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如何绘制滴定曲线？

tag-icon • tag-icon tikz-pgf plot chemistry
如何绘制滴定曲线？

我正在尝试绘制酸碱滴定曲线，如下图所示：

滴定曲线

我画出了曲线，但我不知道如何画切线和\frac{\dd pH}{\dd V_b}，下面是我尝试画曲线：

\begin{center} 
\begin{tikzpicture}[ultra thick,scale=1]
\begin{axis}[ axis x line=bottom,axis y line = left, smooth,  minor  tick num=4,ymin=0,ymax=12,ultra thick, xlabel={$V_{B}$ ml},ylabel={pH }]
\addplot[smooth, black] coordinates {
(0,2) (2,2.1) (4,2.2) (6,2.3) (8,2.4) (10,2.5) (12,2.6) (14,2.7) (16,2.9) (18,3.3) (18.5,3.45)(19,3.6)
(19.5,4.2)(20,7)(20.5,9.3)(21,10)(21.5,10.3)(22,10.5)(24,10.9)(26,11)(28,11.1)(30,11.2)};
\end{axis}
\end{tikzpicture}
\end{center}

在此处输入图片描述

有没有什么方法可以画出两条切线、角平分线以及函数g(V_b)？

答案1

如果您想要更平滑的滴定曲线，您可以使用 查看我的答案tikz。35° 角作为切线效果很好。

\documentclass[border=5pt]{standalone}

\usepackage{tikz}
\usetikzlibrary{intersections}

\tikzset{%
    every pin/.style={font=\small, pin distance=5mm, inner sep=0pt},
    every pin edge/.style={draw=black, line width=0.5*\pgflinewidth},
    small dot/.style={fill=black, circle, scale=0.25}
}

\begin{document}
    \begin{tikzpicture}

%draw grid and axix with ticks 

        \draw[help lines, gray!25!white] (0,0) grid[step=0.5] (15,6);
        \draw[-stealth] (0,0) -- (0,6.5) node[above] {pH};
        \draw[-stealth] (0,0) -- (15.5,0) node[right] {$\mathrm{V_B~/~mL}$};
                
        \foreach [evaluate=\i as \n using (\i)*2] \i in {0,2.5,5,...,15} {
            \draw (\i,0) -- (\i,-0.125) node[below] {\n};
        }
        \foreach [evaluate=\i as \n using (\i)*2] \i in {0,1,...,6} {
            \draw (0,\i) -- (-0.125,\i) node[left] {\n};
        }

% draw titration curve
        
%       \draw [gray!50]  (0,1) -- (2,1.5) -- (8,2) -- (9,5) -- (15,6);
        \draw [black, name path=a] plot [smooth, tension=0.5] coordinates {(0,1) (2,1.5) (8,2) (9,5) (15,6)};

% draw second function g(VB)
        
%       \draw [gray!50]  (7,0) -- (8.25,0.1) -- (8.5,1) -- (8.75,0.1) -- (10,0);
        \draw [black, name path=b] plot [smooth, tension=0.5] coordinates {(7,0) (8.25,0.1) (8.5,1) (8.75,0.1) (10,0)};

% draw linear funktion with 35° slope which points through (9,5); (8.5,3.5); (8,2)
        
        \draw[domain=6:10, smooth, variable=\x] plot ({\x, \x*0.47381472+0.735667516});
        \draw[domain=6.5:10.5, smooth, variable=\x] plot ({\x, \x*0.47381472-0.527425124});
        \draw[domain=7:11, smooth, variable=\x] plot ({\x, \x*0.47381472-1.790517763});
        
% draw linear function perpendicular to the upper ones (m1*m2=-1) which penetrates (9.75 and y value of first liea function)

        \draw[domain=9.75:10.73, smooth, variable=\x] plot ({\x, \x*-2.1105296+25.9330248});

% draw equiv point
        
        \draw[densely dashed] (0,3.5) node[left] {$\mathrm{{pH}_{equiv}}$} -- (8.5,3.5) node[above left] {$\mathrm{E}$} -- (8.5,0) node[below] {$\mathrm{V_{equiv}}$};

% label functions

        \path[name path=c] (0,5) -- (15,5);
        \path[name intersections={of=c and a},];
        \coordinate (P1)  at (intersection-1);
        
        \path[name path=d] (0,0.75) -- (15,0.75);
        \path[name intersections={of=d and b},];
        \coordinate (P2)  at (intersection-2);
        
        \node[small dot, pin={above left:$\mathrm{pH=f(V_B)}$},] at (P1) {};
        \node[small dot, pin={above right:$\mathrm{\frac{d(pH)}{d(V_B)}=g(V_B)}$},] at (P2) {};
    \end{tikzpicture}
\end{document}

在此处输入图片描述

答案2

一个简单的解决方案是使用tkz-euclide。 滴定曲线

我决定在左边画，因为曲率非常接近图片的右侧。您可以将代码适配到任何切线，因为点坐标就在切线上。

\documentclass[tikz,border=3.14mm]{standalone}
\usepackage{pgfplots,tkz-euclide}

\begin{document}
    \begin{tikzpicture}[ultra thick,scale=1]
    
        \begin{axis}[ axis x line=bottom,axis y line = left, smooth,  minor  tick num=4,ymin=0,ymax=12,ultra thick, xlabel={$V_{B}$ ml},ylabel={pH }]
        \addplot[smooth, black] coordinates {
        (0,2) (2,2.1) (4,2.2) (6,2.3) (8,2.4) (10,2.5) (12,2.6) (14,2.7) (16,2.9) (18,3.3) (18.5,3.45)(19,3.6)
        (19.5,4.2)(20,7)(20.5,9.3)(21,10)(21.5,10.3)(22,10.5)(24,10.9)(26,11)(28,11.1)(30,11.2)};
        
        % Tangent lines
        \addplot[domain=5:27, samples=100,thin]{0.2*x+6.2} coordinate[pos=0.1] (A) coordinate[pos=0.9] (A');
        \addplot[domain=10:30, samples=100,thin]{0.2*x-0.4} coordinate[pos=0.1] (C) coordinate[pos=0.9] (D);
        
        \end{axis}
        
        
        \begin{scope}[line width=.75pt]
        
            \tkzDefLine[perpendicular=through A](D,C) \tkzGetPoint{A'}
            \tkzInterLL(A,A')(C,D) \tkzGetPoint{B}
            \tkzDefMidPoint(A,B)\tkzGetPoint{M}
            \tkzDefLine[parallel=through M](C,D) \tkzGetPoint{N}
            \tkzDrawLine[add=0.1 and 0.1](M,N)
            \tkzDrawSegment(A,B)
            \tkzMarkSegments[mark=s||](A,M M,B)
                
            \path (M) -- (N) node[pos=0.65] (e) {};
            \pgfgetlastxy{\xe}{\ye}
            \draw[dashed] (\xe,0) |- (0,\ye);
            \node[above left] at (e) {E};
            
        \end{scope}
        
    \end{tikzpicture}
\end{document}

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