12 Consider a cylindrical batch reactor that has one end fitted with a frictionless piston attached to a spring (Figure P4-11C). The reaction A+B8C with the rate law rA=k1CA2CB is taking place in this type of reactor. (a) Write the rate law solely as a function of conversion, numerically evaluating all possible symbols. (Ans.: rA=5.03109[(1X)3/(1+3X)3/2]lbmol/ft3s. ) (b) What is the conversion and rate of reaction when V=0.2ft3 ? (Ans.: X=0.259,rA=8.63 1010lbmol/ft3s.) Additional information: Equal moles of A and B are present at t=0 Initial volume: 0.15ft3 Value of k1:1.0(ft3/lbmol)2s1 The spring constant is such that the relationship between the volume of the reactor and pressure within the reactor is V=(0.1)(P)(Vinft3,Pinatm) Temperature of system (considered constant): 140F Gas constant: 0.73ft3atm/lbmolR