A fuel gas produced by gasifying coal is to be burned with 20% excess air. The gas contains 50.0 mole% nitrogen and the balance carbon monoxide and hydrogen. A sample of the gas is passed through an infrared spectrometer, which registers a signal R that depends on the mole fraction of carbon monoxide in the sample and a reading R 38.3 is recorded. Analyzer calibration data are as follows: A power law (x = aR^b) should be suitable for fitting the calibration data. Derive the equation relating x and R (use a graphical method), and then calculate the molar flow rate of air required for a fuel feed rate of 175kmol/h, assuming that CO and H₂ are oxidized but N₂ is not.

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x(mol CO/mol) 0.05 0.10 0.40 17.0 49.4 R 10.0 0.80 1.00 73.6 73.6 99.7