Two waters are in equilibrium with the atmosphere $)=(400pp{m}_v$ and then mixed together at a $1$:$1$ volumetric ratio without gas exchange. If water $A$ is at $pH9\mathrm{.}5$ and water $B$ is at $pH7\mathrm{.}3,$ answer the following questions:

$($a$)$ What is the $C_{T,CO3}$ concentration of each solution and of the mixture? Report as $M.$

$($b$)$ What is the alkalinity of each solution and of the mixture? Report as mgCaC$\frac{O_3}{L}.$

$PC{O}_2=400pp{m}_v$;$T=25C$;$P=1$atm

$C{O}_2(g)+H_{2}O(l)H_{2}C{O}_3(aq),K_{H,CO2}={10}^{-1\mathrm{.}47}(\frac{M}{a}tm)$

$H_{2}C{O}_3{H}^{+}+HC{O}_3^{-},K_{a1,CO3}={10}^{-6\mathrm{.}35}$

$HC{O}_3^{-}{H}^{+}+C{O}_3^{2-},K_{a2,CO3}={10}^{-10\mathrm{.}33}$