The table below presents the adsorption data of $\mathrm{AuCl_4^-}$ at different concentrations on the surface of a certain material under the same temperature, which can be used to evaluate the interactions between adsorbed species on the material surface.  

| $c$ /(mmol/L) | $q _ { \mathrm { e } }$ / (mmol $\mathrm{AuCl_4^-}$/g material) |  
|------|------|  
| 0.114 | 5.706 |  
| 0.205 | 6.935 |  
| 0.310 | 7.595 |  
| 0.405 | 7.921 |  

Two commonly used models are the Langmuir model and the Freundlich model. In these models, the relationship between the equilibrium adsorption capacity $q _ { \mathrm { e } }$ and the concentration $\boldsymbol { \mathscr { c } }$ of the species to be adsorbed in the solution (i.e., the adsorption isotherm) is given as follows (where $q _ { \mathrm { m } }$ represents the maximum adsorption capacity per unit mass of the material surface, $K _ { \mathrm { L } }$ and $K _ { \mathrm { f } }$ are the equilibrium constants of the adsorption process, and $n$ is a related parameter):  

Langmuir model:  

$q _ { \mathrm { e } } { = }  q _ { \mathrm { m } } K _ { \mathrm { L } } c  / ( 1 { + } K _ { \mathrm { L } } c ) ^ {  }$  

Freundlich model:  

${ q _ { \mathrm { e } } = K _ { \mathrm { f } } c ^ { 1 / n  }}$  

By analyzing the fitting results of different adsorption models, select the correct statement from the following options.
下表给出了相同温度下、不同浓度$\mathrm{AuCl_4^-}$在某材料表面的吸附数据，其可用于判断材料表面吸附物种之间的相互作用情况。

| $c$ /(mmol/L) | $q _ { \mathrm { e } }$ / (mmol $\mathrm{AuCl_4^-}$/g材料) |
|------|------|
| 0.114 | 5.706 |
| 0.205 | 6.935 |
| 0.310 | 7.595 |
| 0.405 | 7.921 |

常用的两种模型是Langmuir模型和Freundlich模型，在这两种模型中，平衡状态吸附量 $q _ { \mathrm { e }}$与溶液中待吸附物种的浓度 $\boldsymbol { \mathscr { c } }$ 的关系(即吸附等温式)分别为 $( q _ { \mathrm { m } }$ 表示单位质量材料表面的最大吸附量， $K _ { \mathrm { L } }$ 、 $K _ { \mathrm { f } }$ 为吸附过程的平衡常数， $n$ 为相关参数)：

Langmuir 模型： 

$q _ { \mathrm { e } } { = }  q _ { \mathrm { m } } K _ { \mathrm { L } } c  / ( 1 { + } K _ { \mathrm { L } } c ) ^ {  }$

