First order versus 2nd order kinetics in a CSTR

Normalize the concentration ,Ca with the feed concentration, Ca0,  η = Ca/CA0.  τ= V/q.

eq1 =  1 -  η - k1 τ η

eq2 =  1 -  η - k2 τ η^2

Solve[eq1==0,η]

Answer for first order.

ans1 = η/.%[[1]]

Solve[eq2 ==0, η]

ans2 = η/.%[[2]]

This is the exit composition of the feed.  So

Plot[ (ans2/ans1)/.{k1->1,k2->1},{τ,.01,.1},PlotRange->{0,1.1}]

1/117.

1/102.

Series[ans2/ans1,{τ,0,3}]

So for equal k’s

%/.{k1->1, k2->1}

Plot[ (ans2/ans1)/.{k1->1,k2->2},{τ,.01,5}]

Plot[ (ans2/ans1)/.{k1->1,k2->10},{τ,.01,10}]

Plot[Evaluate[{ans1,ans2}/.{ k1->1,k2->10}],{τ,0,15},PlotRange->{0,1},PlotLegends->"Expressions",AxesLabel->{"τ","concentratiomn"}]