Mechanism of a reaction

[hitmankratos]

Hi,

 

We've had this chem assignement at school, and I'm stuck! I've tried everything but it just doesn't work. I don't even think anyone here can help me, but meh, might as well just give it a try.

 

So we have this reaction : 2NH₃ ---> N₂ + 3H₂

 

So we're asked to find a plausible mechanism (basically invent one!) that can give the following rate law:

Rate = k[NH₃] / [H₂]

 

I've spent about 3 hours trying diffrent mechanisms that take in account the balanced equation, but it never gives the right rate law.

 

For example. I'Ve had this mechanism (the * means radical):

NH₃] --> NH₂* + H*

NH₂* --> N* + H2

N* + NH₃ --> N₂H* + H₂

N₂H* + H* --> N₂ + H₂

 

When I take the last step for the slow step (as the rate law depends only on the slow step), I get something like

Rate = k[NH3]² / [H2]² ... AND I ALWAYS GET SOMETHING SIMILAR!

So any ideas?

[Pwyll Pendefig Dyfed]

When I take the last step for the slow step (as the rate law depends only on the slow step), I get something like

The first step (not the last step) is the slow, rate determining step.

[hitmankratos]

yes you're right, it can't be the last step. But in my case it cannot be the first step.

[mississippichem]

The rate equation you've made for the overall reaction is not necessarily true:

 

[math] \frac{d[N_{2}]}{dt}=-k[NH_{3}]^{2}[H_{2}]^{-2} [/math]

 

Remember the order of each reactant in a rate equation can only be determined by stoichiometry if that equation is for an elementary step. Show me how you derived that rate law. To check, you can always derive integrated rate laws to see if everything is internally consistent:

 

[math]-\frac{d[X]}{dt}=-k_{1}[X][/math]

 

[math]\frac{d[X]}{[X]}=-k_{1} dt[/math]

 

[math]\int\frac{d[X]}{[X]}=\int-k_{1} dt[/math]

 

[math]ln[X]=-k_{1}t+r_{0}[/math]

 

*where r_0 is the instantaneous initial rate

 

After deriving those for every particular reactant you can use graphical methods to make all the curves fit. That integrated rate law above is for a 1st order elementary step. The math is a little different for 0th and 2nd order steps.