[Rutherford]

For the photochemical reaction:
Cl₂ ²Cl· the rate of production of Cl· is r=2I_abs (where I_abs is the intensity of the absorbed light). Where is the concentration of chlorine in this expression? Why isn't it mentioned?

[Borek]

Think of radiation as of a "limiting reagent". Concentration of chlorine is treated as constant. Doesn't have to be this way always.

[Rutherford]

Doesn't have to be this way always.

That's the problem. From the task there is no way to know for sure.

[Big-Daddy]

What task is this? Or, is it a textbook question unrelated to the Olympiad?

If they told you r=2I then you don't really need to ask why [Cl2] (or P(Cl2)) is missing - it is because Cl2 is concentrated enough for the rate of production of radicals to depend only on light. OTOH I'm assuming that your issue is that they expected you to realize r=2I without being told. If we saw the whole thing, maybe there is a clue in there somewhere.

[Rutherford]

It is the fifth problem of INChO 2012: http://www.100marks.in/News/previous-year-question-papers-of-indian-national-chemistry-olympiad-incho-with-solutions/

[Big-Daddy]

It is the fifth problem of INChO 2012: http://www.100marks.in/News/previous-year-question-papers-of-indian-national-chemistry-olympiad-incho-with-solutions/

You're told that "1 photon converts 1 molecule of Cl₂ to radicals" from which the rate of production of radicals can certainly be written only in terms of number of photons, which is directly proportional to intensity. As if that wasn't enough, you're told that "the rate of this step depends only on the intensity of light absorbed". I think the information given is pretty clear then.

I am surprised there is no rate constant though. dN/dt where N is the number of photons absorbed appears to be used as the intensity, but I don't think this is a usual definition of intensity. Rather they should have defined intensity of light properly and then there would have been a constant.

[Rutherford]

When they said ''the rate of this step depends only on the intensity of light absorbed'' I think that by that they mean that it doesn't depend on temperature.

1 photon converts 1 molecule, so I don't see why Cl₂ should be excluded.

[Borek]

1 photon converts 1 molecule, so I don't see why Cl₂ should be excluded.

Questions clearly states "under steady state approximation", and explains how this approximation is obtained. Constant Cl₂ is part of assumptions.

[Rutherford]

For steady state, the reactive intermediate's concentration is assumed to be constant, and that is Cl· but not Cl₂.

[Borek]

You have an excess of Cl₂ and photons are considered to be a "limiting reagent", from that it follows concentration of Cl· is constant.

Basically you are asked to solve the problem using assumptions given. If you prefer to contest these assumptions - your choice, but you are just wasting time.

[Rutherford]

Okay, never mind then.