## 3 Results and Discussion
### Uptake Experiment
The oxidation of mercury with sulfuric acid, which contradicts to the activity series, has been studied for a long time. The overall oxidation mechanism has been postulated as follows [18]:  
\[Hg^{0}+2H_{2}SO_{4}=~{}HgSO_{4}+~{}SO_{2}+2H_{2}O\]Figure 4: Concentration of dissolved oxidized mercury (Hg\({}^{2+}\)aq) in a variety of uptake solutions as a function of the exposure time to the standard gas of 101–153 ng m\({}^{-3}\) gaseous elemental mercury. The gray horizontal lines shown in each plot are for the lowest and highest equilibrated concentrations of Hg\({}^{0}\)aq, according to [PERSON]’s law, estimated through the use of the temperature and GEM concentrations provided in Table 2 and [PERSON]’s constants in the literature [7] The linear regressions are also shown in the figures, and the uncertainties shown for each regression are standard errors. The lowest \(\text{Hg}^{2+}\)aq concentration data point in the seawater plot is below the detection limit. Figure 3: Concentration of dissolved elemental mercury (Hg\({}^{0}\)aq) in the variety of uptake solutions as a function of the exposure time to the standard gas of 101–153 ng m\({}^{-3}\) gaseous elemental mercury. The gray horizontal lines shown in each plot are for the lowest and highest equilibrated concentrations of Hg\({}^{0}\)aq, according to [PERSON]’s law, estimated with the use of the temperature and GEM concentrations provided in Table 2 and [PERSON]’s constants in the literature (7). Linear regressions are also shown in the figures, and the uncertainties shown for each regression are standard errors. [PERSON] et al. [19] studied the oxidation mechanism of mercury with sulfuric acid. They confirmed the enhancement of GEM uptake by activated carbon coated with sulfuric acid. However, their free energy calculation results showed that the reaction above is not spontaneous. To the best of our knowledge, the oxidation mechanism of Hg\({}^{0}_{\text{aq}}\) by sulfuric acid (particularly in a dilute sulfuric acid solution) has not been elucidated yet. The transport processes of GEM in the bulk liquid phase are depicted in Figure 5. A similar illustration with different gaseous reactants has been presented in many publications [16]. Under our experimental conditions, the GEM concentration change from before exposure to the solution to after exposure was very small and insignificant. To have an idea of whether the GEM already reached equilibrium in the four hours of exposure, the concentration of Hg\({}^{0}_{\text{aq}}\) diffused at the bottom of the solution was estimated. According to [PERSON] [9], the diffusion coefficient for Hg\({}^{0}_{\text{aq}}\) in fresh water at 298 K is 1.7 \(\times\) 10\({}^{-5}\) cm\({}^{2}\) s\({}^{-1}\). Using this value, together with an arbitrary concentration of Hg\({}^{0}_{\text{aq}}\) at the surface and a surface area of 500 cm\({}^{2}\), only 9% of the Hg\({}^{0}_{\text{aq}}\) reached to the bottom of the solution, and it took nearly 24 h to have a uniform concentration throughout the solution, suggesting the condition was not at equilibrium in our experiments. The fact that the concentrations of Hg\({}^{2+}_{\text{aq}}\) exceeded the equilibrium in the dilute sulfuric acid solution was likely due to the reactive uptake. The experimental uptake coefficient \(\gamma_{\text{meas}}\) (the total number of atoms of THg\({}_{\text{aq}}\) found in the solution divided by the total number of GEM collisions at the solution's surface) for the dilute sulfuric acid solutions was determined by the following equation:  
\[\gamma_{\text{meas}}=\frac{N_{THg\text{aq}}}{\frac{ACN_{\text{GEM}}}{4}}\]  
where \(N_{THg\text{aq}}\), \(A\), \(\ell\), and \(N_{GEM}\) are the total number of THg\({}_{\text{aq}}\) atoms in the solution, the surface area of the solution, the mean atomic speed of GEM and the number density of GEM atoms in the gas phase, respectively. The denominator of the equation indicates the total number of collisions of GEM atoms at the solution's surface.