In the production of m-xylene (C8H10) from mesitylene (C9H12) over a catalyst, some of the xylene reacts to form toluene (C7H8):
C9H12 + H2 → C8H10 + CH4
C8H10 + H2 → C7H8 + CH4
The second reaction is undesirable because m-xylene sells for $0.65/lb, whereas toluene sells for $0.22/lb.
The CH4 is recycled in the plant. One pound of catalyst is degraded per 500 lb of C7H+ produced, and the spent catalyst has to be disposed of in a landfill that handles low-level toxic waste at a cost of $25/lb. If the overall selectivity of C8H10 to C7H8 is changed from 0.7 mole of xylene produced per mole of toluene produced to 0.8 by changing the residence time in the reactor, what is the gain or loss in dollars per 100 lb of mesitylene reacted?
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