Phosphate modified ordered mesoporous carbon (MOMC-NP) has been synthesized and proven to be an effective adsorbent for Pb(II) removal from aqueous solutions. However, the key application components of the mass transfer operations and diffusion coefficient have not been determined. In this study, a modified Finite Bath Diffusion Control Model was mathematically developed containing a constant related to the radius of the adsorbent particle and the fractional attainment of adsorption. The adsorption experiments were conducted under various initial Pb(II) concentrations ranging from 60 mg L⁻¹ to 100 mg L⁻¹. The results suggested that the modified Finite Bath Diffusion Control Model was more applicable to the experimental data than the original Finite Bath Diffusion Control Model. The average value of the diffusion coefficient ($\lambda \overline{D}$) obtained from the modified finite bath diffusion control model was 1.63 × 10⁻² cm² s⁻¹ indicating the effective diffusivity in the adsorption of Pb(II) on MOMC-NP. Overall, the modified Finite Bath Diffusion Control Model exhibited the precise description and simulation of the mass transfer kinetics for Pb(II) adsorption onto MOMC-NP. Therefore, the modified Finite Bath Diffusion Control Model could be effectively used to investigate the mass transfer kinetics of the adsorption process.

合成了磷酸盐改性的有序介孔碳（MOMC-NP），并被证明是从水溶液中去除Pb（II）的有效吸附剂。但是，尚未确定传质操作和扩散系数的关键应用成分。在这项研究中，用数学方法开发了一种改进的有限浴扩散控制模型，该模型包含一个与吸附剂颗粒的半径和部分吸附率有关的常数。在60 mg L ^-1至100 mg L ^-1的各种初始Pb（II）浓度下进行吸附实验。结果表明，改进的有限浴扩散控制模型比原始有限浴扩散控制模型更适用于实验数据。扩散系数的平均值（$\lambda \overline{d}$从改进的有限浴扩散控制模型获得的）为1.63×10 ^-2  cm ²  s ^-1，表明Pb（II）在MOMC-NP上的吸附有效扩散率。总体而言，改进的有限浴扩散控制模型展示了Pb（II）吸附到MOMC-NP上的传质动力学的精确描述和模拟。因此，改进的有限浴扩散控制模型可以有效地用于研究吸附过程的传质动力学。