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### AuthorTopic: Rate Law for Halogenation of a Hydrocarbon?  (Read 866 times) !function(d,s,id){var js,fjs=d.getElementsByTagName(s)[0];if(!d.getElementById(id)){js=d.createElement(s);js.id=id;js.src="https://platform.twitter.com/widgets.js";fjs.parentNode.insertBefore(js,fjs);}}(document,"script","twitter-wjs"); (function() {var po = document.createElement("script"); po.type = "text/javascript"; po.async = true;po.src = "https://apis.google.com/js/plusone.js";var s = document.getElementsByTagName("script")[0]; s.parentNode.insertBefore(po, s);})();

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#### ruetherford

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##### Rate Law for Halogenation of a Hydrocarbon?
« on: December 06, 2018, 08:57:11 AM »

Hi, I'm working on this problem for PChem and am getting some rather hairy answers!

Work:

The rate of the reaction should be: $$R = \frac{-d[RH]}{dt} = \frac{-d[Br_{2}]}{dt} = \frac{d[RBr]}{dt} = \frac{d[HBr]}{dt}$$

I used the steady-state approximation to solve for: $$0 = \frac {d(Br)}{dt} = 2k_{1}Br_{2} - k_{2}BrRH + k_{2}RBr_{2} - k_{4}BrR$$ and $$\frac{d(R)}{dt} = 0 = k_{2}*Br*RH - k_{3}*R*Br_{2} - k_{4}*Br*R$$

And eventually got: $$[R] = \frac{[ B][RH]k_2 - [Br_2]k_1}{[Br2]k_3}$$ and $$= \frac{[Br2]([R]k_3 + k_1)}{[RH]k_2}$$

However, when I go on to plug these back into the SS equations (to get [R] and [ Br] in terms of [RH] and [Br2] only), I get some pretty nasty-looking stuff and end up with a crazy-looking quadratic. Am I approaching the problem wrong?
« Last Edit: December 06, 2018, 11:51:04 AM by Borek »
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#### Corribus

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##### Re: Rate Law for Halogenation of a Hydrocarbon?
« Reply #1 on: December 07, 2018, 09:53:27 AM »

First, maybe it's just a typo in your syntax here but your first steady state approximation expression is wrong (there should be a k3 term). I'm also not following how you got from your steady state expressions to your "and eventually got" expressions. What happened to your k4 terms?
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#### mjc123

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##### Re: Rate Law for Halogenation of a Hydrocarbon?
« Reply #2 on: December 09, 2018, 09:59:02 PM »

If you add the equations for d[Br·]/dt and d[R·]/dt, you get that k1[Br2] = k4[R·][Br·].
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