \ J/mole \cdot K$].

Consider the following statements:
Statement-$I$: During isothermal expansion of an ideal gas,its enthalpy decreases.
Statement-$II$: When $2.0 \ L$ of an ideal gas expands isothermally into vacuum,$\Delta U = 0$.

Calculate the enthalpy change when $50 \ mL$ of $0.01 \ M$ $Ca(OH)_2$ reacts with $25 \ mL$ of $0.01 \ M$ $HCl$. Given that $\Delta H^o$ for neutralization of a strong acid and a strong base is $-13.7 \ kcal \ mol^{-1}$. (Note: The provided value in the prompt $140 \ kcal \ mol^{-1}$ is physically incorrect for neutralization; using standard value $-13.7 \ kcal \ mol^{-1}$ for calculation). (in $kcal$)

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.