Stoichiometry water vapour pressure

This impressively simple formula shows that the water vapour pressure at the outlet depends, quite simply, on the air stoichiometry and the air pressure at the exit Pexit- In this derivation, we ignored any water vapour in the inlet air - thus this formula gives us the worst case situation, with dry inlet air. We will consider the effect of inlet water vapour later. 

Fig. 3.4. Influence of water vapour partial pressure (/hio) on water content (n) and conductivity (o ) for (a) an intrinsic conductor, a crystalline hydrate HUP well-defined steps corresponding to various stoichiometries can be observed, e.g. in H Sb,P203,+5. nH20 (n = 2-10), X = 1, 3, 5 (b) a mixed surface-bulk conductor V205.nH20 or Zr(HP04)2- H20 (c) surface conductor CeHP04.nH20. Brunauer adsorption isotherms (Kds) nf given for comparison (with permission).

Water non-stoichiometry associated with the presence of P2O7 defects is also possible . Atmospheric humidity may also play a role as shown for RbH2P04 by Baranowski et al. The enthalpy of a phase transition (352 K) in RbH2P04 is directly related to the time of contact between the crystal (1-100 mm Hg) and the water vapour at various pressures. The mechanism is not well understood but the experimental evidence indicates the influence of defects. 

There are of course also cases - also of practical interest - where the concentration of ionic defects vary, e.g. with temperature in intrinsically disordered compounds, and with temperature and non-stoichiometry in non-stoichiometric compounds. In proton conducting oxides the proton conductivity varies with proton concentration, typically a function of water vapour partial pressure. 

If the optimal stoichiometry is achieved, molar ratios in the off-gas would be around 2/3 CO2 and 1/3 isobutene. Since the solubility of isobutene in water is only 267 mg/L at 30 °C and 1 atm and considering partial vapour pressure, concentration of isobutene dissolved in the fermentation broth will be of the order of magnitude around 0.1 g/L. This is probably not yet toxic to the microorganism (van Leeuwen et al. 2012 Zhang et al. 2002b Straathof 2003). 

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