## 4 Validation of Model; Discussing and Comparing the Model With Experimental Data
It is worth to note that presented in aforementioned paper experimental data show that the presence of molecules of CO2 in the system can lead to a decrease in the permeance of H2 molecules in the GO membrane in comparison with diffusion only H2 molecules (without the presence of CO2 molecules). This effect can be explained by the influence of strongly adsorbed CO2 molecules on the scattering of weakly adsorbed H2 molecules. The fraction of diffusely scattered H2 molecules \(f_{\rm H}\) can be estimated as \(f_{\rm H}=\)\(f_{1}(1-\theta_{\rm C})+f_{2}\theta_{\rm C}=\theta_{\rm C}(f_{2}-f_{1})+f_{1}\)[20], where \(f_{1}\) is the fraction of diffusely scattered H2 molecules on a part of the surface not occupied by adsorbed CO2 molecules, \(f_{2}\) is the fraction of diffusely scattered H2 molecules on a part of the surface occupied by adsorbed molecules of CO2, \(\theta_{\rm C}\) is the surface coverage by molecules of CO2 of the pore walls. Let us consider for simplicity the case when the parameter \(\gamma_{\rm i}\) in Equation (17) is much less than the value of \(\psi_{\rm i}\) and the effect of surface diffusion on mass transfer through the slit-like pore can be neglected (in particular this can take place for molecules H2 due to small values of the adsorption energy and sticking coefficient for these molecules). In this case, the value of \(W_{\rm H}=\)\(J_{\rm H}\)/\(J_{\rm H,Kn}\), where \(J_{\rm H}\) is the flux of molecules H2 passing through the slit-like pore, \(J_{\rm H,Kn}\) is the flux of H2 molecules passing through the pore in accordance with the classic Knudsen equation, is given by  
\[W_{\rm H}=\psi_{\rm H}=\frac{2-f_{\rm H}}{f_{\rm H}}=\frac{2-[\theta_{\rm C}( f_{2}-f_{1})+f_{1}]}{\theta_{\rm C}(f_{2}-f_{1})+f_{1}}. \tag{18}\]  
Figure 2 shows the dependence of \(W_{\rm H}\) on \(\theta_{\rm C}\) at \(f_{1}\) = 0.2 for different values of \(f_{2}\). It is seen from Figure 2 that the value of \(J_{\rm H}\) decreases with an increase in \(f_{2}\) and \(\theta_{\rm C}\). Figure 3 shows the dependence of \(W_{\rm H}\) on \(f_{1}\) for different values of \(\theta_{\rm C}\) at \(f_{2}\) = 1. It is seen from Figure 3 that the value of \(W_{\rm H}\) increases with a decrease in \(f_{1}\). Taking into account [20; 26] and aforementioned assumptions, we can write the following equation for the permeance \(F_{\rm H}\) for H2 molecules passing through the GO membrane by aforementioned pathway A in the presence of adsorbed molecules of CO2 on the walls of the slit-like pores:  
\[F_{\rm H}=\left(\frac{1}{L}\right)\left(\frac{H^{\prime}\
u_{\rm H}\varepsilon [2-\theta_{\rm C}(f_{2}-f_{1})-f_{1}]}{3 RT\varepsilon[\theta_{\rm C}(f_{2}-f_ {1})+f_{1})]}\right), \tag{19}\]where \(L\) is the GO membrane thickness, \(H^{\prime}\) is the mean value of \(H\) for slit-like pores, \(v_{\rm H}\) is the mean thermal velocity of molecules of H\({}_{2}\), \(R\) is the gas constant, while \(\varepsilon\) and \(\xi\) are the porosity and tortuosity for the aforementioned pathway A in the GO membrane. Let us consider the correlation between the experimental results for permeance of H\({}_{2}\) in the GO membrane from reference [12] and the results obtained on the basis of the proposed model. It is worth to note that the aforementioned correlation can be made only qualitatively. This is related to the fact that in the description of experimental results in the above-mentioned paper do not participate parameters characterizing the interaction of gas molecules with the pore walls but in the approach used in the present paper the aforementioned parameters play an essential (in some cases the main) role. It is seen from Figure 2 in the above-mentioned paper that the permeance of weakly adsorbed molecules of pure H\({}_{2}\) can be relatively far above the data which correspond to the classic Knudsen diffusion. The similar dependence for the permeance of pure H\({}_{2}\) (when \(\theta_{\rm C}=0\)) follows from Equation (19) of the present paper in \(f_{1}<1\).