Is there a chemical reaction that speeds up when the temprature gets lower?

We were talking about chemical reaction speed on our chemistry class, and I asked my teacher if there is a chemical reaction that speeds up when the temprature gets lower? I think this is not everyday chemistry and my teacher didn't have an example for one.

• Well, no I guess, since that's what the Arrhenius equation tells ya. You can't tell anything like "are there any positive charges that attract other positive charges?" so you can't say "Is there a chemical reaction that speeds up when the temprature gets lower?" – M.A.R. Jan 29 '16 at 9:50
• It seems like a bit of a cheat, but would enzyme-catalysed reactions count? Above some temperature, enzymes denature and become less effective, so as you cool the system below that critical temperature, it would go faster? – gilleain Jan 29 '16 at 9:55
• Related - Geoff's answer here chemistry.stackexchange.com/questions/18924/… – orthocresol Jan 29 '16 at 10:58
• +M.A.R "You can't tell anything about "are there any positive charges that attract other positive charges?" so you can't say "Is there a chemical reaction that speeds up when the temperature gets lower?" Those two are not the same thing. The Arrhenius equation works in only a few simple reactions and is not always applicable. So there are many reactions whose rate increases with a dip in temperature. – shre_sudh_97 Jan 30 '16 at 5:35

That's a good question.

A reaction slowing down on a rise in temperature seems counter intuitive but it's not so always.

The Arrhenius equation works for only a few limited elementary reactions and the transition state theory is a much better explanation of rate laws and their variation with temperature.

The dependence on temperature of the reaction rate cannot always be analysed purely using the Arrhenius equation. It can be better understood by knowing the mechanism of the reaction.

For instance $$\ce{2NO + O2-> 2NO2}$$

Has its first step as $$\ce{2NO <=> N2O2}$$

And the second step as: $$\ce{N2O2 + O2->2NO2}$$

The first step is exothermic in nature. And the equilibrium shifts to the left on increasing temperature based on the Van't Hoff equation of gaseous equilibrium.

So the effective rate constant of the overall reaction decreases on increasing the temperature.

Thus, we see a reaction whose rate slows down with the rise in temperature.

There are in fact many such reactions.

To give another example, I could take an enzymatic reaction in a living cell and show that the rate of reaction falls down drastically with a rise in temperature. Ever wondered why your body rises its temperature during a fever? The aim there is to slow down the reactions in the cells of the invading germ and hence kill it.

From these examples, one could conclude that the famous Arrhenius equation works in only a few limited(and ideal) cases.

• But isn't this a special case of a complex reaction which is rather artificial in the sense that the overall reaction rate decreases because a reactant is depleted? It doesn't say anything about how the reaction rates of the elementary reactions in this network change with temperature. If one focuses on elementary reactions and elementary reaction rates, can we observe a speed up when temperature decreases? Are there cases where the free energy of activation decreases when the temperature decreases? – The Quark Feb 2 '17 at 16:12