An idealized structure for the one$-$dimensional planar detonation wave,

referred to as the ZND structure, is one consisting of a leading hydrodynamic shock of

infinitesimal thickness and Mach number M$\_($l$),$ followed by a period of induction before the

shocked mixture ignites. The flow velocity is usually so high that diffusion can be considered

negligible throughout the detonation structure. Evaluate the ignition distance behind the shock

for the stoichiometric mixture of methane and air at P$\_($l$)=1$bar and T$\_($l$)=300$K using the global

reaction mechanism given in Problem $1$ and considering M$\_($l$)=5.$