On global scales $O_3$ is produced in the troposphere by $CO$ and mainly $C{H}_4$ oxidation. Consider the following reactions for oxidation of $CO$ and $C{H}_4$ to $C{O}_2.$ We wish to write out net reactions for $CO$ and $C{H}_4$ oxidation, which means there should be no NOx in the net reaction.

${?}^{C{H}_4}+OHC{H}_3{O}_2+H_{2}O$

$C{H}_3{O}_2+NOC{H}_{3}O+N{O}_2$

$C{H}_{3}O+O_2$HCHO$+H{O}_2$

$C{H}_3{O}_2+H{O}_{2}C\frac{H_3}{O}OH+O_2$

$C\frac{H_3}{O}OH+OH$HCHO$+OH+H_{2}O$

$O_2$

$N{O}_2+hvNO+O_3$

$H{O}_2+NOOH+N{O}_2$

HCHO$+OH$CHO$+H_{2}O$

CHO$+O_{2}CO+H{O}_2$

$O_2$

$CO+OHC{O}_2+H{O}_2$

$($a$)$ Consider the case of NOx$=0.$ Write out the net reaction for the oxidation of $CO$ to $C{O}_2$ and a net reaction for the oxidation of $C{H}_4$ to $C{O}_2.$ In this case, how many molecules of $O_3$ are produced per molecule of $CO$ oxidized and how many molecules of $O_3$ are produced per molecule of $C{H}_4$ oxidized by these reactions?

$($b$)$ Now consider the high NOx case. Write out the net reaction for the oxidation of $CO$ to $C{O}_2$ and a net reaction for the oxidation of $C{H}_4$ to $C{O}_2.$ In this case, how many molecules of $O_3$ are produced per molecule of $CO$ oxidized and how many molecules of $O_3$ are produced per molecule of $C{H}_4$ oxidized by these reactions?

$($c$)$ If present global emissions for $CO$ are $4{10}^{13}$mole$\frac{s}{y}r$ and for $C{H}_{4}3{10}^{13}$mole$\frac{s}{y}r.$ Estimate the global production rate of $O_3$ in the troposphere from your results above for the two cases, in moles$/$yr$.$