Vapor–Liquid Equilibrium (VLE) in Water-Lean Solvents

As verified before, substitution of water by an organic diluent shifts the vapor–liquid equilibrium curve toward less CO₂ absorption for a fixed CO₂ partial pressure. (10,11,14) Much like what has been reported for k₂ and k_b/k_–1, this is hypothesized to be due to the increased destabilization of the carbamate in water-lean solvents. In a previous study, (14) a point was made in that ε alone is not enough to explain this equilibrium shift. The reason for this is that there are several mechanisms for electrolyte stabilization in liquid solvents other than dipole–dipole interactions typically associated with ε; as a matter of fact, the combined actions of van der Waals forces, dipole–dipole forces, and hydrogen-bonding forces should all be considered when discussing the solvation of carbamate and protonated amine salts.

In the present study, however, a decision was made to take a step back and try to focus on the effects of ε on α versus p_A alone. This comes both from convenience as from necessity. It is convenient because, as shown in Wanderley et al., (14) at least for MEA-based water-lean solvents, the dielectric permittivity of the diluent correlates quite well with the magnitude of the equilibrium shift. This is also consistent with the discussion presented by Fialkov and Chumak (37) and by Sen et al., (38) who clearly express the shift in equilibrium constants of a reaction as a function of the dielectric permittivity of its diluent. It is necessary because no other practical working correlation has been found in the literature or observed so far. Moreover, although many VLE data points for water-lean solvents were obtained in Wanderley et al., (10) most of them referred to loadings very close to or above α = 0.5, an interval where the assumption that the only pathways for CO₂ fixation are physical absorption and carbamate formation ceases to have strength.

Therefore, we have borrowed the data reported previously by our group (14) for directly correlating the shift in VLE to the dielectric permittivity ε. Such an approach, as it shall be seen, has a great impact on the results obtained in the parametric analysis. To curb this impact, two very clear case studies will be delimitated.

• Case A: In this scenario, the equilibrium shift happens as reported by Wanderley et al., (14) and its intensity will be represented by eq 19a–c, with the clear admonition that eq 19c has been interpolated only for MEA-based solvents. Equation 19a–c shows that, given a function α* = f(p_A) that describes how α* varies with p_A in aqueous solvents of a certain amine, the equilibrium shift can be approximated by employing the same function applied to a modified CO₂ partial pressure p_A/ψ.

• Case B: No equilibrium shift will be considered at all, and the VLE behavior of the water-lean solvent will be set to be the same as that of the aqueous solvent.

  

  (19a)
  

  (19b)
  

  (19c)

   

These case studies, case A and case B, are defined in such a way that the behavior of a real water-lean solvent would be expected to fall between one approach and the other. In a way, they serve to delimit a confidence interval for the conclusions obtained in the course of this research.