The results of a mineral analysis of a raw water are as follows: $H_{2}C{O}_3^{**}=72m\frac{g}{L},C{a}^{2+}=100m\frac{g}{L},M{g}^{2+}=15m\frac{g}{L},N{a}^{+}=20m\frac{g}{L},$Alk$(HC{O}_3^{-})=220m\frac{g}{L}$ as $CaC{O}_3,S{O}_4^{2-}=60m\frac{g}{L},C{l}^{-}=5\mathrm{.}15m\frac{g}{L}.$ This source will supply $50,000\frac{m^3}{d}$ and will undergo single$-$stage lime$-$soda ash softening to reduce the hardness. Assume the residual hardness in the softened water is $30m\frac{g}{L}$ as $CaC{O}_3.$ Molar masses $($g$/$mol$)$ are as follows: $H_{2}C{O}_3^{**},62$;$C{a}^{2+},40$;$M{g}^{2+},24\mathrm{.}4$;$N{a}^{+},23$; $HC{O}_3^{-},61$;$CaC{O}_3,100$;$S{O}_4^{2-},96$;$C{l}^{-},35\mathrm{.}5,$CaO,$56$;$N{a}_{2}C{O}_3,106$;$C{O}_2,44.$

Calculate the soda ash dose $(m\frac{g}{L}N{a}_{2}C{O}_3)$ required to remove the calcium noncarbonate hardness.