Freundlich模型： 

${ q _ { \mathrm { e } } = K _ { \mathrm { f } } c ^ { 1 / n  }}$

分析不同吸附模型的拟合结果，选出下列选项中正确的说法。
The interaction between $\mathrm{Au}$ species adsorbed on the material surface is negligible, and the equilibrium constant for the adsorption process is 8.
The interactions between adsorbed $\mathrm{Au}$ species on the material surface are negligible, and the equilibrium constant for the adsorption process is 14.
The interaction between $\mathrm{Au}$ species adsorbed on the material surface cannot be ignored, and the equilibrium constant for the adsorption process is 8.
The interaction between $\mathrm{Au}$ species adsorbed on the material surface cannot be neglected, and the equilibrium constant for the adsorption process is 14.
The interaction between $\mathrm{Au}$ species adsorbed on the material surface is negligible. According to the expression, the maximum adsorption capacity (in terms of $\mathrm{Au}$) is calculated to be 1800 mg $\mathrm{Au}$ / g material.
The interaction between adsorbed $\mathrm{Au}$ species on the material surface is negligible, and the maximum adsorption capacity (calculated in terms of $\mathrm{Au}$) derived from the expression is 1600 mg $\mathrm{Au}$ / g material.
The interaction between $\mathrm{Au}$ species adsorbed on the material surface cannot be neglected. The maximum adsorption capacity (calculated based on $\mathrm{Au}$ content) derived from the expression is 1800 mg $\mathrm{Au}$ / g material.
The interaction between $\mathrm{Au}$ species adsorbed on the material surface cannot be ignored. The maximum adsorption capacity (calculated in terms of $\mathrm{Au}$) obtained from the expression is 1600 mg $\mathrm{Au}$ / g material.
在材料表面吸附的$\mathrm{Au}$物种之间的相互作用可忽略，吸附过程的平衡常数为10。
在材料表面吸附的$\mathrm{Au}$物种之间的相互作用可忽略，吸附过程的平衡常数为14。
在材料表面吸附的$\mathrm{Au}$物种之间的相互作用不可忽略，吸附过程的平衡常数为10。
在材料表面吸附的$\mathrm{Au}$物种之间的相互作用不可忽略，吸附过程的平衡常数为14。
在材料表面吸附的$\mathrm{Au}$物种之间的相互作用可忽略，根据表达式求出的最大吸附量（以 $\mathrm{Au}$ 计）为1800 mg $\mathrm{Au}$ / g材料。
在材料表面吸附的$\mathrm{Au}$物种之间的相互作用可忽略，根据表达式求出的最大吸附量（以 $\mathrm{Au}$ 计）为1600 mg $\mathrm{Au}$ / g材料。
在材料表面吸附的$\mathrm{Au}$物种之间的相互作用不可忽略，根据表达式求出的最大吸附量（以 $\mathrm{Au}$ 计）为1800 mg $\mathrm{Au}$ / g材料。
在材料表面吸附的$\mathrm{Au}$物种之间的相互作用不可忽略，根据表达式求出的最大吸附量（以 $\mathrm{Au}$ 计）为1600 mg $\mathrm{Au}$ / g材料。
First, the Langmuir model is discussed. By rearranging the adsorption isotherm equation, we obtain:

$1 /  q _ { \mathbb { e } } = 1  /  ( q _ { \mathrm { m } } K _ { \mathrm { L } } c )    +  1  /  q _ { \mathrm { m } }$  

<Checkpoint>[$1 /  q _ { \mathbb { e } } = 1  /  ( q _ { \mathrm { m } } K _ { \mathrm { L } } c )    +  1  /  q _ { \mathrm { m } }$  ](1)</Checkpoint>

Thus, by performing linear regression with $1 /  c$ as the independent variable and $1  / q _ { \mathrm { e } }$ as the dependent variable, we obtain:

$1 /  q _ { \mathbb { e } } = 0.0078(1  /   c)     +  0.1066(R^2=0.99986)$

<Checkpoint>[$1 /  q _ { \mathbb { e } } = 0.0078(1  /   c)     +  0.1066(R^2=0.99986)$](1)</Checkpoint>

Next, the Freundlich model is discussed. By rearranging the adsorption isotherm equation, we obtain:

$\mathrm{ln}q _ { \mathbb { e } } = \mathrm{ln}K_f+(1/n)\mathrm{ln}c$

<Checkpoint>[$\mathrm{ln}q _ { \mathbb { e } } = \mathrm{ln}K_f+(1/n)\mathrm{ln}c$](1)</Checkpoint>

By performing linear regression with $\ln c$ as the independent variable and $\mathrm{ln} { q _ { \mathrm { e } } }$ as the dependent variable, we obtain:

$\mathrm{ln}q _ { \mathbb { e } } =2.32+0.26\mathrm{ln}c(R^2=0.98927)$

<Checkpoint>[$\mathrm{ln}q _ { \mathbb { e } } =2.32+0.26\mathrm{ln}c(R^2=0.98927)$](1)</Checkpoint>

Therefore, based on the fitted $R^2$ values, the adsorption of $\mathrm{AuCl_4^-}$ is more consistent with the Langmuir model, indicating that the adsorbed $\mathrm{Au}$ species form a monolayer with negligible interactions. Thus, options C, D, G, and H are incorrect.

<Checkpoint>[The interactions between adsorbed $\mathrm{Au}$ species on the material surface are negligible](1)</Checkpoint>

The corresponding saturation adsorption capacity can be calculated from the intercept:

$q _ { \mathrm { m }}=1/0.1066=9.381  \mathrm{mmol}$ $\mathrm{AuCl_4^-}$/g material

Converting this to mass yields the maximum adsorption capacity (in terms of $\mathrm{Au}$) as 1848 mg $\mathrm{Au}$ / g material. Thus, option B is correct.

