$(20\%)($a$)$ Calculate the ionic strength for the water sample given below. Before you start calculation, make sure if the electroneutrality is satisfied for the given ionic composition. If it is not, balance the extra charge using either bicarbonate $(HC{O}_3^{-})$or proton $(H^{+}).$

Sample water: $[S{O}_4^{2-}]=0\mathrm{.}0007M$;$[C{l}^{-}]=0\mathrm{.}014M$;$[N{a}^{+}]=0\mathrm{.}007M$;$[M{g}^{2+}]=0\mathrm{.}0002M$;$[C{a}^{2+}]=0\mathrm{.}0004M$;$[K^{+}]=0\mathrm{.}0005M$

$($b$)$ Find the activity of each species in the sample, including either $HC{O}^{-}$or $H^{+}.$ Use the extended Debye Huckel equation.

$($c$)$ Determine the alkalinity of the sample, written in $m\frac{g}{L}$ as $CaC{O}_3.$