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Answer 1 · 2018-03-14T20:04:31

The essence of these problems is determining the rate determining step: which the rate law is derived from.

Consider,

#"Rate" = k[NOCl]^2#

In the first mechanism, the slow step is the RDS, and there is only one mole of #NOCl#. So, that is wrong.

In the second mechanism, the slow step is the RDS, and there are two moles of #NOCl#. This may be a mechanism for this reaction.

In the third mechanism, we'll need to do some analysis,

#NOCl rightleftharpoons NO + Cl# fast, eq.

This isn't the RDS, but it makes the intermediate in the RDS (the slow step after). So let's substitute,

#k_1[NOCl] = k_(-1)[NO][Cl]#
#=> [Cl] = (k_1[NOCl])/(k_(-1)[NO])#

for the intermediate in the RDS and see what we come up with.

Consider,

#NOCl + Cl to NO + Cl_2# slow (RDS)

where,

#"Rate" = (k_1[NOCl])/(k_(-1)[NO]) * k_2[NOCl] = (k_1k_2[NOCl]^2)/(k_(-1)[NO])#

Hence, the only reliable mechanism we have that matches that rate law is #d.# or the second mechanism.