Hydrocarbon cracking takes place in the gas phase in a tubular reactor (PFR) according to the following reaction: A ------> 2B + 2C

Data given: The feed consists of an equimolar mixture of reagent A and inert. The reaction is of order 2 with a kinetic constant k = 9 dm3/mol.s, Q0 = 1dm3/s, T= 230C, P = 2 atm and the section of the reactor A = 1.0 dm2. The reaction takes place in an isothermal phase and without pressure change.

If the desired conversion rate to A at the outlet of the reactor is 90%, calculate the length of the tubular reactor necessary for this transformation. If the change in the density of the reaction medium is not taken into account, recalculate the length of the reactor. What would be the error that we introduce in the sizing of the reactor?