A power generation plant produces combustion gases with a mass flow rate of $2$ million lb$/$hr$.$ Out of these, $180,000$ lb$/$hr are water vapor, and $20,000$ lb$/$hr are SO$2.$ All other gases that are not SO$2$ or water have an average molecular weight of $29.($a$)$ Calculate the concentration of SO$2$ in the combustion gases in ppm$($v$)($on a dry basis$).$ Regulations require the capture of $90\%$ of SO$2,$ and for this purpose, a scrubber with limestone will be used. $($b$)$ Calculate the concentration of SO$2$ in the outgoing gases in ppm$($v$)($on a dry basis$).($c$)$ Assume there is no HCl in the gases, and the commercial limestone used contains $95\%$ CaCO$3$ and $5\%$ inert material. The supplied alkalinity will be $1\mathrm{.}15$ times the stoichiometric ratio. Calculate the limestone feed rate in lb$/$hr$.$