[Rutherford]

Rate of the reaction:
2CO(g)+O₂(g) 2CO₂(g)
expressed as the change of CO₂ concentration in time unit is in the 5th minute in relation to the first minute:
a) bigger;
b) smaller;
c) same;
d) bigger if a catalyst is present;
e) lower if a catalyst is present;

b) is correct. When the reaction starts, the concentration of CO₂ increases and so does the speed, why isn't a) true then? When a catalyst is added, the concentration should be even more increased, why isn't this true?

[Corribus]

I had to read this several times to completely understand what you're asking.  I presume you're asking why the (forward) reaction rate gets smaller as time increases.

If you assume that you start with a closed vessel with only CO and dioxygen, it's pretty easy to see that the forward rate of the reaction will be initially high whereas the rate of the reverse will be exactly zero, because there's no carbon dioxide to begin with.  Reaction rate between CO and dioxygen is proportional to the frequency (rate) of collision between the two reactants, which in turn is based on their concentration.  As the reaction proceeds, the amount of CO and dioxygen decreases (and the amount of carbon dioxide increases), which reduces the probability per unit time of a collision between these two reactants.  Therefore the rate goes down as time increases.  At the same time, the rate of the reverse reaction will increase because the rate of collision between two carbon dioxide molecules increaes per unit time - because as time increases the concentration of carbon dioxide grows.  This trend continues until the forward rate equals the reverse rate, at which point equilibrium is reached and there are no further reaction dynamics.

(I realize that this reaction is not framed as an equilibrium, but the same argument generally holds.  In "irreversible" reaction, it simply is that the reverse reaction rate is just so incredibly slow as to be negligible.  Even so, the rate of the forward reaction still slows down, even if the reverse reaction rate is ZERO, because the frequency of reactant collision still approach zero as the reactants are consumed.)

The presence of a catalyst doesn't really change anything, other than to reduce all reaction rates by various mechanisms.  Rates of collisions may not be significantly changed by a catalyst, but even if they are, they are still proportional to the concentration at a given time.  As before, when the concentration of the reactants drop, the collision rate also drops, so the overall rate of reaction drops, regardless of whether there is a catalyst there or not.  Primary function of a catalyst is often just to increase the likelihood of a reaction taking place once a collision has happened.  (I.e., collision between reactants often isn't enough to make a reaction go - catalysts help out by making conditions for reaction more favorable once a collision has happened.)

Does this help?

[By the way, the rate of the forward reaction can be expressed either as a function of the increase in concentration of the product or the decrease in concentration of the reactant(s).  The rate of the forward reaction is not dependent on which way you choose to express this, assuming this is the only reaction taking place in the chamber, of course.  Typically rate laws are expressed in terms of the reactants, though, because it is frequency of collisions between reactants that is usually a primary determinant of reaction rate.  This might be your point of confusion, though, since your question is framing the forward reaction in terms of a change in the product concentration, not a change in the reactant concentration.]

[Rutherford]

Thanks for the nice explanation.

I can write: r=d[CO₂]/dt. At the beginning the reactants are colliding more as their concentrations are relatively big. Then, they decrease, so the number of collision per time unit decreases, too and less amount of CO₂ will be produced, so it is b).

It is lower anyway, so a catalyst presence won't change anything instead of lowering the rate even more.

"Primary function of a catalyst is often just to increase the likelihood of a reaction taking place once a collision has happened.  (I.e., collision between reactants often isn't enough to make a reaction go - catalysts help out by making conditions for reaction more favorable once a collision has happened.)"

This part I don't understand. How catalysts make a reaction more favorable after a collision? I think they should either take part in a collision to produce an intermediate or to absorb molecules that will react on their surface.

[Corribus]

Different catalysts speed up reactions in different ways.  There's no general way to describe their function, although most of them tend to reduce the reaction rate by lowering the activation energy for reaction in some way.  This could be something as simple as increasing the likelihood that reactants collide in such a way as to more easily produce a required transition state (i.e., by forcing them to come together with favorable geometry), to something more complicated like forcibly removing electrons from one reactant and transferring them to another, as in the case of certain biological enzymes. 

