Problem $3(12$ points$)$A lake has natural inflow with a flow rate of $10,000$ m$3/$year and alkalinity of $100$ mg$/$L as CaCO$3.$ If the lake's alkalinity is to be at a steady state level of $50$ mg$/$L as CaCO, what input rate of sulfuric acid $($HSO$4)$ is possible $($in moles$/$year and g H$2$SO$4/$year$)?$