For the formation of phosgene from CO(g) and chlorine.
`CO(g)+Cl(g)rarr CoCl_(2)(g)`
the exermientally detrmined rate equation is,
`(d[COcl_(2)])/(dt)=k[CO][Cl_(2)]^(2//3)`
Is the following mechanism consistent with the rate equation
`{:((i),Cl_(2)hArr2Cl,("fast")),((ii),Cl+COhArrCOCl,("fast")),((iii),COCl+Cl_(2)hArrCOCl_(2)+Cl,("slow")):}`

Explanation

Multiplying equation (ii) by and adding (i), we get : ltbr `Cl_(2)2COhArr2COCI
`K=([COCI]^(2))/([C_(2)][CO]^(2))`
`[COCI=(K)^(1//2)[CI_(2)]^(1//2)[CO]" ".....(i)`
Slowest step is rate determine hence,
Rate =`k[COCI][CI_(2)]" "....(ii)`
From eqs(i). and (ii) we, get
Rate `=kK^(1//2)[CI_(2)][CI_(2)]^(1//2)[CI_(2)][CO]`
Rate `=k[CI_(2)]^(3//2)[CO]`
Thus, rate law is in accordane with the mechanism.