n$-$Pentane is burned with excess air in a continuous combustion chamber.$($a$)$ A technician runs an analysis and reports that the product gas contains $0\mathrm{.}270$ mole$\%$ pentane,$5\mathrm{.}3\%$ oxygen, $9\mathrm{.}1\%$ carbon dioxide, and the balance nitrogen on a dry basis. Assume $100$ mol of dry product gas as a basis of calculation, draw and label a flowchart, perform a degree$-$of$-$ freedom analysis based on atomic species balances, and show that the system has $1$ degrees of freedom. Interpret this result.$($b$)$ Use balances to prove that the reported percentages could not possibly be correct.$($c$)$ Thetechnicianrerunstheanalysisandreportsnewvaluesof$0\mathrm{.}304$mole$\%$pentane,$5\mathrm{.}9\%$oxygen, $10\mathrm{.}2\%$ carbon dioxide, and the balance nitrogen. Verify that this result could be correct and, assuming that it is$,$ calculate the percent excess air fed to the reactor and the fractional conversionof pentane.