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## Two-Parameter Data Fitting Method for the Curve of Surface Tension and Concentration with Origin Software

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 基金资助: 国家基础科学人才培养基金.  J1103306

 Fund supported: 国家基础科学人才培养基金.  J1103306

Abstract

A two-parameter data fitting method for classical surface tension experiment with Origin software was introduced.The method is not only more rigorous, but also easier for study and use; thus it is suitable for innovation of chemistry laboratory and computer aided design (CAD) teaching.

Keywords： Surface tension ; Physical chemistry experiment ; Two-parameter data fitting method ; Origin software

GAN Quan, DU Yuan, LEI Hang, YAN Xiao-Qi. Two-Parameter Data Fitting Method for the Curve of Surface Tension and Concentration with Origin Software. University Chemistry[J], 2016, 31(11): 97-100 doi:10.3866/PKU.DXHX201603023

## 1 输入实验数据

 c/(mol·L-1) Δp1/Pa Δp2/Pa Δp3/ Pa \begin{document}$\overline {\Delta p} /{\rm{Pa}}$\end{document} σ/(N∙m-1) 0 588 570 575 577.7 0.07118 0.020 552 562 559 557.7 0.06872 0.050 509 509 510 509.3 0.06276 0.100 449 450 447 448.7 0.05528 0.200 383 383 387 382.3 0.04711 0.300 344 341 347 344.0 0.04234 0.400 312 313 310 311.7 0.03840 0.500 282 283 284 283.0 0.03487

## 2 σ和c关系的推导

$\mathit{\Gamma = - }\frac{c}{{RT}}{\left( {\frac{{{\rm{d}}\sigma }}{{{\rm{d}}c}}} \right)_T}$

$\mathit{\Gamma } = {\mathit{\Gamma }_\infty }\frac{{Kc}}{{1 + Kc}}$

${\rm{d}}\sigma = - RT\frac{{K{\mathit{\Gamma }_\infty }}}{{1 + Kc}}{\rm{d}}$

## 3 自定义函数进行拟合

1) 单击菜单栏中的Analysis选项，选择Fitting，选择Nonlinear curve fit，选择Open Dialog…(或直接按Ctrl+Y打开) NLFit ()窗口，如图1所示。

### 图1

2) 点击Create New Fitting Function按钮，在Function Name栏输入函数名称。单击Next，在Parameters栏中输入T, S, A, B；在Constants栏中输入R。单击Next。

3) 在Parameters栏中勾选T和S参数的Fix方框，在Constant栏中将R值定为8.3144621。在Function Body栏中输入S-R*T*A*ln (1+B*x)，如图2所示。

### 图2

4) 在之后的设置页中点击Next，直到设置完成。

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