: In a bioreactor study on ethanol production using immobilized Saccharomyces cerevisiae in a packed bed reactor, the rate of ethanol production $($R$)$ in the system can be described by the Arrhenius equation:R $=$ Ka $*$ exp$(-$Ea $/$ RT$)$where: R $=$ rate of ethanol production $($in g$/$L$/$h$)$ Ka $=$ rate constant Ea $=$ activation energy $($in J$/$mol$)$ R $=$ gas constant $(8\mathrm{.}314$ J$/$mol$*$K$)$ T $=$ temperature $($in Kelvin$)$During the experiment, the rate of ethanol production was measured at two different temperatures: T$1=300$ K and T$2=320$ K$.$ The corresponding rates of ethanol production were R$1=0\mathrm{.}05$ g$/$L$/$h and R$2=0\mathrm{.}08$ g$/$L$/$h$,$ respectively.Calculate the rate constant $($Ka$)$ for the ethanol production reaction.Determine the activation energy $($Ea$)$ for the reaction.C$6$H$12$O$62$ C$2$H$5$OH $+2$ CO$2$