{ "cells": [ { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "% some housekeeping stuff\n", "register_graphics_toolkit (\"gnuplot\");\n", "available_graphics_toolkits ();\n", "graphics_toolkit (\"gnuplot\")\n", "clear\n", "% end of housekeeping" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Cd hydroxycomplexation\n", "\n", "The overall complexation constants for Cd$^{2+}$ with OH$^-$ are $\\log{\\beta_1}=4.1$, $\\log{\\beta_1}=7.7$, $\\log{\\beta_3}=10.3$ and $\\log{\\beta_3}=12$ corresponding to the following reactions (in order)\n", "\n", "$\\mathrm{Cd^{2+}}+\\mathrm{OH^-} \\leftrightharpoons \\mathrm{CdOH^+}$\n", "\n", "$\\mathrm{Cd^{2+}}+2\\mathrm{OH^-} \\leftrightharpoons \\mathrm{Cd(OH)_2^0}$\n", "\n", "$\\mathrm{Cd^{2+}}+3\\mathrm{OH^-} \\leftrightharpoons \\mathrm{Cd(OH)_3^-}$\n", "\n", "$\\mathrm{Cd^{2+}}+4\\mathrm{OH^-} \\leftrightharpoons \\mathrm{Cd(OH)_4^{2-}}$\n", "\n", "We derived the alpha expressions for these 5 species in class\n", "\n", "$\\alpha_{\\mathrm{Cd^{2+}}} = \\dfrac{1}{1+\\beta_1[\\mathrm{OH^-}]+\\beta_2[\\mathrm{OH^-}]^2+\\beta_3[\\mathrm{OH^-}]^3+\\beta_4[\\mathrm{OH^{-}}]^4}$\n", "\n", "\n", "$\\alpha_{\\mathrm{CdOH^{+}}} = \\dfrac{\\beta_1[\\mathrm{OH^-}]}{1+\\beta_1[\\mathrm{OH^-}]+\\beta_2[\\mathrm{OH^-}]^2+\\beta_3[\\mathrm{OH^-}]^3+\\beta_4[\\mathrm{OH^{-}}]^4}$\n", "\n", "\n", "$\\alpha_{\\mathrm{Cd(OH)_2^{0}}} = \\dfrac{\\beta_2[\\mathrm{OH^-}]^2}{1+\\beta_1[\\mathrm{OH^-}]+\\beta_2[\\mathrm{OH^-}]^2+\\beta_3[\\mathrm{OH^-}]^3+\\beta_4[\\mathrm{OH^{-}}]^4}$\n", "\n", "\n", "$\\alpha_{\\mathrm{Cd(OH)_3^{-}}} = \\dfrac{\\beta_3[\\mathrm{OH^-}]^3}{1+\\beta_1[\\mathrm{OH^-}]+\\beta_2[\\mathrm{OH^-}]^2+\\beta_3[\\mathrm{OH^-}]^3+\\beta_4[\\mathrm{OH^{-}}]^4}$\n", "\n", "$\\alpha_{\\mathrm{Cd(OH)_4^{2-}}} = \\dfrac{\\beta_4[\\mathrm{OH^{-}}]^4}{1+\\beta_1[\\mathrm{OH^-}]+\\beta_2[\\mathrm{OH^-}]^2+\\beta_3[\\mathrm{OH^-}]^3+\\beta_4[\\mathrm{OH^{-}}]^4}$\n", "\n", "In class we learned how to quickly sketch the distribution diagram using the step-wise formation constants. We can make a more quantitative sketch though using these expressions (note, since pH would be a known quantity we do not need to make any additional assumptions.)." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "ans = -74.440\n" ] }, { "data": { "image/svg+xml": [ "\n", "\n", "Gnuplot\n", "Produced by GNUPLOT 5.2 patchlevel 7 \n", "\n", "\n", "\n", "\n", "\n", "\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t \n", "\t \n", "\t\n", "\t\n", "\t \n", "\t \n", "\t\n", "\n", "\n", "\n", "\n", "\t\n", "\t\t\n", "\t\n", "\n", "\n", "\t\t\n", "\t\t0\n", "\t\n", "\n", "\n", "\t\t\n", "\t\t0.2\n", "\t\n", "\n", "\n", "\t\t\n", "\t\t0.4\n", "\t\n", "\n", "\n", "\t\t\n", "\t\t0.6\n", "\t\n", "\n", "\n", "\t\t\n", "\t\t0.8\n", "\t\n", "\n", "\n", "\t\t\n", "\t\t1\n", "\t\n", "\n", "\n", "\t\t\n", "\t\t6\n", "\t\n", "\n", "\n", "\t\t\n", "\t\t8\n", "\t\n", "\n", "\n", "\t\t\n", "\t\t10\n", "\t\n", "\n", "\n", "\t\t\n", "\t\t12\n", "\t\n", "\n", "\n", "\t\t\n", "\t\t14\n", "\t\n", "\n", "\n", "\n", "\n", "\t\n", "\t\ta\n", "\t\n", "\n", "\n", "\t\n", "\t\tpH\n", "\t\n", "\n", "\n", "\t\n", "\t\tDistribution