152 Chemical thermodynamics
whichallows another pathnot shown on thegraph,whichhas alowerbarrier or none
at all. As an example, let us consider one possible mechanism for the gaseous reaction
A+B→AB. Perhaps the reaction willonly proceedifwe succeedin gettingAand
Bsufficientlyclose together that an electron canjumpfrom one atom to theother.
In the gaseous phase, this close approach may need a very high energy collision, the
reasonfor thehighenergybarrierV,inorder to overcome the usualshort-range
repulsionbetween the atoms; otherwise the atoms willmerelycollideelasticallyand
bounce away without reaction. A possible catalyst here is to introduce a large surface
area ofasuitablesubstance (e.g.platinumblack, veryfine platinum metal). Atoms
can now stick to the surface for a while and,given the right catalytic material, come
into sufficiently close contact upon it, rather than having to await a mid-air encounter.
However,intheabsence ofsuchan artificialaid,theonlyroute remainingis route
(iii), findingenough energytoget right over theVbarrier.For this reasonVis
often termed theactivation energyfor the reaction. The energy must be found from
thehighenergytailofthethermalBoltzmanndistribution. Thecollision mechanism
mentioned above can be used as an illustration of what this implies. A collision
between an A and a B atom will usually not cause a reaction. Only in the (unlikely)
event ofa nearhead-on collisionbetween twofast-movingatoms willtheclose
encounter takeplace. This implies a reaction rateR(reaction probability per second)
of the formRfexp(−V/kkkBT),wherefis an attemptfrequency (thecollision
rate) andthe exponentialBoltzmannfactor represents the probabilityofthe energy
condition being satisfied. Needless to say, an exact treatment of reaction rates is much
more elaborate than thisquicksketch. Howeveritgives the correctflavourfor almost
allreactionsinsolids,liquidsorgases. Thermalactivation over an energy barrier
always invariably plays a fundamental role and its probability is well governed by
theBoltzmannfactor.
In manychemical reactions, the activation energyis of order of 0.5–1 eV, the typical
energyscaleforanyelectronictransitionsinatoms. ThusitisthattheBoltzmannfactor
canbe very small(say 10−^10 at room temperature), andhence also the temperature
dependence ofRis veryfierce. Asmall temperature rise oftengives a marked increase
in rate, as a cook’s timetable shows; and also the rateRbecomes effectively zero when
the temperaturefallssignificantly,leadingto metastability(i.e. zero reactivityinthis
context)as stated at the start of this section.