I can’t think of a simple real example of a catalyst changing reaction likelihood after collision, but it should be easy for you to visualize how every collision between two generic reactants might not yield a reaction – all reactions proceed through transition states (intermediate, short-lived states) of very particular geometries.  Generally the relative orientations of reactants when they collide are random, and only specific relative orientations will allow the reactants to combine in the right way to allow them to react.  (Think of two LEGO bricks – they only fit together in a certain way, with the top of one brick having to fit into the bottom of another brick.  If you were to close your eyes and bring them together in random orientations, only sometimes will you bring them together so that they lock and form your two-brick product.  At other times, and probably the majority of times, they’ll just bounce off each other and remain separate.)  Anyway, in the Arrhenius expression – which is reasonably accurate for most simple reactions - the pre-exponential factor A can be approximated as being related to how likely two reactants are to collide, and the exponential term ([itex]e^{\frac{-E_a}{RT}}[/itex]) can be thought of as the likelihood that two molecules will react once they do collide.  One of the things many catalyst do – particularly enzyme catalysts – is force reactants to collide in geometrically favorable ways by bringing them together with particular orientations, which increases the likelihood that colliding molecules will in fact “stick together” and readily form transition states required to complete reactions. 

Perhaps a simple case demonstrating how a catalyst works is that of hydrogen peroxide, which spontaneously decomposes to from water and oxygen gas. 

2H₂O₂ 2H₂O + O₂

It is an electrochemical disproportionation reaction that involves collision of two hydrogen peroxide molecules, and to proceed the oxidation state of one of the oxygen atoms must change from formally -1 to -2 and the other must change from -1 to 0.  I.e., one oxygen atom is reduced and the other is oxidized.  This is thermodynamically favorable for a variety of reasons, including the fact that oxygen is not particularly happy at -1 oxidation state, and there's a lot of electron-electron repulsion in an O-O single (sigma) bond, which renders it unstable.  Still, despite the thermodynamic favorability of this reaction, the decomposition is reasonably slow.  Here we highlight a distinction between kinetics and thermodynamics.  (A similar result can be observed in combustion of a simple alkane - a reaction that is very thermodynamically favorable but which will not go at ambient temperature without an ignition source and/or quite a bit of latent heat.  Here the primary kinetic activation barrier is incompatible spin states between oxygen [triplet] and the alkane [singlet].)  The reason the peroxide decomposition is slow is that there is that transferring two electrons through space simultaneously is a reasonably unfavorable process – it takes a fair bit of energy to accomplish, which is represented as an energy barrier: an activation energy. 

Anyway, the reaction WILL proceed on its own, but a variety of catalysts speed the rate up quite significantly.  A ferric iron source, (Fe³⁺) is a common catalyst for hydrogen peroxide decomposition in simple solution.  Ferric ions do not increase the reaction by changing the likelihood of any kind of collision between two hydrogen peroxide molecules.  What iron does is facilitate the transfer of electrons between itself and a series of intermediate iron-oxygen complexes.  This mechanism is more complex than the simple catalyst-free reaction and one might think it should be slower, but in fact electrons are transferred much more readily to and from a “flexible” metal atom like iron (which can easily handle many oxidation states, and can do the transfers one at a time), which effectively lowers the activation energy and speeds up the reaction significantly. 

A similar type of catalysis happens in living organisms – the enzyme catalase speeds up decomposition of hydrogen peroxide (a reactive oxidant which would otherwise destroy important biological membranes) using a similar iron source.  Actually the effect in catalase seems to be much stronger than in “bare” ferric ions, a process which I do not think is completely understood.  As mentioned earlier, enzyme catalysts typically are engineered to not only reduce activation energies but force reactants into favorable geometries for reaction, which I wager is probably involved in the enzyme’s function at some level.

