Water Activities and Osmotic Coefficients of Aqueous Solutions of Five Alkylaminium Sulfates and Their Mixtures with H₂SO₄ at 25^oC

Figures & data

FIG. 1. Experimentally determined stoichiometric osmotic coefficients (φ_st) plotted against the square root of the total sulfate molality (mSO₄²⁻), for aqueous mixtures of two aminium sulfates with H₂SO₄, at three different aminium:sulfate molar ratios (noted on the plots). Different symbols are used for each ratio. The solid line shows values for aqueous (NH₄)₂SO₄ (Clegg et al. 1995), and the dashed line aqueous H₂SO₄ (Clegg and Brimblecombe 1995). (a) Methylaminium sulfate (MAS). (b) Dimethylaminium sulfate (DMAS). Uncertainties in φ_st resulting from the H₂SO₄ titration, as well as the IC and a_w Measurements as propagated through the calculations, are displayed on the vertical dimension unless they are smaller than the symbols.

FIG. 2. Aminium sulfate (m_salt) and H₂SO₄ molalities (m_acid) in the mixtures, interpolated for fixed water activities from 0.65 to 0.95 (indicated on the plots). Symbols: values from Table S2. Lines: calculated using the fitted extended ZSR model (Equation (3)) using coefficients from Table 1. (a) MAS. (b) EAS. (c) DMAS. (d) DEAS. (e) TMAS. (f) Molalities of aqueous (NH₄)₂SO₄–H₂SO₄ mixtures, calculated using the model of Clegg et al. (1998).

FIG. 3. The mass (kg) of water per mole of total solutes, at a water activity of 0.70, plotted against the dry mole fraction of aminium sulfate salt present (x_salt), from pure aqueous H₂SO₄ (x_salt = 0.0) to pure aqueous aminium sulfate (x_salt = 1.0). Symbols: open circle—interpolated values from Table S2; filled circle—pure aqueous H₂SO₄ from the work of Clegg and Brimblecombe (1995). Lines: calculated using the fitted extended ZSR model (Equation (3)) using coefficients from Table 1. (a) MAS. (b) EAS. (c) DMAS. (d) DEAS. (e) TMAS. Uncertainties are not shown because they are smaller than the sizes of the plotted symbols.

FIG. 4. Stoichiometric osmotic coefficients (φ_st) plotted against the square root of the total sulfate molality (mSO₄²⁻), for aqueous mixtures of all five aminium sulfates with H₂SO₄, at two different aminium:sulfate molar ratios (noted on the plots). Symbols: solid and shaded—experimental values and uncertainties (Table S1); open symbols—interpolated (Table S2). Lines: solid—from the fit of the extended ZSR model (Equation (3)), with coefficients listed in Table 1; dashed—these indicate the effects of the uncertainties in the fit of Equation (3). (a) MAS. (b) EAS. (c) DMAS. (d) DEAS. (e) TMAS. (f) Additional results for EAS and TMAS (as indicated) for ratios close to those shown in plots (b) and (e).

FIG. 5. Stoichiometric osmotic coefficients (φ_st) of aminium bisulfates (aminium:sulfate ratio 1:1) and aminium sulfates (ratio 2:1) plotted against the square root of total sulfate molality (mSO₄²⁻). Symbols: values, with uncertainties, calculated using the extended ZSR model (Equation (3)) with parameters listed in Table 1. Lines: values for aqueous NH₄HSO₄ (plot a) and (NH₄)₂SO₄ (plot b) calculated from the results of Clegg et al. (1998), and Clegg et al. (1995), respectively. The identities of the aminium salts in the mixtures are indicated on the plots. (a) Aqueous aminium bisulfates, and NH₄HSO₄. For clarity, the results for sulfates EAS to TMAS are offset vertically by the amounts indicated in parentheses on the plot. (b) Aqueous aminium sulfates, and (NH₄)₂SO₄.

FIG. 6. Comparison of water uptake by different aminium salts plotted as moles of water (nH₂O) per mole of salt against equilibrium relative humidity (RH, as a fraction). Symbols: circle—methylaminium; solid circle—ethylaminium; square—dimethylaminium; solid square—diethylaminium; triangle—trimethylaminium. (a) Sulfates (this study). Values for the points were calculated using the extended ZSR model (Equation (3)), with coefficients in Table 1. The lowest line on the plot is for aqueous (NH₄)₂SO₄ and was calculated using the results of Clegg et al. (1995). Other lines, for each aminium sulfate, were calculated using Equation (4) and the parameters in Table 2. (b) Sulfates (Clegg et al. 2013). The values for the points were taken from their Table 6. The line is for aqueous (NH₄)₂SO₄, the same as in (a). (c) Nitrates (Bonner 1981). The line is for aqueous NH₄NO₃, calculated using the results of Clegg et al. (1998). (d) Chlorides (Macaskill and Bates 1986). The line is for aqueous NH₄Cl, calculated using the equation of Liang and Chan (1997) and results of Myerson et al. (1996).

FIG. 7. Stoichiometric osmotic coefficients (φ_st) of the aqueous aminium sulfates, plotted against the square root of sulfate molality (mSO₄²⁻). Symbols: osmotic coefficients of each salt (as indicated on the plot) calculated using Equation (3) with the coefficients in Table 1. Lines: osmotic coefficients fitted using the ion interaction model (Equation (4)), and calculated using the parameters in Table 2. The uncertainties associated with the data points are omitted from this plot, but can be seen in Figure 5b.

