The problem involves concentrated sulfuric acid completely filling a closed volume, where slow corrosion is evolving H2 gas at a known rate. I need to quantify the internal pressure of the container for a safety analysis.
Even liquids have a finite compressibility.Therefore the pressure in the evolving gas should be in equilibrium with the compressed liquid phase. The calculation is not easy, however. You have to know the pressure dependent solubility of hydrogen in sulfuric acid and the compressibility of liquid sulfuric acid as a function of the pressure. As the chemical potential should be uniform in the system, the increasing pressure may even push back the electrochemical equilibrium.
Even liquids have a finite compressibility.Therefore the pressure in the evolving gas should be in equilibrium with the compressed liquid phase. The calculation is not easy, however. You have to know the pressure dependent solubility of hydrogen in sulfuric acid and the compressibility of liquid sulfuric acid as a function of the pressure. As the chemical potential should be uniform in the system, the increasing pressure may even push back the electrochemical equilibrium.
From the description that you provided, you can easily know the volume of the gas space since you know how much liquid acid is in the tank. Now, apply the ideal gas law:
P x V = n x R x T
Because you know the H2 release rate, you can then calculate how many moles of H2 are released at discrete time steps. You can even plot the cumulative number of H2 moles evolved as a function of time. You can then apply the ideal gas law (as a first approximation) and calculate the pressure P(t) as a function of n(t), temperature and R (the gas law constant). You will have the pressure in the gas space as a function of time, that is, P(t).
Hope this helps answer your question.
Professor Yehia Khalil
Yale University
USA
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