diagram, Cd hydroxo complexation\n", "\t\n", "\n", "\n", "\n", "\n", "\t\n", "\tCd2+\n", "\n", "\n", "\n", "\t\n", "\t\tCd2+\n", "\t\n", "\n", "\n", "\t\t\n", "\n", "\n", "\t\n", "\tCdOH+\n", "\n", "\t\n", "\t\tCdOH+\n", "\t\n", "\n", "\n", "\t\t\n", "\n", "\n", "\t\n", "\tCd(OH)2\n", "\n", "\t\n", "\t\tCd(OH)2\n", "\t\n", "\n", "\n", "\t\t\n", "\n", "\n", "\t\n", "\tCd(OH)3-\n", "\n", "\t\n", "\t\tCd(OH)3-\n", "\t\n", "\n", "\n", "\t\t\n", "\n", "\n", "\t\n", "\tCd(OH)42-\n", "\n", "\t\n", "\t\tCd(OH)42-\n", "\t\n", "\n", "\n", "\t\t\n", "\n", "\n", "\t\n", "\tgnuplot_plot_6a\n", "\n", "\t\n", "\t\n", "\tgnuplot_plot_7a\n", "\n", "\t\n", "\t\n", "\tgnuplot_plot_8a\n", "\n", "\t\n", "\t\n", "\tgnuplot_plot_9a\n", "\n", "\t\n", "\t\n", "\n", "\t\n", "\n", "\n", "\n", "\n", "\n", "" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%plot -s 600,500 -f 'svg'\n", "logB1=4.1; logB2=7.7; logB3=10.3; logB4=12; Kw=1e-14;\n", "B1=10^logB1; B2=10^logB2; B3=10^logB3; B4=10^logB4;\n", "pH=6:0.1:14; H=10.^(-pH); OH=Kw./H;\n", "denominator=1+B1*OH+B2*OH.^2+B3*OH.^3+B4*OH.^4;\n", "alphaCd=1./denominator;\n", "alphaCdOH=(B1*OH)./denominator;\n", "alphaCdOH2=(B2*OH.^2)./denominator;\n", "alphaCdOH3=(B3*OH.^3)./denominator;\n", "alphaCdOH4=(B4*OH.^4)./denominator;\n", "\n", "plot(pH,alphaCd,'b','linewidth',2)\n", "hold on\n", "plot(pH,alphaCdOH,'g','linewidth',2)\n", "plot(pH,alphaCdOH2,'m','linewidth',2)\n", "plot(pH,alphaCdOH3,'k','linewidth',2)\n", "plot(pH,alphaCdOH4,'c','linewidth',2)\n", "xlabel('pH'); ylabel('\\alpha');\n", "legend('Cd^{2+}','CdOH^+','Cd(OH)_2','Cd(OH)_3^-','Cd(OH)_4^{2-}','location','west')\n", "set(gca,'linewidth',2)\n", "title('Distribution diagram, Cd hydroxo complexation')\n", "\n", "% add stepwise values (pH=pKa but we need to convert because we were given overall association constants)\n", "\n", "plot([9.9 9.9],[0 1],'k:','linewidth',2)\n", "plot([10.4 10.4],[0 1],'k:','linewidth',2)\n", "plot([11.4 11.4],[0 1],'k:','linewidth',2)\n", "plot([12.3 12.3],[0 1],'k:','linewidth',2)\n", "\n" ] } ], "metadata": { "kernelspec": { "display_name": "Octave", "language": "octave", "name": "octave" }, "language_info": { "file_extension": ".m", "help_links": [ { "text": "GNU Octave", "url": "https://www.gnu.org/software/octave/support.html" }, { "text": "Octave Kernel", "url": "https://github.com/Calysto/octave_kernel" }, { "text": "MetaKernel Magics", "url": "https://metakernel.readthedocs.io/en/latest/source/README.html" } ], "mimetype": "text/x-octave", "name": "octave", "version": "6.4.0" } }, "nbformat": 4, "nbformat_minor": 4 }