The rate of the oxidation of $CO$ on $Pd$ at low pressure is $1^{st}$ order in $O_2$ and inverse $1^{st}$ order

in CO$.$ Show that the following set of elementary steps is consistent with this observation.

$(1)CO+**harrC{O}^{**}$

$(2)O_2+**O^{**}O$

$(3)O^{**}O+**2O^{**}$

$(4)C{O}^{**}+O^{**}C{O}_2+2**$

Additional information:

$CO$ adsorbs very strongly on $Pd$ and therefore the first step will be nearly equilibrated.

The slow step in the mechanism is the irreversible adsorption of $O_2.$