Text S3. Henry’s Law constant considerations for monoamines
MA, DMA, EA and DEA are monoamines with small alkyl group(s) and their measured p0 ranges (described by the Antoine equation parameters) are generally well below 298 K.5Opposite to these small alkylamines, AN-N has extremely lowp0 at 298 K and therefore has an Antoine equation applicable only at 415–609 K.5 It is therefore difficult to use p0 to study these amines, without introducing unknown levels of uncertainties by extrapolating their Antonie equations to 298 K. Alternatively, Henry’s Law constant KH for these amines can be used to describe their partition between gas and aqueous solution and has been determined on these amines previously.5,6 The values recommended by Ge et al.3 were considered the default input parameters in our study (corresponding results reported in Table 1).
Additional simulations were carried out using the extrapolatedp0 for each of the five monoamines with initial moles of the amine, sulfuric acid and nitric acid at 1.11151×10−9, 2.03777×10−11 and 8.86895×10−8, respectively, and a fixed initial mole of water at 0.07848 (corresponding to 60 % RH at 263.15 K and 101,325 Pa). The results were plotted in Figure S2(b), except for AN-N which showed negligible difference (< 0.05%). While the results for the four alkylamines using the KH and the extrapolated p0 appeared to be very different, it is important to note that in all four cases theTc values calculated using the extrapolatedp0 values are higher than those calculated using the KH values, suggesting that the reportedTc values in our Table S1 are the lower bound estimation of the transitional temperature at which the amines can condense with nitric acid. Numerically, the choice to useKH or extrapolated p0for our simulations will cause a change in Tcvalues by 6% or less.
Due to the potentially large errors in extrapolating thep0 values, the variability in theTc of DMA associated with its extrapolatedp0 was further tested by increasing and decreasing its extrapolated p0 at 298 K by a factor of 4.8 (limited by the maximum allowedp0 value of 10 atm in E-AIM). In the case of AN-N, the extrapolated p0 value at 298 K from Antoine equation was lower by 30 times based on another vapor pressure estimation method, EPI Suite v 4.11.7 The corresponding relative uncertainties in Tc caused by these drastic changes in extrapolated p0values were within 2%.
It is also important to note the complications in applying theKH values from literatures in our thermodynamic simulations. The KH values at 298 K for the five amines vary significantly in literatures.6 In our simulations, the KH values recommended by Linstrom and Mallard5 were used as default input values (corresponding results reported in Table S1). When applicable, the largest and smallest KH values of an amine (with clearly stated method of determination) at 298 K summarized by Sander6 were used to estimate the possible uncertainties caused by the variability in KH at 298 K. Figure S2(c) illustrated such uncertainty estimation on DMA as an example. The Tc values after varying theKH values at 298 K for the four amines are included in Table S2.
Note that among available data, there are also significant uncertainties in the temperature dependence of KH for amines. A systematic uncertainty analysis was difficult due to the lack of such literature data for most of the amines in our study, which could be a potential issue in the accurate determination ofTc values. However, for the five amines with available alternative temperature dependence coefficients ofKH ,6 the uncertainties inTc values caused by the alternative coefficients are within 3%.