A $$10 \mathrm{~g}$$ mixture of hydrogen and helium is contained in a vessel of capacity $$0.0125 \mathrm{~m}^{3}$$ at 6 bar and $$27^{\circ} \mathrm{C}$$. The mass of helium in the mixture is ____________ g. (nearest integer)
Given: $$\mathrm{R}=8.3 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$$
(Atomic masses of $$\mathrm{H}$$ and $$\mathrm{He}$$ are $$1 \mathrm{u}$$ and $$4 \mathrm{u}$$, respectively)
Consider an imaginary ion $${ }_{22}^{48} \mathrm{X}^{3-}$$. The nucleus contains '$$a$$'% more neutrons than the number of electrons in the ion. The value of 'a' is _______________. [nearest integer]
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: $$\mathrm{R}=8.314 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$$.
The elevation in boiling point for 1 molal solution of non-volatile solute A is $$3 \mathrm{~K}$$. The depression in freezing point for 2 molal solution of $$\mathrm{A}$$ in the same solvent is 6 $$K$$. The ratio of $$K_{b}$$ and $$K_{f}$$ i.e., $$K_{b} / K_{f}$$ is $$1: X$$. The value of $$X$$ is [nearest integer]