TABLE 1 Parameters of the extended ZSR model (Equation (3)), at fixed water activities (a_w), for mixtures of aminium sulfate salts and H₂SO₄

aw			A^o
MAS
0.975	1.4725	1.5727 ± 0.2800	−0.769 ± 0.880
0.95	0.7904	0.8026 ± 0.0480	−0.593 ± 0.180
0.925	0.5641	0.5647 ± 0.0200	−0.516 ± 0.076
0.9	0.4496	0.4389 ± 0.0099	−0.430 ± 0.037
0.85	0.3312	0.3043 ± 0.0057	−0.330 ± 0.021
0.8	0.2682	0.2335 ± 0.0060	−0.278 ± 0.023
0.75	0.2276	0.1901 ± 0.0052	−0.250 ± 0.021
0.7	0.1984	0.1592 ± 0.0056	−0.238 ± 0.022
0.65	0.1759	0.1357 ± 0.0047	−0.226 ± 0.019
0.6	0.1578	0.1148 ± 0.0066	−0.208 ± 0.022
EAS
0.975	1.4725	1.6755 ± 0.0200	−0.765 ± 0.063
0.95	0.7904	0.8775 ± 0.0190	−0.615 ± 0.055
0.925	0.5641	0.6224 ± 0.0190	−0.526 ± 0.054
0.9	0.4496	0.4795 ± 0.0160	−0.438 ± 0.044
0.85	0.3312	0.3283 ± 0.0116	−0.353 ± 0.033
0.8	0.2682	0.2569 ± 0.0125	−0.331 ± 0.034
0.75	0.2276	0.2051 ± 0.0099	−0.296 ± 0.028
0.7	0.1984	0.1678 ± 0.0098	−0.266 ± 0.027
0.65	0.1759	0.1388 ± 0.0097	−0.249 ± 0.027
0.6	0.1578	0.1185 ± 0.0089	−0.232 ± 0.025
DMAS
0.95	0.7904	0.9017 ± 0.0330	−0.635 ± 0.120
0.925	0.5641	0.6586 ± 0.0130	−0.606 ± 0.055
0.9	0.4496	0.5250 ± 0.0100	−0.543 ± 0.042
0.85	0.3312	0.3796 ± 0.0083	−0.456 ± 0.032
0.8	0.2682	0.3014 ± 0.0059	−0.416 ± 0.023
0.75	0.2276	0.2505 ± 0.0048	−0.372 ± 0.020
0.7	0.1984	0.2139 ± 0.0054	−0.347 ± 0.021
0.65	0.1759	0.1861 ± 0.0046	−0.325 ± 0.019
DEAS
0.975	1.4725	1.9987 ± 0.1340	−1.528 ± 0.335
0.95	0.7904	1.0246 ± 0.0630	−0.948 ± 0.180
0.925	0.5641	0.7269 ± 0.0510	−0.740 ± 0.140
0.9	0.4496	0.5644 ± 0.0160	−0.607 ± 0.056
0.85	0.3312	0.4023 ± 0.0130	−0.493 ± 0.046
0.8	0.2682	0.3178 ± 0.0130	−0.445 ± 0.046
0.75	0.2276	0.2634 ± 0.0120	−0.406 ± 0.043
0.7	0.1984	0.2188 ± 0.0130	−0.373 ± 0.043
TMAS
0.975	1.4725	1.8522 ± 0.0620	−1.416 ± 0.220
0.95	0.7904	1.0241 ± 0.0140	−0.958 ± 0.044
0.925	0.5641	0.7553 ± 0.0140	−0.862 ± 0.041
0.9	0.4496	0.6082 ± 0.0190	−0.773 ± 0.056
0.85	0.3312	0.4432 ± 0.0200	−0.651 ± 0.058
0.8	0.2682	0.3582 ± 0.0150	−0.565 ± 0.043
0.75	0.2276	0.2988 ± 0.0120	−0.495 ± 0.035
0.7	0.1984	0.2592 ± 0.0110	−0.446 ± 0.032
0.65	0.1759	0.2234 ± 0.0100	−0.404 ± 0.029

TABLE 2 Fitted parameters of the ion interaction model (Equation (4)) for the aminium sulfate salts^a,b

	BMX	Ww,MX	Uw,MX	Vw,MX^c
MAS	−7.5248 ± 62.6909	−0.9172 ± 0.1226	4.5909 ± 0.3043	−4.0524
EAS	25.3847 ± 99.5183	−1.0045 ± 0.2158	4.5156 ± 0.5236	−2.3439
DMAS	−43.3109 ± 37.9502	−2.8277 ± 0.2547	6.8415 ± 0.4641	−6.2113
DEAS	44.6350 ± 140.0407	−2.5182 ± 1.5148	6.2800 ± 2.5315	−3.1156
TMAS	−94.4591 ± 124.0575	−4.2897 ± 1.4157	8.3745 ± 2.3377	−5.6426

^aValues of other coefficients and constants in the equation are: A_x = 2.917, α = 13.0, and ρ = 13.0. ^bParameter uncertainty at 90% confidence level. ^cThis parameter was constrained artificially and not fitted.

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