Problem $1.(29)$ The ignition process for H$2$O$2$ can be simplified so that it is described by three representative reactions: Initiation: H$2+02$ H$02+$ H$,$ ki Branching: H $+$ O$2+$ xH $+$ other products, ky Termination: H $+$ O$2+$ M $$ HO$2+$ M$,$ kt $(1)$ Write the production rate of H$.(10\text{'})(2)$ Solve for the concentration of H$,[$H$]$ from $(1)$ which is an ODE. $(9\text{'})(3)$ Find the ignition delay time tign as a function of x$,$ T$,[02]$ and an arbitrary constant, given kp $=8\mathrm{.}3$ x $10$'exp$(-7253/$T$)($m$/$mol$/$s$)$ and branching overwhelms termination $($explosive regime$).(10\text{'})$