We want to hydrolyze 500 lb per day of an ester at an initial concentration of 5 m (the ester has a molecular weight of 130) in aqueous basic solution in a batch process, and we need product that is 99% hydrolyzed. in benchtop experiments in a flask, we find that 50% of the ester hydrolyzes in 15 min for initial ester concentrations of either 1 or 5 m. we also find that, when we react for 8 h, all of the ester has hydrolyzed. it takes 1 h to empty the reactor and refill and heat it to start another batch. what size reactor will we need?

Consider a double atwood machine constructed as follows: a mass 4m is suspended from a string that passes over a massless pulley on frictionless bearings. the other end of this string supports a second similar pulley, over which passes a second string supporting a mass of 3m at one end and m at the other. using two suitable generalized coordinates, set up the lagrangian and use the lagrange equations to find the acceleration of the mass 4m when the system is released. explain why the top pulley rotates even though it carries equal weights on each side.