'x' g of molecular oxygen $$\left(\mathrm{O}_{2}\right)$$ is mixed with $$200 \mathrm{~g}$$ of neon (Ne). The total pressure of the non-reactive mixture of $$\mathrm{O}_{2}$$ and Ne in the cylinder is 25 bar. The partial pressure of Ne is 20 bar at the same temperature and volume. The value of 'x' is _________.

[Given: Molar mass of $$\mathrm{O}_{2}=32 \mathrm{~g} \mathrm{~mol}^{-1}$$.

Molar mass of $$\mathrm{Ne}=20 \mathrm{~g} \mathrm{~mol}^{-1}$$]

For a real gas at $$25^{\circ} \mathrm{C}$$ temperature and high pressure (99 bar) the value of compressibility factor is 2, so the value of Vander Waal's constant 'b' should be __________ $$\times 10^{-2} \mathrm{~L} \mathrm{~mol}^{-1}$$ (Nearest integer)

(Given $$\mathrm{R}=0.083 \mathrm{~L}$$ bar $$\mathrm{K}^{-1} \mathrm{~mol}^{-1}$$)

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

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)