The amount of heat released when $20 \ mL$ of $0.5 \ M$ $NaOH$ is mixed with $100 \ mL$ of $0.1 \ M$ $HCl$ is $x \ kJ$. The heat of neutralization is:

If the standard enthalpy change $\left(\Delta_{r} H^{\theta}\right)$ for a certain reaction at $298 \ K$ and constant pressure is $-1860 \ kJ \ mol^{-1}$,and the standard entropy change $\left(\Delta_{\text{sys}} S^{\theta}\right)$ of the same reaction is $-550 \ J \ K^{-1} \ mol^{-1}$,which one of the following statements is correct?

$2.4 \ g$ coal is burnt in a bomb calorimeter in excess of oxygen at $298 \ K$ and $1 \ atm$ pressure. The temperature of the calorimeter rises from $298 \ K$ to $300 \ K$. The enthalpy change during the combustion of coal is $-x \ kJ \ mol^{-1}$. The value of $x$ is. (Nearest Integer) (Given: Heat capacity of bomb calorimeter $20.0 \ kJ \ K^{-1}$. Assume coal to be pure carbon)

The molar heats of fusion and vaporisation of benzene are $10.9$ and $31.0 \ kJ \ mol^{-1}$ respectively. The changes in entropy for the solid $\rightarrow$ liquid and liquid $\rightarrow$ vapour transitions for benzene are $x$ and $y \ JK^{-1} \ mol^{-1}$,respectively. The value of $(y-x)$ (in $JK^{-1} \ mol^{-1}$) is (At $1 \ atm$,benzene melts at $5.5^{\circ} C$ and boils at $80^{\circ} C$).

Calculate the heat produced in $kJ$ when $280 \ g$ of $CaO$ is completely converted to $CaCO_3$ by reaction with $CO_2$ at $27 \ ^{\circ}C$ and at constant volume :-
(Given) $\Delta H^o_f (CaCO_3, s) = -1207 \ kJ/mol$
$\Delta H^o_f (CaO, s) = -635 \ kJ/mol$
$\Delta H^o_f (CO_2, g) = -394 \ kJ/mol$ (in $kJ$)

For the reaction $CaCO_{3(s)} \rightleftharpoons CaO_{(s)} + CO_{2(g)}$ at $977 \ ^oC$,given $\Delta H = 176 \ kJ \ mol^{-1}$,the value of $\Delta E$ is ............. $kJ$.