<Checkpoint>[The saturation adsorption capacity can be calculated from the intercept](1)</Checkpoint>

<Checkpoint>[The maximum adsorption capacity (in terms of $\mathrm{Au}$) is 1848 mg $\mathrm{Au}$ / g material](1)</Checkpoint>

The equilibrium constant of the adsorption process can be calculated from the ratio of the intercept to the slope:

$K _ { \mathrm { L } }=0.1066/0.0078=14$

<Checkpoint>[The saturation adsorption capacity can be calculated from the ratio of the intercept to the slope](1)</Checkpoint>

<Checkpoint>[$K _ { \mathrm { L } }=0.1066/0.0078=14$](1)</Checkpoint>

Therefore, the correct answer is B.
首先讨论Langmuir模型，对吸附等温式进行整理可得： 

$1 /  q _ { \mathbb { e } } = 1  /  ( q _ { \mathrm { m } } K _ { \mathrm { L } } c )    +  1  /  q _ { \mathrm { m } }$  

<Checkpoint>[$1 /  q _ { \mathbb { e } } = 1  /  ( q _ { \mathrm { m } } K _ { \mathrm { L } } c )    +  1  /  q _ { \mathrm { m } }$  ](1)</Checkpoint>

因此以 $1 /  c$ 为自变量， $1  / q _ { \mathrm { e } }$ 为因变量进行线性拟合可得：

$1 /  q _ { \mathbb { e } } = 0.0078(1  /   c)     +  0.1066(R^2=0.99986)$

<Checkpoint>[$1 /  q _ { \mathbb { e } } = 0.0078(1  /   c)     +  0.1066(R^2=0.99986)$](1)</Checkpoint>

再讨论Freundlich模型，对吸附等温式进行整理可得：

$\mathrm{ln}q _ { \mathbb { e } } = \mathrm{ln}K_f+(1/n)\mathrm{ln}c$

<Checkpoint>[$\mathrm{ln}q _ { \mathbb { e } } = \mathrm{ln}K_f+(1/n)\mathrm{ln}c$](1)</Checkpoint>

以 $\ln c$ 为自变量、 $\mathrm{ln} { q _ { \mathrm { e } } }$ 为因变量进行线性拟合可得：

$\mathrm{ln}q _ { \mathbb { e } } =2.32+0.26\mathrm{ln}c(R^2=0.98927)$

<Checkpoint>[$\mathrm{ln}q _ { \mathbb { e } } =2.32+0.26\mathrm{ln}c(R^2=0.98927)$](1)</Checkpoint>

因此根据拟合所得的$R^2$值，相比之下$\mathrm{AuCl_4^-}$的吸附更符合Langmuir模型，即吸附的$\mathrm{Au}$物种形成单分子层、无显著的相互作用，相互作用可忽略，因此选项C、D、G、H有误。

<Checkpoint>[在材料表面吸附的$\mathrm{Au}$物种之间的相互作用可忽略](1)</Checkpoint>

对应的饱和吸附量可由截距计算：

$q _ { \mathrm { m }}=1/0.1066=9.381  \mathrm{mmol}$ $\mathrm{AuCl_4^-}$/g材料

换算成质量可得最大吸附量（以 $\mathrm{Au}$ 计）为1848 mg $\mathrm{Au}$ / g材料，因此选项B正确。

<Checkpoint>[饱和吸附量可由截距计算](1)</Checkpoint>

<Checkpoint>[最大吸附量（以 $\mathrm{Au}$ 计）为1848 mg $\mathrm{Au}$ / g材料](1)</Checkpoint>

吸附过程的平衡常数可由截距与斜率的比值计算：

$K _ { \mathrm { L } }=0.1066/0.0078=14$

<Checkpoint>[饱和吸附量可由截距与斜率的比值计算](1)</Checkpoint>

<Checkpoint>[$K _ { \mathrm { L } }=0.1066/0.0078=14$](1)</Checkpoint>

因此正确答案是B。