[noor123]

Say i have been given  reaction that happens in a two step process. And it does not say which one of them is slow and which one is fast... how do i then decide which one is the RDS?

(1) ClO−+ClO−→ClO2−+Cl−

(2) ClO2−+ClO−→ClO3−+Cl−

the only info. given is that the rate of formation of ClO3- depends on the square of concentration  of CLO- , [ClO-]²

The first part of the question asked for the 'total reaction formula',
which i did by adding both the reactions and canceling out if product and reactant were same:

total:   3 ClO−→ClO3−+2 Cl−

But not sure if this can be used to determine the RDS.

[Plontaj]

The most common applied assumptions in kinetics are:
(i) steady-state
(ii) preequilibrium
(iii) reaction separation

At first approach, try all of them to develop global equation rate of formation of ClO3-

d[ClO3-]/dt = ?

EDIT: There is no equilibrium so 2nd is out off consideration

[noor123]

Thank you for reply!

I looked at the answer sheet, and it suggested that since the rate laws for each of the elementary rxn is like:

1) v=k₁[ClO−]²
(2) v=k[ClO2−][ClO−]

and the rate law for the (1) step is in accordance with the total concentration dependence, it is therefore the rate determining step.


What i am now not so confident about is how this conclusion can be made... how can i say that step 1 is the RDS based on the dependence of concentration.

[Plontaj]

(1) ClO− + ClO− → ClO2− + Cl−
(2) ClO2− + ClO− → ClO3− + Cl−

The mathematical explanation is:

if k2 >> k1 and ClO2- concentration is very low, you can assume SS:

d[ClO2-]/dt= 0 = v1 - v2 = k1[ClO−]2 - k2[ClO2−][ClO−]
k1[ClO−]2 = k2[ClO2−][ClO−]
k1[ClO−] = k2[ClO2−]
[ClO2−]=k1/k2 [ClO−]

so, now if you want to determine ClO3- rate:
d[ClO3-]/dt= v2 = k2[ClO2−][ClO−] = k1/k2 [ClO−][ClO−] = kexp*[ClO−]2

There you have straight mathematical expression which proved that the production rate of ClO3- is 2nd order in respect to [ClO-]