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%.