Processes comprising: (a) providing a reactant comprising a component selected from the group consisting of o-xylene, naphthalene and mixtures thereof, and a gas comprising oxygen; (b) reacting the reactant and the gas in a reaction system, in the presence of a catalyst, to form phthalic anhydride; wherein the reaction system comprises: (i) at least two reaction zones, each reaction zone cooled with a coolant; and (ii) an intermediate cooling zone disposed between a first of the at least two reaction zones and a second of the at least two reaction zones; and wherein the coolant entering the first of the at least two reaction zones has a temperature which is more than 20° C. higher than a temperature of the coolant entering the second of the at leas two reaction zones.