Reaction, find the k for the overall reaction

[flyingpig]

Homework Statement

The following three step mechanism has been proposed for the reaction of chlorine and chloroform

(1) $$Cl_2 (g) \rightleftharpoons 2Cl(g)$$

(2) $$Cl (g) + CHCl_3 (g) \rightarrow HCl (g) + CCl_3 (g)$$

(3) $$CCl_3 (g) + Cl(g) \rightarrow CCl_4$$

The numerical values of the rate constants are for these steps are $$k_1 = 4.8 x 10^3$$, $$k_{-1} = 3.6 x 10^3$$, $$k_2 = 1.3 x 10^-^2$$, $$k_3 = 2.7 x 10^2$$ respectively.

Derive the magnitude of k for the overall reaction

2. Irrelevant Information

I spent two days on this problem (with another problem which I am about to post) and I am about to give up, it is due tonight and I just want to get over this and start studying my other midterm tomorrow

The Attempt at a Solution

So I wrote down the rate laws for each reaction

(1) Rate = k₁[Cl₂] = k_-1[Cl]

(2) Rate = k₂[Cl][CHCl₃]

(3) Rate = k₃[CCl₃][Cl]

CL, CCl₃ are intermediates so I got rid of them(1) Rate = k₁[Cl₂]

(2) Rate = k₂[CHCl₃]

(3) Rate = k₃[CCl₃]

 

[epenguin]

The Attempt at a Solution

So I wrote down the rate laws for each reaction

(1)[STRIKE] Rate =[/STRIKE]

k₁[Cl₂] = k_-1[Cl] and that's still wrong. Look at the back reaction again.


(2) Rate = k₂[Cl][CHCl₃]

(3) Rate = k₃[CCl₃][Cl]

wrong again. You just can't write rate = . If you wrote rate of what you would not make these mistakes. Write d[something]/dt = and you might realize what you are talking about and get somewhere.

CL, CCl₃ are intermediates so I got rid of them. You can't 'get rid of' intermediates by just forgetting them! They are what the reaction depends upon! You have to get them out of your equations by (elementary) algebra, so that the rates are expressed in terms of the knowable bulk concentrations.

Then, this problem depends on (and is simplified by) the fact that different reactions here have very different rates. There are surely examples in your texts or notes of using this fact in equation derivations. You surely have models for how it is done in your course material.

Finally, but as essential as anything else, you quote the rate constants without any units, as pure numbers which they are not - wouldn't mean anything. If you gave them their units probably some of your errors would be avoided.