The molar heat capacity for an ideal gas at constant pressure is $$20.785 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$$. The change in internal energy is $$5000 \mathrm{~J}$$ upon heating it from $$300 \mathrm{~K}$$ to $$500 \mathrm{~K}$$. The number of moles of the gas at constant volume is ____________. [Nearest integer] (Given: $$\mathrm{R}=8.314 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$$)

For the reaction

$$\mathrm{H}_{2} \mathrm{F}_{2}(\mathrm{~g}) \rightarrow \mathrm{H}_{2}(\mathrm{~g})+\mathrm{F}_{2}(\mathrm{~g})$$

$$\Delta U=-59.6 \mathrm{~kJ} \mathrm{~mol}^{-1}$$ at $$27^{\circ} \mathrm{C}$$.

The enthalpy change for the above reaction is ($$-$$) __________ $$\mathrm{kJ} \,\mathrm{mol}^{-1}$$ [nearest integer]

Given: $$\mathrm{R}=8.314 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$$.

$$2.4 \mathrm{~g}$$ coal is burnt in a bomb calorimeter in excess of oxygen at $$298 \mathrm{~K}$$ and $$1 \mathrm{~atm}$$ pressure. The temperature of the calorimeter rises from $$298 \mathrm{~K}$$ to $$300 \mathrm{~K}$$. The enthalpy change during the combustion of coal is $$-x \mathrm{~kJ} \mathrm{~mol}^{-1}$$. The value of $$x$$ is ___________. (Nearest Integer)

(Given : Heat capacity of bomb calorimeter $$20.0 \mathrm{~kJ} \mathrm{~K}^{-1}$$. Assume coal to be pure carbon)

While performing a thermodynamics experiment, a student made the following observations.

HCl + NaOH $$\to$$ NaCl + H_{2}O $$\Delta$$H = $$-$$57.3 kJ mol^{$$-$$1}

CH_{3}COOH + NaOH $$\to$$ CH_{3}COONa + H_{2}O $$\Delta$$H = $$-$$55.3 kJ mol^{$$-$$1}

The enthalpy of ionization of CH_{3}COOH as calculated by the student is _____________ kJ mol^{$$-$$1}. (nearest integer)