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Chemical equilibrium constants

https://doi.org/10.1039/C9RA00164F

In order to accurately predict the enthalpy change of each reaction, it is important to obtain accurate chemical equilibrium constants. According to eqn (8), the enthalpy change for each individual reaction ((R1)–(R7)) is directly related to the equilibrium constant. The chemical equilibrium constants can be found on mole fraction basis and/or molality basis. In this paper mole fraction basis is used. However, some equilibrium constants available in literature are on molality basis. In this case, unit conversion is done using eqn (18)ln Km = ln Kx + Δn ln(55.51)(18)where Km is the molality based equilibrium constant; Kx is the mole fraction based equilibrium constant; Δn is the change in moles across the equation excluding water and solid. In this study, the protonation of NH3(R4) is taken as an example to explain the choice of the equilibrium constants. The similar method is applied for the other reactions. The equilibrium constants available in literature are listed in Table 2.

Table 2 References for choosing chemical equilibrium constants of reactions (R1)–(R7)
Reaction no. Parameter References
(R1) K1 Austgen et al.,48 Weiland et al.,41 Pazuki et al.,49 Beutier and Renon50
(R2) K2 Austgen et al.,48 Pazuki et al.,49 Beutier and Renon,50 Oscarson et al.51
(R3) K3 Austgen et al.,48 Oscarson et al.,51 Weiland et al.41
(R4) K4 Edwards et al.,52 Kawazuishi and Prausnitz,53 Clegg and Brimblecombe,54 Pazuki et al.,49 Aspen Plus
(R5) K5 Edwards et al.,52 Kawazuishi and Prausnitz,53 Pazuki et al.,49 Beutier and Renon,50 Aspen Plus
(R6) K6 Aspen Plus
(R7) kH Austgen et al.,48 Oscarson et al.,51 Que and Chen,55 Kawazuishi and Prausnitz,53 Pazuki et al.49

2.3.1 Chemical equilibrium constant for NH3 protonation (R4)

 

Comparing the chemical equilibrium constants from different sources, the one given by Edwards et al.52 is chosen for NH3 protonation (R4) in the current study. Fig. 2(a) shows the equilibrium constants for NH3 protonation (R4), in which ln K4 is given by Edwards et al.,52 Kawazuishi and Prausnitz,53 Pazuki et al.,49 Clegg and Brimblecombe,54 and Aspen Plus (V7.2). The corresponding enthalpy change, −ΔHNH3, calculated by eqn (8) are shown in Fig. 2(b) and compared with the experimental data reported by Bates and Pinching.56 All equilibrium constants has similar values and tendency except that reported by Pazuki et al.49 at different temperatures. In Fig. 2(b), the corresponding enthalpy change calculated by Edwards et al.52 and Aspen Plus (V7.2) have the same values. The enthalpy change calculated by Kawazuishi and Prausnitz53 and Pazuki et al.49 have similar values as well. However, the enthalpy change predicted by Clegg and Brimblecombe54 has little difference with the others’. Besides, the prediction of enthalpy change by Edwards et al.52 is the closest to the experimental data. It should be noted that Edwards et al.52 and Aspen Plus predict the same values. The black solid line overlaps with the red dotted line in Fig. 2; therefore, only four curves are seen in Fig. 2. The similar method is applied to other reactions. The default equilibrium constant from Aspen Plus (V7.2) databank is used for NH4HCO3(s) formation (R6). The constants C1C2C3 and C4 for each reaction are summarized in Table 3. One may notice that the values of the parameters for the CO32−(R3), NH3(R4) and NH2COO formation (R5) in this paper are different from those in the original references, because they are converted using eqn (18) to mole fraction basis.

Fig. 2 (a) ln K4 and (b) corresponding −ΔHNH3 as a function of temperature for NH3 protonation in the water (R4).
Table 3 Chemical equilibrium constants and Henry’s constant for reactions (R1)–(R7)
Reaction no. Parameters C1 C2 C3 C4 Sources
(R1) K1 132.90 −13445.90 −22.48 0.00 Austgen et al.48a
(R2) K2 231.47 −12092.10 −36.78 0.00 Austgen et al.48a
(R3) K3 216.05 −12431.70 −35.48 0.00 Oscarson et al.51b
(R4) K4 −1.26 −3335.70 1.50 −0.03706 Edwards et al.52b
(R5) K5 −4.58 2900.00 0.00 0.00 Edwards et al.52b
(R6) K6 554.82 −22442.53 −89.01 0.06473 Aspen Plusa
(R7) kH 170.71 −8477.71 −21.96 0.00578 Aspen Plusa
a Mole fraction based chemical equilibrium constants in references mentioned. b Molality based equilibrium constants in references mentioned.

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