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)

A mixture of hydrogen and oxygen contains $$40 \%$$ hydrogen by mass when the pressure is $$2.2$$ bar. The partial pressure of hydrogen is bar. (Nearest Integer)

A sealed flask with a capacity of 2 dm^{3} contains 11 g of propane gas. The flask is so weak that it will burst if the pressure becomes 2 MPa. The minimum temperature at which the flask will burst is ___________ $$^\circ$$C. [Nearest integer]

(Given : R = 8.3 J K^{$$-$$1} mol^{$$-$$1} , Atomic masses of C and H are 12u and 1u, respectively.) (Assume that propane behaves as an ideal gas.)