1) There is considerable interest in converting coal into liquid fuels. One approach is to partially combust the coal to form a mixture of CO and H2, which can then be reacted to produce methanol, a viable liquid fuel. Consider the process sketched aside. The reactor feed contains 67.3%H2,32.5%CO, and 0.2%CH4 at a flow rate of 100mol/s the methane is generated from the coal combustion and is not involved in the reaction to form methanol. The separator recovers 99.5% of the methanol in a pure product stream at a flow rate of 31.96mol/s, with all of the CO,H2, and CH4 recovered for recycle (and purge). The maximum allowable CH4 concentration in the purge stream is 4.95%. A) Perform a degree of freedom analysis for this system as a whole. B) Evaluate all flow rates and the rate of reaction (RV). Provide enough details so that it is clear how you completed the mole balance table