Fractional distillation calculations

[Umar Awan]

Say I have got a super cooled cylinder of half hydrogen and half helium. This cylinder has a pressure of 100,000 Pascal's. At this pressure, hydrogen boils at 20 Kelvin and helium at 4.21 Kelvin. I hope to separate helium by cooling gas down to 4.21 Kelvin but I know that even at the temperature, some hydrogen will still evaporate.

I hope you can introduce me to the formulas used to find the amount of hydrogen that will evaporate along with helium, therefore allowing me to find the purity of the hydrogen I will have obtained.

Please do not be discouraged with having to teach me basic physics if it's called for.

 

[DrDu]

The vapour pressure depends on temperature like
$p=p_0 \exp(-\Delta H/ (1/T-1/T_0))$ where $\Delta H$ is the enthalpy (or heat) of vapourisation, T absolute temperature, $T_0$ absolute temperature at boiling point, $p_0$ the vapour pressure at boiling point (i.e. 1000hPa) and R the gas constant.
For an ideal mixture, the vapour pressure is $p=x_1 p_1 +x_2 p_2$ where $p_1$ and $p_2$ are the vapour pressures of the pure components while $x_1$ and $x_2$ are the molar fractions of the two components in the mixture. The concentration of component 1 or 2 can be calculated from the ideal gas law, e.g. $c_1=n_1/V=p_1/RT$.