vZero = 400;
cA0 = 0.1;
cB0 = 0.2;
xAf = 0.999;
ratio = cB0/cA0;
k = 200;
rate = k*cA0^2*(1 - xA)*(ratio - xA)
rateMFR = k*cA0^2*(1 - xAf)*(ratio - 
            xAf)

fA0 = vZero*cA0
volume = 
      fA0*xAf/rateMFR

volumePFR = 124;
Solve[xA == volumePFR/fA0*rate]

Plot[1/rate, {xA, 0, 1}];

Plot[1/rate, {xA, 0, 1}, PlotRange -> {0, 20}];