Problem #$2$: Carbonic acid to form bicarbonate and carbonate. Carbonic acid is an

important acid for buffering our natural waters and our bodies. The first reaction is

carbonic acid dissociating to form bicarbonate. The second one is bicarbonate

dissociating to form carbonate. Both create hydrogen ions. You have a tank of water

with an inlet flow that contains $1{10}^{-3}$ mole$/\frac{?}{Lo{f}_{2}C{O}_3}$ and ${10}^{-8}$mole$\frac{s}{L}$ of hydrogen

ions. There is no bicarbonate or carbonate. The water flowing out of the tank contains $5$

${10}^{-5}$ moles $\frac{?}{L}$ of bicarbonate, $2{10}^{-6}$ moles $\frac{?}{L}$ of carbonate. Assume the reactor is at

equilibrium. You can write the amount of each species in moles$/$L$.$ You can assume

that the flowrate in and out is $1\frac{L}{m}in.$

$H_{2}C{O}_3=H^{+}+HC{O}_3^{-}$

$HC{O}_3^{-}=H^{+}+C{O}_3^{2-}$

a$.(2)$ Draw the diagram and label the inlet and outlet.

b$.(2)$ Write a mole balance on each species using the concentrations and volume.

You can assume that the extents of reaction are in moles$/$time and you can

assume a constant volume.

c$.(2)$ Write out a SPICE table and use the material balance on each component to

solve for ${}_1$ and ${}_2.$ Calculate the $pH$ of the water exiting the tank.