A coil visbreaker operates at 500°C for 1 min. Assume that visbreaking follows an apparent first-order kinetics with no significant volume change. An apparent Arrhenius activation energy for the visbreaking reaction is given as 50 kcal/mol.
Derive an equation to calculate the visbreaking conversion (x=1-[C/C0], Where C0 is concentration of feed (reactant) at time 0 and C is the concentration of feed at time t) as a function of temperature and time. Calculate an apparent Arrhenius pre-exponential factor for the reaction rate constant, if visbreaking at 500°C for 1 min leads to a conversion of 10%.