Conceptual tussle with kinetics of equilibrium and non-equilibrium processes Prologue:
Recently started with Chemical Kinetics at class. Came across a couple of points in Levine's Physical Chemistry (the book was recommended on Chem.SE; so I thought I'd give it a read :D) that I'm having serious issues wrapping my head around. This query is about the kinetics of equilibrium (and non-equilibrium) processes, and the fact that this has puzzled me for quite a while... I attribute to my (seriously questionable) understanding of equilibrium processes (courtesy: High-school education). It would be prudent to keep my shortcomings in Kinetics (newbie) and Equilibrium (possibly flawed understanding) in mind while addressing my query in your answer or the comments section. Thanks!

According to Physical Chemistry (Levine,I.N), Chapter 15, &quot;Kinetics&quot;:

Processes in systems in equilibrium are reversible and are comparatively easy to treat. This chapter and the next deal with non-equilibrium processes, which are irreversible and hard to treat. The rate of a reversible process is infinitesimal. Irreversible processes occur at nonzero rates.

Which, if I understood correctly, can be paraphrased as:

Equilibrium processes are reversible and have infinitesimal (practically &quot;non-existent&quot;) rates.
Non-equilibrium process are irreversible and have non-zero (&quot;finite&quot; or &quot;significant&quot;?) rates.


From my &quot;understanding&quot; of Equilibrium; chemical equilibrium is an example of dynamic equilibrium. When a chemical reaction, $$\ce{A + B -&gt; C + D}$$
has proceeded to equilibrium. The &quot;forward&quot; rate of reaction (rate at which $C$ + $D$ is spit out) must equal the &quot;backward&quot; rate of reaction (rate at which $A$ + $B$ is spit out). There is no net formation of products/reactants, but both the forward and backward rates are positive and finite.

My question?
Why does Levine say that equilibrium processes have &quot;infinitesimal&quot; (almost non-existent) reaction rates? I thought the forward and backward reaction rates in a reaction at equilibrium are finite...
OK, I think I am correct about this. If not then I suppose somebody will come along and correct me anyway.

The author here is referring to the net rate being infinitesimal. To understand where the infinitesimal comes from, we need to figure out what is being meant by an "equilibrium process", or a "reversible process". On page 43, Levine describes a reversible process as


  one where the system is always infinitesimally close to equilibrium, and an infinitesimal change in conditions can reverse the process to restore both system and surroundings to their initial states.


Often these are exemplified using thermodynamics processes, e.g. expansion/compression of a gas, but since we're talking about chemical kinetics, we could use an example where the temperature of the system is being increased in a reversible fashion. This means that the temperature is being increased in infinitesimal steps of $\mathrm{d}T$. The total change in temperature of the process is calculated via integration:

$$\Delta T = \int_{T_1}^{T_2}\mathrm{d}T = T_2 - T_1$$

and likewise for other properties. If something (e.g. the pressure $p$) depends on temperature, i.e. $p = p(T)$, then we can find the overall change in pressure

$$\Delta p = \int_{p(T_1)}^{p(T_2)} p(T)\,\mathrm{d}T$$

If the system is at equilibrium ($Q = K$), then an infinitesimal increase in temperature leads to an infinitesimal change in the equilibrium constant $K$, and hence an infinitesimal change in $Q$ (essentially this is due to Le Chatelier's principle, but more properly it is explained by the system moving in the direction of decreasing Gibbs free energy). This leads to an infinitesimal change in the concentrations of the reacting species, and hence the overall rate of reaction is infinitesimal.

If nothing is changing, the system would still be considered as being at equilibrium. The net rate in this case is, of course, zero. However, such a system is not particularly interesting, as there is no process actually occurring.

So, the bottom line is that for a system in equilibrium, its properties must be changing at most infinitesimally.