In a coal gasification process, carbon (the primary constituent of coal) reacts with steam to produce carbon monoxide and hydrogen (synthesis gas). The gas may either be burned or subjected to further processing to produce any of a variety of chemicals. A coal contains 10.5 wt% moisture (water) and 22.6 wt% noncombustible ash. The remaining fraction of the coal contains 81.2 wt% C, 13.4% 0 and 5.4% H. A coal slurry containing 2.00 kg coal/kg water is fed at 25?C to an adiabatic gasification reactor along with a stream of pure oxygen at the same temperature. The following reactions take place in the reactor:?

C (s) + H₂O (v) ? CO (g) + H₂ (g): ??H?_? = +131.3 kJ/mol ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?(1)

C (s) + O₂ (g) ? CO₂ (g): ?H?_? = ? 3 93.5 kJ/mol ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?(2)

2H (in coal) + ? O₂ (g) ? H₄O (v): ?H?_? ? ? 242 kJ/mol ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?(3)

Gas and slag (molten ash) leave the reactor at 2500?C. The gas contains CO, H₂, CO₂, and H₂O.?

(a) Feeding oxygen to the reactor lowers the yield of synthesis gas, but no gasifier ever operates without supplementary oxygen. Why does the oxygen lower the yield? Why it is nevertheless always supplied.?

(b) Suppose the oxygen gas fed to the reactor and the oxygen in the coal combine with all the hydrogen in the coal (Reaction 3) and with some of the carbon (Reaction 2), and the remainder of the carbon is consumed in Reaction 1. Taking a basis of 1.00 kg coal fed to the reactor and Letting no equal the moles of O₂ fed, draw and label a flowchart. Then derive expressions for the molar flow rates of the four outlet gas species in terms of no. (Partial solution: n_H2, = 51.5 ? n₀.)

(c) The standard heat of combustion of the coal has been determined to be ? 21,400 kJ/kg, taking CO₂ (g) and H₂O (I) to be the combustion products. Use this value and the given elemental composition of the coal to prove that the standard heat of formation of the coal is ? 1510kJ/kg. Then use an energy balance to calculate n₀, using the following approximate heat capacities in your calculation: Take the heat of fusion of ash (the heat required to convert ash to slag) to be 710 kJ/kg.

Species C,[kJ/(mol-C)] C,[kJ/(kg-C)] 0 CO H 0.0336 0.0332 0.0300 - CO HO(v) 0.0508 0.0395 Slag(1) - 1.4