Order of reaction with and without the presence of catalyst

When ethene reacts with hydrogen to give ethane in the presence of Ni, the order of the reaction is 2, if I am not wrong, please correct me if I am. But if we remove the catalyst, and simply allow ethene with hydrogen to react (assuming the reaction does indeed take place without the catalyst, albeit slowly probably), will the order of the reaction change? Because it might undergo via a different mechanism. If it does change, what is the order of this reaction without the catalyst?




The reaction of hydrogen with ethylene (ethene) will be very very slow. The HOMO of hydrogen and the LUMO of ethylene are such that there will be no net orbitial overlap. As a result the gas phase reaction of H2 with ethylene will be impossible.


[![enter image description here](https://i.stack.imgur.com/F0dtC.png)](https://i.stack.imgur.com/F0dtC.png)


There might be a possibility that we could react hydrogen and ethylene in a free radical reaction but I will ignore that possibility.


The order of a reaction normally relates to a homogenous reaction, it normally relates to the rate limiting step (rate determinign step, RDS). The order of the reaction normally is determined by the number of molecules of a given species which must react in this step. It is worth noting that equilbria might be hidden from the casual viewer, cosndier the order of the reaction of NO (nitric oxide) and oxygen in the gas phase.


The problem of reactions on metal surfaces is that the reaction is not of free ethylene and hydrogen, but instead it is of metal bound molecules. The most simple model for dealing with the adsorption of gases onto surfaces is the Langmuir isotherm model.


I have dug up some real life data for alkene hydrogenation and the order of the reaction is not simple (Journal of Molecular Catalysis A: Chemical
Volume 320, Issues 1–2, 1 April 2010, Pages 34-39). On sulfided NiMo the order of reaction for the alkene (olefin) is about 0.25 while the order for hydrogen is about 1.2.


If you read Kinetics of ethylene hydrogenation over a supported nickel catalyst, Ho-Peng Koh and R. Hughes, Journal of Catalysis, Volume 33, Issue 1, April 1974, Pages 7-16 you will see that the reaction is first order with respect to hydrogen but about 0.25 order with respect to ethylene. The order with respect to ethylene changes as a function of temperture.


I think that you are thinking about a very difficult problem, I think it is one which a lot of PhD students would struggle with. So if you are having trouble then please do not panic.


If you want to understand the problem then there are several ways to deal with it. You need to consider the adsorption of two substances onto the metal surface. What has to happen is that the hydrogen molecules must first adsorb as H2 molecules, they then dissociate into hydrogen atoms which are on the nickel surface.


Next the ethylene which is adsorbed onto the nickel has to react with a hydrogen atom to form a ethyl group. The ethyl group then has to react with another hydrogen atom to form ethane. The ethane will be far less able to bind to the surface so it will fly away.


You have have to consider what is the slow step on the nickel surface, also the binding of one of the substrates can reduce the number of active sites which are able to bind to the other one. The langmuir model is pretty good and it has three core rules.


1. A site is either empty or occupied by a thing
2. All sites are identical
3. What happens at one site has no effect on another site.


If you want to get an insight into alkene hydrogenation, one thing you could consider is thinking about the chemistry of Wilkinson's cataylst, this is likely to be one of the best small molecule models for the hydrogenation of alkenes on a metal surface.


The cycle for Wilkinson's catalyst is this four step cycle.


[![enter image description here](https://i.stack.imgur.com/luLkf.png)](https://i.stack.imgur.com/luLkf.png)


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