pls derive the eqaution above. reversible reaction for pfr First$-$order reversible reaction, A$$ r R$,$ C$\_$R $0/$ C$\_$A $0=$M$,$ kinetics approximated or fitted by $-$r$\_$A$=$k$\_1$ C$\_$A$-$k$\_2$ C$\_$R with an observed equilibrium conversion X$\_$Ae$,$ any constant $\backslash$epsi $\_$A$,$

k$\_1\backslash$tau $=$M$+$r X$\_$Ae$/$M$+$r$[-(1+\backslash$epsi $\_$A X$\_$Ae$)$ ln$(1-$X$\_$A$/$X$\_$Ae$)-\backslash$epsi $\_$A X$\_$A$]$