Spontaneous/Non-Spontaneous Reactions and Reversible Reactions

My chemistry textbook states "Reversible reactions constitute a limiting case between spontaneous and non-spontaneous processes."

Does this mean that some of the reversible reactions are spontaneous and others are not? Or that the reversible reactions are sort of intermediary between said two types of reactions? Or something else?

• Your "non-spontaneous" in this context probably means with lowering of entropy of universe - there's no such process, reversible with constant entropy also doesn't really exist and spontaneous with raising entropy of univ. - all processes, so generally this sentence is stupid. – Mithoron Jan 4 '16 at 14:34
• – Mithoron Jan 4 '16 at 14:36
• Also I have a feeling you'd better get better textbook... – Mithoron Jan 4 '16 at 14:38
• cant its sort of a standard. – Batwayne Jan 4 '16 at 14:42

"Reversible reactions constitute a limiting case between spontaneous and non-spontaneous processes." So what does this mean?

To me this sentence is meaningless gobbledygook and should be ignored. That is, this sentence is unhelpful and trying to understand it will just make you more confused and less able to master chemistry. Here is a short summary version of the points I make in the "Advanced discussion" below:

• All reactions can be viewed as reversible from a mathematical standpoint, if the reacting system is "big enough". Reactions that are highly spontaneous in the forward direction mean that at equilibrium, the number of "reactant" molecules will be very very small (but not zero!).

• Many times, "big enough" would mean astronomically big, such as bigger than the Earth. In these cases, reactions can be regarded as "irreversible", although there is no strict, universally agreed upon boundary between "reversible" and "irreversible".

• Whether a reaction is spontaneous isn't that much related to whether it is "reversible". Don't worry about understanding the connection between these concepts until you have understood each concept independently.

The meaning of spontaneous

Spontaneous processes have negative Gibbs free energy changes ($dG < 0$) and also result in positive entropy changes in the universe ($dS_{univ} > 0$). However, $dG$ is a function of state.
For chemical reactions, this means that $dG$ depends on the concentration of the reactants and products, i.e.

$$dG = dG^\circ + RT \ln Q$$

where $Q$ is the reaction quotient.

Thus, if we start off with all "product" and no reactant, then the "reverse" direction of the reaction will be spontaneous. But if we start off with all reactants and no product, then the forward direction is spontaneous.

The meaning of reversible

The short answer is that for chemical reactions, "reversible" does not have a precise thermodynamic definition.

$$dG = dG^\circ + RT \ln Q = -RT \ln K + RT \ln Q = RT \ln \frac{Q}{K}$$

where $K$ is the equilibrium constant. People will usually call reactions with a "large" equilibrium constant irreversible and those with a "small" equilibrium constant reversible. But the exact definition of "large" and "small" isn't well-defined. Many people might say $\frac{Q}{K} \leq .01$ represents an "irreversible" reaction. For chemical reactions with very large equilibrium constants, the size of the system required to ensure that an equilibrium can be reached can get very large, as explained here.

Your textbook has it backwards. Reversible reactions are not a limiting case of spontaneous reactions and non-spontaneous reactions. Spontaneous reactions and non-spontaneous reactions are limiting cases of reversible reactions. As several responders have pointed out, if a reaction only proceeds a little before reaching equilibrium, it approaches the case where no reaction occurs (aka non-spontaneous reaction). If the reaction proceeds to nearly completion before reaching equilibrium, it approaches the case of complete conversion (aka spontaneous reaction).

I agree with other answers and comments that your textbook does not have things stated correctly so I have explained below in words only what I see as the difference between Irreversible and Reversible processes. (You will find spontaneous reactions hidden in these statements)

Every system left to itself will change, rapidly or slowly, in such a way as to reach a state of rest defined in a statistical way and this is also called the state of equilibrium. The system will only move away from its state of equilibrium through the influence of some external events. We are familiar with many processes that reach equilibrium, diffusion of a concentrated solution into a dilute one leading to uniform concentration, transfer of heat from a hot to a cold body leading to uniform temperature, oxidation of substances by the atmosphere, self demagnetisation of magnets are all examples of spontaneous events in nature.

These processes and all other natural processes are similar in one respect, that they all bring the system to equilibrium, and we may think of these systems as loosing some measure of their capacity for spontaneous change.

A system far from equilibrium is one which we would choose to harness for doing useful work, for example the combustion of coal in air to cause a steam engine to operate. However, the second law shows us that it is not the loss of energy that is important but rather the availability of the energy for external purposes.

The essential content of the second law can be given by the statement that when any actual process occurs it is impossible to invent a means of restoring every system concerned to its original condition. Therefore, in a technical sense, any actual process is said to be irreversible.

The ideal or reversible process

We now distinguish between an actual system, which is always irreversible, and an ideal one, which although never occurring in nature is nonetheless imaginable. Such an ideal process is called reversible. In such a process each stage is conducted so that an infinitesimal change in the external conditions would cause a change in the direction of the process. In this sense such an imaginary system is called reversible.

An example is a system of water and water vapour inside a cylinder with a frictionless moveable piston. (In practice, by careful engineering, we can make the friction so small that it is negligible). Outside the piston is gas at some pressure. At constant temperature the system comes to equilibrium with respect to external conditions (pressure , temperature). If now the external pressure is increased, by the piston moving in by an infinitesimal amount, water vapour condenses. If the pressure is now reduced by an infinitesimal amount, some water evaporates. Thus the work required to vaporise 1 mole of water and to condense 1 mole of vapour differs only by an infinitesimal amount.

Another example is provided by an electrochemical cell where the cell potential can be measured extremely accurately with a voltmeter. The cell can be balanced so finely against an external emf that the current that can be made to flow in one direction or the other is only microamps.

A similar situation applies to thermal processes, since if two bodies differ in temperature by only an infinitesimal amount, the transfer of heat is likewise a reversible process for it would be possible to restore the system to its original condition with only an infinitesimal change in the external system.

(for a fuller description see Lewis & Randall 'Thermodynamics')

Reversible reactions constitute a limiting case between spontaneous and non-spontaneous processes [?]

A reversible process is a hypothetical process where the entropy of the system and its surrounding is constant. This is hypothetical because nothing happens unless the entropy increase at least a tiny bit. In other words, if the system is at equilibrium, the entropy does not increase, but nothing happens either.

Colloquially, a reversible reaction is one where forward and reverse reaction happen, i.e. one that would attain equilibrium at some point (if "left alone").

What I think the textbook is trying to say is that the Gibbs energy is negative for a spontaneous process, is positive for a non-spontaneous process, and is zero for a process that is at equilibrium. (This would be at constant pressure in the absence of non-PV work). So if you have an axis with the Gibbs energy for a process, there is a point where the system is at equilibrium. On one side of it are the spontaneous and on the other side are the non-spontaneous processes.

I'm not sure how that statement helps to understand anything, though. I also don't think it is the correct way of using the term "limiting case". Wikipedia gives the following definition:

In mathematics, a limiting case of a mathematical object is a special case that arises when one or more components of the object take on their most extreme possible values.

So maybe one could say a reaction that goes to completion is the limiting case of a reaction with a high equilibrium constant. In the statement in question, however, there is talk about a "limiting case between" two cases, not the most extreme value of either of them.