Question $4.(14$ points$)$

Construct a graph depicting the solubility of the mineral amorphous silica $(St{O}_2,$ a pure solid$)$ as a function of $pH$ at $25C.$ Plot the $log$ solubilities $(logmole{s}^L)$ of $H_{4}Si{O}_4(ag),H_{3}Si{O}_4(ag),H_{2}Si{O}_4^{2-}(ag)$ and of $log$ total dissolved Si$.$ Draw the diagram $($in portrait orientation$)$ from $pH2$ to pH $14$ on the $x-$axis, with Si solubilities plotted on a log scale $($from $-10$ to $+4)$ on the y$-$axis. Graph paper is provided, and additional graph paper is available on WebCampus $($if necessary$)$ Assume activities $=$ concentrations, and use the following data:

$Si{O}_2(amorphous$ silica$)+2H_{2}O=H_{4}Si{O}_4(aq),K={10}^{-2\mathrm{.}71}$

$H_{4}Si{O}_4(aq)=H^{+}+H_{3}Si{O}_4^{-}(aq),K={10}^{-9\mathrm{.}82}$

$H_{3}Si{O}_4^{-}(aq)=H^{+}+H_{2}Si{O}_4^{2-}(aq),K={10}^{-13\mathrm{.}10}$