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I hope this is the right place!
I need help with steady state theory. Assuming that the concentrations of Cl, ClOOCl and ClOO are in steady state, below what is the steady state concentration of Cl.

I keep going over and over it, but never quiet getting the right answer i.e. ending up with cancelling [M] out or having CLOO in the numerator etc. The correct answer should be [Cl] = 2J1 k1[ClO]² [M]/k4[O3](J1 + k2)

I have spent ages doing it, so could someone help me please?? I know it is something stupid I am doing wrong. Thank you in advance!

(1) ClO + ClO + M -> ClOOCl + M (k1)
(2) ClOOCl + hn -> Cl + ClOO (J1)
(3) ClOOCl + M -> 2 ClO + M (k2)
(4) ClOO + M -> Cl + O2 + M (k3)
(5) Cl + O3 -> ClO + O2 (k4)

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I've just noticed - hn in the 2nd reaction is supposed to be hv (as in photon energy)

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As nobody has replied and the fact i am getting pretty desperate here is my working:

(d[O3])/dt=J1[ClOOCl]+ K3[ClOO][M]- K4[Cl][O3]

(d[ClOOCl])/dt=K1[ClO]^2 [M]- J1[ClOOCl]- K2[ClOOCl][M]

(d[ClOO])/dt=J1[ClOOCl]- K3[ClOO][M]

Assuming steady state of all three, then:

[Cl]=(J1[ClOOCl]+ K3[ClOO][M])/(K4[O3])

[ClOOCl]=(K1[ClO]^2 [M])/(J1+K2[M])

[ClOO]=J1[ClOOCl]/(K3[M])

Substituing in ClOOCl from above,into [ClOO]equation
=(J1K1[ClO]^2 [M])/(K3[M]  (J1+K2[M]))

Substituing both ClOO and ClOOCl from above,into [Cl]equation
=(J1 K1[ClO]^2 [M]+K3J1K1[ClO]^2 [M][M])/(K4[O3]J1+K2[M]K3[M]  (J1+K2[M]))

Which even after collecting like terms together and cancelling out terms do not get the right answer:
=(J1 K1[ClO]^2+K1[ClO]^2)/(K4[O3]  (J1+K2)  K2)


So where am i going wrong??

[x1d57U]

Can anyone help??