A blog, or more like a rant, against the use of Le Châtelier’s Principle in learning and teaching chemistry

Eric Scerri

UCLA

Department of Chemistry & Biochemistry

Los Angeles, CA

website: ericscerri.com/

Following my recent post on the sloppy use of the aufbau principle,

http://ericscerri.blogspot.com/2012/06/trouble-with-using-aufbau-to-find.html

I have been encouraged to try my hand at another blog on a topic in chemical education, namely the Le Châtelier Principle.

Here is a typical version of the principle that you might find in a chemistry textbook,

If a dynamic equilibrium is disturbed by changing the conditions, the position of equilibrium moves to counteract the change.

I want you to notice the use of the word “counteract” which is frequently also rendered as “oppose”, because I am going to argue that this is the root of all the problems associated with the use of this principle.  The principle is supposed to aid the student or even the expert in predicting the effect brought about by a change in conditions such as changing the total pressure on a system, or the concentration of one or more reactants or products or the temperature. 

In fact this is going to be more of a rant than a blog because I believe that this principle is more of a hindrance than a help.  The first time I ever taught a chemistry class was in a high school in London when I was standing in for another teacher and had to teach equilibrium theory and the use of the Le Ch telier Principle.  I made such a mess of the class and tied myself up in so many knots that I swore I would quit teaching immediately.  That is until I began to think more carefully about this issue and started to realize that the problem lay more with the wording in the principle rather than just with me.  

So what’s the problem?

Pretend for a moment that you are a novice student coming to this topic for the first time.  You are presented with the principle as a means of predicting the outcome of making one of three possible changes as mentioned above.  Of course you are happy to be given this guide and begin applying it to changes in pressure for example.  Let us assume we are discussing the case of the Haber reaction in which three moles of hydrogen react with one mole of nitrogen to yield two moles of ammonia.  You might visualize this mixture as being placed in a large balloon for example.  Now let’s apply the principle.  If the total pressure is increased you might be tempted to predict that the system or balloon will expand to a larger volume in order to “counteract” or “oppose” the increased pressure that is being applied in squeezing the balloon.  

But that’s wrong says the instructor

Unfortunately if you follow the letter of the principle in this way the instructor will soon tell you that you have made a wrong prediction.  Experiments show that on increasing the total pressure the equilibrium position shifts in such a way as to produce more ammonia, that is to say the equilibrium moves in the direction of a volume decrease rather than an increase. 

3 H_{2 (g)}     +      N_{2 (g)}       <---->       2 NH_{3 (g)}

So what went wrong?  Well you were supposed to assume that the volume remains constant for one thing so the analogy with squashing the balloon was invalid.  But nobody tells that to the poor student.  The change that does actually occur is more a case of ‘accommodating’ the change rather than opposing it, something which leads many textbooks[i] to alter the wording of the principle to something like the following version,

If a chemical system at equilibrium experiences a change… then the equilibrium shifts to accommodate the imposed change and a new equilibrium is established.

But just a moment!  This means making a 180⁰ change to the original statement.  Accommodating is surely the opposite of counteracting?  If I try to push you away and you oppose my push you push me back.  If on the other hand I try to push you away and you accommodate this change you might yield to my push and fall down to the floor.  It seems rather odd that the principle needs to be rescued by substituting a word for “oppose” which in facts means the very opposite of oppose.  

So how can it be done properly?

As anyone who teaches high school or college chemistry is aware there is a amore categorical way to predict the outcome of raising or lowering the total pressure on a mixture of gases in equilibrium.  This involves setting up an expression for the equilibrium constant for the reaction and expanding the partial pressure of each gas in terms of products of mole fractions and total pressures,

  
                K_p          =               (p NH₃)²

                                           (p H₂)³ (p N₂)

                          =             (M.F. NH₃)² (P_total)²

                             (M.F. H₂)³ (P_total)³. (M.F. N₂)(P_total)

where M.F. denotes mole fraction in each case. 

                           =                (M.F. NH₃)²

                                    (M.F. H₂)³ (M.F. N₂)(P_total)²

We can now argue that since pressure changes do not alter the value of the equilibrium constant, raising P_total results in an increase in the ratio of ,

                            =             (M.F. NH₃)²

                                   (M.F. H₂)³ (M.F. N₂)

which in turn implies an increase in the yield of ammonia at the expense of the mole fraction of the two reacts of hydrogen and nitrogen. 

The bottom line is that more ammonia is produced by raising the total pressure of the system.  

How about changes in concentration?

