Hydrofluoric acid $($IF$)$ can be munufactured by treating caiciom fiuoride $($CaFe with sulfuric acid $($H$-$SO$4).$ A sample of Muorospar $($the raw mutemalcontains $79\%\%$ by weight CaF: and $25\%$ inert $($nonreacting$)$ materials. The pure sulfutic aerd ised in the process is in $30\%$ excess of that theoretically required. Most of the manutactured IF leaves the reaction chamber as a gas, but a solid cake is also removed mom the reaction chamber that contains $5\%$ of all the HF formed, plus Cas@s$,$ inerts, and unreacted sulfuric acid.Calculate the kilograms of cake are produced per $100$ kg of fluorospur charged to the process using atomic balance method.