Note that in the case of the iron catalysis of hydrogen peroxide decomposition, iron doesn’t increase the frequency of collision between two hydrogen peroxide molecules.  In fact, with an extra species in solution involved – especially when one of them, the iron, is at very low concentration – you might expect the necessary frequency of collision to decrease and therefore the rate to decrease.  But this is more than offset by the huge gains in rate that you achieve by decreasing the activation energy.  If you look at the Arrhenius expression, you’ll see the rate is proportional to A (the pre-exponential factor is essentially a measure of, among other things, frequency of collision) but the impact of activation energy has an inverse exponential influence.  So the activation energy effect will ultimately dominate.   That said, I’m not sure to be honest if the hydrogen peroxide decomposition follows Arrhenius kinetics, and when the iron catalyst gets involved, it almost certainly doesn’t (because the mechanism then involves several steps), so that kind of simplistic argument doesn’t really apply.  Even so, I hope it is a useful example to you of how a catalyst works with respect to changing the likelihood of reaction.

By the way, this topic seems very advanced for high school level chemistry.  So either this discussion is in the wrong place or perhaps I’m approaching it from too high a conceptual level.  If I am being unnecessarily confusing, please let me know and I can endeavor to simplify the explanation.

[Rutherford]

No, you explained it very deeply and accurately. What I understood by the decrease of activation energy is that instead of the product of a reaction that has a big activation energy, an intermediate is formed with the catalyst (this usually happens in homogenous catalysis). The intermediate has a lower activation energy and then we say that the activation energy decreased.
In heterogeneous catalysis, the reactants are bounded to the catalyst sites where they react. This time the activation energy didn't change, but the collisions are more efficient. Now A changes, or better said P (steric factor). Is my reasoning correct?

I posted this problem in the High School section because it is from a high school competition.

[Corribus]

Raderford, in general the only difference between heterogeneous and homogeneous catalysts is that in the former, the catalyst is in a separate phase from the reactants.  Usually this kind of catalysis happens at a solid surface.  For instance, something like Raney nickel (a fine nickel powder used in hydrogenation reactions) would be considered a heterogeneous catalyst.  Like all catalysts, heterogeneous catalysts usually work by decreasing the activation energy of a reaction, although unlike homogeneous catalysts diffusion of the reactants to the catalytic surface can be rate limiting in a heterogeneous catalyst.  This is why the fineness of the catalyst particle size can greatly impact the efficiency of heterogeneous catalysis - and why nanoscale surface structure is such a huge area of catalysis research right now.

[Rutherford]

I knew the difference in general, but I was speaking more specially.

"heterogeneous catalysts usually work by decreasing the activation energy of a reaction"

How does it do this? I thought it's only changing the factor A (or steric factor P).

[Corribus]

Again it's hard to speak generally, since every catalyst is different.  Raney nickel, for instance, is a highly porous, fine nickel-aluminum powder that is activated with sodium hydroxide.  This causes a reaction between the aluminum and the hydroxide which essentially loads up the porous material with hydrogen gas - easily adsorbed (trapped) in all the fine pores.  This activated catalyst is very efficient for hydrogenation reactions, whereby substrates to be hydrogenated themselves bind to the catalyst and are brought within close proximity of bound hydrogen - thereby increasing the rate of reaction.  Essentially the catalyst works by providing a region of very high concentration of one of the reactants.  A similar effect happens with the catalyst in the Haber process, an industrial catalyzed reaction to turn nitrogen and hydrogen gas into ammonia.

I would say that most surface-based catalysts function in some similar fashion, although some may facilitate transfer of electrons in much the same way iron does in the peroxide example above.

I think that while the Arrhenius equation is a convenient place to start, it can be misleading to rigorously discuss the effect of a catalyst in terms of A or the activation energy.  The common wisdom is that catalysts speed a reaction up by reducing the activation energy - and generally by changing a reaction with one high energy step into a process which has multiple lower energy steps.  However I think this is a rather simplistic view - once catalysts get involved, particularly those that involve complex adsorption or desorption steps, an Arrhenius approximation is likely not a very good way to discuss the reaction kinetics, even if it still can be used to approximate the actual overall rates involved.  Remember, the Arrhenius expression is a semi-empirical formula that isn't based on any first-principles theory - connection to fundamental quantum mechanical and statistical mechanical considerations were only made later on, and the Arrhenius parameters are experimentally determined quantities. 

In short, there are better, more sophisticated ways to view, model and explain the impact of catalysts on the dynamics of a reaction than the Arrhenius equation.

[Rutherford]

Okay, thanks very much for clarifying this.