Use the single$-$step global mechanism for combustion of hydrocarbon with air to perform the following steps:

a$.$ Write down the stochiometric global chemical reaction $($e$.$g$.,$ see Eq$.5\mathrm{.}1)$ for methane fuel and air.

b$.$ Write down the expression for the reaction rate of fuel $($in gmol$/$cm$3-$s$),$ see Eq$.5\mathrm{.}2,$ and list parameters A$,$ Ea$,$ m$,$ and n from the table.

c$.$ For P $=1$ atm and T $=1600$ K$,$ calculate the initial molar concentrations of methane and oxygen in gmol$/$cm$3$ and kmol$/$m$3$

d$.$ Compute the reaction rate of fuel in gmol$/$cm$3-$s and kg$/$m$3-$s$.$

e$.$ Compute the reaction rate of oxygen in gmol$/$cm$3-$s and kg$/$m$3-$s$.$

f$.$ Compute the reaction rate of oxidizer in kg$/$m$3-$s$.$ Note that oxidizer includes both oxygen and nitrogen.

g$.$ Compute the production rates of CO$2,$ H$2$O$,$ and N$2$ in gmol$/$cm$3-$s

h$.$ Compute the production rates of CO$2,$ H$2$O$,$ and N$2$ in kg$/$m$3-$s

i$.$ Add d and f to compute the reaction rate of reactants $($both fuel and oxidizer$)$ in kg$/$m$3-$s

j$.$ Add production rate of all products in h to show that the reaction rate and production rate are the same in units of kg$/$m$3-$s