To characterize the reaction kinetics at the gas-solution interface, here we consider the physical and chemical processes of CO

_{2} mass transfer from gas phase to solution. After transporting CO

_{2} into solution, three reactions can promote the transformation of molecular CO

_{2}(aq) to

${\mathrm{HCO}}_{3}^{-}$ (Equations (1)–(3)). Since the concentration of water is a constant, and the solution pH is fixed, the reaction rates of Equations (1) and (2) should be constant, i.e., CO

_{2} absorption rate should be stable in a pH-controlled NaOH solution (experiment X,

Figure 3a and

Figure 4a). In contrast, CO

_{2} absorption rates in NH

_{3} solutions exhibit an increasing trend even with a fixed solution pH. The enhanced CO

_{2} absorption rates in NaOH versus NH

_{3} solutions can be explained by the promotion of reaction kinetics, as shown by Equation (3), likely as the result of an increasing concentration of NH

_{3}(aq) (

Figure 6c).

To link the CO

_{2} absorption rate to reaction kinetics, a “two-film” model is adopted to describe the mass transfer process.

Figure 7 illustrates the concept of this model. In essence, the diffusion film on the gas side and the solution side determine the efficiency of mass transfer. In this framework, the rate of CO

_{2} absorption (

${\phi}_{{\mathrm{CO}}_{2}}$) can be written as:

and

where

$\Delta {P}_{{\mathrm{CO}}_{2}}$ is the pressure gradient of CO

_{2} from bulk gas phase to bulk solution, and

${k}_{ov}$ is the overall mass transfer coefficient.

${k}_{ov}$ consisted of a gas-side (

${k}_{g}$) and solution-side (

${k}_{l}$) mass transfer coefficient, and their reciprocal forms represent mass transfer resistance at the gas side and solution side, respectively (Equation (21)). The magnitude of

${k}_{g}$ is determined by fluid properties of the gas phase, which has been calibrated by previous studies [

57]. In the two-film model, an enhancement factor (E) is used to describe the mass transfer accelerated by a chemical reaction on the solution side (i.e., the solution-side mass transfer coefficient with reactions (

${k}_{l}$) versus physical mass transfer coefficient with no chemical reaction (

${k}_{l}^{0}$)). Methods to calculate

${k}_{l}^{0}$ can be found elsewhere [

40].

Table 3 lists the experimental results of the enhancement factor (

${\mathrm{E}}_{exp}$) at different sampling times. To link reaction kinetics to E, two additional parameters, the Hatta modulus (

${\mathrm{M}}_{\mathrm{H}}^{2}$) and an enhancement factor for an infinitely fast reaction (

${\mathrm{E}}_{i}$), are introduced below:

where

${D}_{{\mathrm{CO}}_{2},\mathrm{L}}$ is the diffusion coefficient of CO

_{2} in the liquid phase,

${D}_{{\mathrm{NH}}_{3},\mathrm{L}}$ and

${C}_{{\mathrm{NH}}_{3}}$ are the diffusion coefficient and the bulk concentration of ammonia in the liquid phase, respectively, and

${P}_{{\mathrm{CO}}_{2}}^{int}$ is the partial pressure of CO

_{2} in the liquid phase at the gas-liquid interface. Although,

${D}_{{\mathrm{CO}}_{2},\mathrm{L}}$ and

${D}_{{\mathrm{NH}}_{3},\mathrm{L}}$ are inversely proportional to solution viscosity (i.e., the Stokes–Einstein equation), which is a function of solution composition and temperature. The diffusion coefficient of CO

_{2} and NH

_{3} in water at 25 °C is used as approximation of diffusion in NH

_{3}–MgCl

_{2} solutions due to the limited concentration effect on viscosity [

70]. To calculate the theoretical enhancement factor (

${\mathrm{E}}_{cal}$), we refer to an explicit approximate expression [

71]:

Since Equations (22)–(25) only contain one variable

${k}_{app}$, one can fit

${\mathrm{E}}_{cal}$ to

${\mathrm{E}}_{exp}$ by tuning this parameter. Fitting results show that

${\mathrm{E}}_{exp}$ can be reproduced satisfactorily using the models built above (

Figure 8), but notable deviations exist when

${\mathrm{E}}_{exp}$ is larger than 4.

Table 4 shows the fitted

${k}_{app}$ value together with the values compiled from other studies. The

${k}_{app}$ value obtained in this work is similar to but slightly higher than in earlier studies conducted at relatively low NH

_{3} concentrations [

62,

72]. Concerning the deviations in

Figure 8a, it should be noted that we assume a constant

${k}_{app}$ in the fitting; in reality, however,

${k}_{app}$ may vary when conditions change. Specifically, due to accelerated deprotonating (Equation (8)), the overall rate constant between CO

_{2} and NH

_{3} (Equation (11)) is expected to correlate positively with the NH

_{3} concentration. Thus,

${k}_{app}$ should increase with NH

_{3} concentration. Such dependency is also shown by the observation of greater

${k}_{app}$ under higher NH

_{3} concentrations in previous work [

40,

73] (

Table 4).

The intercept and slope of Equation (26) are obtained through fitting

${\mathrm{E}}_{cal}$ to

${\mathrm{E}}_{exp}$ With this correction, the fit between

${\mathrm{E}}_{exp}$ and

${\mathrm{E}}_{cal}$ is significantly improved (with a smaller sum of squared errors, or SSE), especially when

${\mathrm{E}}_{exp}>4$ (

Figure 8). Notably, the linear form of Equation (26) is similar to the rate constant expression of Equation (3) developed within a “termolecular mechanism” frame, where the initial product is not zwitterions but a loosely bounded termolecular complex involving CO

_{2}, ammonia, and base molecules [

73,

74,

75].