1,3,5 trimethylbenzene may be reacted with hydrogen over a catalyst to form meta- xylene, which is a valuable product at $1.35/kg. However, meta-xylene may also react with hydrogen to form toluene, which is much less valuable at $0.50/kg. Methane is a side product of both reactions, and it gets recycled elsewhere in the plant. 1 kg of catalyst is degraded for each 200 kg of toluene produced, and it must be disposed of in a toxic waste landfill at a cost of $25/kg. It is proposed to alter the conditions of the reactor such that the selectivity of the reaction is increased from 0.8 (the current selectivity) to 0.9 (the proposed selectivity). Calculate the amount of money gained (in dollars) by making this change to the process, for each 100 kg of 1,3,5 trimethylbenzene reacted.
1,3,5 trimethylbenzene may be reacted with hydrogen over a catalyst to form meta- xylene, which is a valuable product at $1.35/kg. However, meta-xylene may also react with hydrogen to form toluene, which is much less valuable at $0.50/kg. Methane is a side product of both reactions, and it gets recycled elsewhere in the plant.
1 kg of catalyst is degraded for each 200 kg of toluene produced, and it must be disposed of in a toxic waste landfill at a cost of $25/kg.
It is proposed to alter the conditions of the reactor such that the selectivity of the reaction is increased from 0.8 (the current selectivity) to 0.9 (the proposed selectivity). Calculate the amount of money gained (in dollars) by making this change to the process, for each 100 kg of 1,3,5 trimethylbenzene reacted.
The reactions taking place in the overall process:
It is apparent that 1 mole of trimethyl benzene produces 1 mol of meta-xylene, which is 120 g of trimethyl benzene produces 106 g of meta-xylene. Likewise, 106 g of meta-xylene produces 92 g of toluene.
100 kg of trimethyl benzene will produce (100×106)/120 = 88.33 of meta-xylene.
with 0.8 selectivities, 80% of this will be extracted as meta-xylene, and 20% will react with hydrogen to form toluene. Hence toluene produce will be (0.2×88.33×92)/106 = 15.33 kg.
with 0.9 selectivities, 90% of this will be extracted as meta-xylene, and 10% will react with hydrogen to form toluene. Hence toluene produce will be (0.1×88.33×92)/106 = 7.67 kg.
Original selectivity is 0.8, that is if 100 kg of trimethyl benzene is reacted, 80 kg is consumed to produce 70.66 kg meta-xylene is produced, and 20 kg is consumed to in 15.33 kg toluene production, which further degrades the catalyst which needs disposal cost.
Net profit in the original selectivity (0.8) per 100 kg trimethyl benzene reacted :
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