$$2.5 \mathrm{~g}$$ of a non-volatile, non-electrolyte is dissolved in $$100 \mathrm{~g}$$ of water at $$25^{\circ} \mathrm{C}$$. The solution showed a boiling point elevation by $$2^{\circ} \mathrm{C}$$. Assuming the solute concentration is negligible with respect to the solvent concentration, the vapor pressure of the resulting aqueous solution is _________ $$\mathrm{mm}$$ of $$\mathrm{Hg}$$ (nearest integer)

[Given : Molal boiling point elevation constant of water $\left(\mathrm{K}_{\mathrm{b}}\right)=0.52 \mathrm{~K} . \mathrm{kg} \mathrm{mol}^{-1}$, $$1 \mathrm{~atm}$$ pressure $$=760 \mathrm{~mm}$$ of $$\mathrm{Hg}$$, molar mass of water $$=18 \mathrm{~g} \mathrm{~mol}^{-1}]$$

Only $$2 \mathrm{~mL}$$ of $$\mathrm{KMnO}_4$$ solution of unknown molarity is required to reach the end point of a titration of $$20 \mathrm{~mL}$$ of oxalic acid $$(2 \mathrm{M})$$ in acidic medium. The molarity of $$\mathrm{KMnO}_4$$ solution should be ________ M.

Consider the following transformation involving first order elementary reaction in each step at constant temperature as shown below.

Some details of the above reactions are listed below.

If the overall rate constant of the above transformation (k) is given as $$\mathrm{k=\frac{k_1 k_2}{k_3}}$$ and the overall activation energy $$(\mathrm{E}_{\mathrm{a}})$$ is $$400 \mathrm{~kJ} \mathrm{~mol} \mathrm{~m}^{-1}$$, then the value of $$\mathrm{Ea}_3$$ is ________ integer)

The enthalpy of formation of ethane $$(\mathrm{C}_2 \mathrm{H}_6)$$ from ethylene by addition of hydrogen where the bond-energies of $$\mathrm{C}-\mathrm{H}, \mathrm{C}-\mathrm{C}, \mathrm{C}=\mathrm{C}, \mathrm{H}-\mathrm{H}$$ are $$414 \mathrm{~kJ}, 347 \mathrm{~kJ}, 615 \mathrm{~kJ}$$ and $$435 \mathrm{~kJ}$$ respectively is $$-$$ __________ $$\mathrm{kJ}$$