Calculate Nitrogen and Xenon Water Solubility at 50 Bar Pressure

Question

Decompression sickness is caused by dissolved gases coming out of solution in the body as pressure is reduced. To remedy this, gas mixtures with lower solubility are used in diving. At 25°C and 1 bar, the solubilities of nitrogen and xenon in water are x_N2 = 1.09 × 10^-5 and x_Xe = 7.69 × 10^-5 respectively. Calculate the solubilities of both these gases at 50 bar if the compressibility factors at 25°C are given by

z_Xe = 1 – 5.16 × 10^-3 P – 3.17 × 10^-3 P2

and

z_N2 = 1 – 9.44 × 10^-4P + 1.62 × 10^-3 P2

Where P is the pressure in bar. Note that due to expense and narcotic effects, xenon is not suitable for use as a breathing gas.

Summary

The question belongs to Chemical Engineering and it is about calculating the solubilities of nitrogen and xenon gases in water as a solution for decompression sickness as these gases exhibit lower solubility in water. The solubilities of these gases at 1 bar of pressure is given. We need to calculate their solubilities at 50 bar pressure.

Note: The solution is in handwritten format