Whereas we are more or less forced to smuggle words like accommodate or alleviate into the original wording of the Le Châtelier Principle in order to make sense of what happens on raising the pressure, when it comes to changes in concentrations of reactants or products, it appears that the original word “oppose” does a perfect job in making sense of the situation.  Consider the following case in which substances A and B react together to form C and D,

A      +      B       <---->            C       +       D

If I raise the concentration of A or of B or even of both of them, the net outcome is that the equilibrium position will shift to the right and that larger concentrations of C and D will be produced.  Here the word “oppose” works fine.  As I increase the concentration of A for example the reaction responds by using up the additional A and as a result larger concentrations of C and D are formed.  

Of course this can all be done more rigorously by writing an expression for the equilibrium constant of the reaction and seeing what happens when one of the concentrations is increased.  It is easy to predict that the concentrations of C and D will be increased since making changes in concentrations of any substance has no effect of the equilibrium constant itself.   

Kc   =        [C] [D]

                  [A] [B]

What about temperature changes?

In the case of temperature the problem returns.  If we try to use the wording that involves “oppose” the constraint we can easily obtain the completely incorrect answer.  And I mean completely incorrect as in the case of pressure changes, in the sense of an error of 180⁰. 

Consider again the Haber reaction from above but now let’s include the sign of the enthalpy change on going from left to right which is in fact negative to denote an exothermic reaction.  

3 H₂      +      N₂     <---->      2 NH₃     : Delta H = - 92 kJ/mol

How might a student reason?

Let us again put ourselves in the shoes of a novice student trying to innocently use the Le Châtelier Principle in order to predict the outcome of raising the temperature on this system.  The student might reason as follows,

If the temperature of the system is raised and if the outcome is that the system attempts to oppose this change then the system will proceed in the exothermic direction so as to remove the increased heat.  Alas the instructor will immediately point out that this is the incorrect prediction.  Experimental evidence shows clearly that raising the temperature on any exothermic reaction has the effect of favoring the reaction which proceeds in the endothermic rather than the exothermic direction. 

Again, as in the case of pressure changes, the student feels let down by Le Châtelier.  Again in order to rescue the principle many textbooks will cheerfully alter the wording of the principle in order to say that the system will accommodate rather than oppose the change.  If so then they can argue that the additional heat is accommodated by the system’s moving in an endothermic direction, since absorbing the extra heat amounts to accommodating or nullifying the change.  So once again it is not a case of opposing the change but quite the opposite a case of yielding to the change or of accommodating it.

Taking stock 

If what I am saying is correct, then in the three classic changes that are typically considered, namely pressure , concentration and temperature changes, the original Le Châtelier Principle which features the word “oppose” only works in one out of three cases.  That’s not a very good success rate by any stretch of the imagination!

What to do?

My recommendation to textbook authors and chemistry instructors is quite simple.  Please ditch the use of Le Châtelier’s Principle as a guide to what happens when changes are made to chemical systems in equilibrium.  Instead do it rigorously from first principles by setting up expressions for the equilibrium constant and seeing what happens when changes are made to pressure of concentrations of reactants and products.  

Except for temperature changes

Notice that I have omitted temperature changes.  This is because the rigorous approach to temperature changes is different from what it is for pressure or concentration for the simple reason that equilibrium constants actually vary with temperature.  But there are simple thermodynamic expressions which can be used to predict what happens when the temperature is raised or lowered in cases of exothermic or endothermic reactions respectively. 

For example it can be shown that for exothermic reactions the equilibrium constant K is related to temperature in the following manner,

ln K  is proportional to  1/T

from which it follows that as temperature increases the natural logarithm of K decreases and so K itself decreases which implies that the reaction proceeds from right to left rather than the other way round.  Bottom line:  Exothermic reactions are favored by lowering the temperature rather than by raising it.  All this without getting tied up in knots with words and hand waving in trying to use the awful Le Châtelier Principle. 

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[i]  I don’t claim to have made a full survey of textbooks but here is an example of the variety in the wording used by a selection of general chemistry books,

•Atkins………………………………..….minimizes

•Chan…………………………………..…relieves

•Petrucci et al……………………..….partially offsets

•Whitten, Davis, Peck…….…….... counteracts

•Moore, Stanitsky, Jurs……………partially counteracts

•Brown, Le May, Bursten……..… counteracts

•Kotz, Trichel……………………..…..reduces or minimizes

•Zumdahl……………………………..…reduces

•Oxtoby, Gillies, Nachtrieb……….counteracts

                                    

Also found, “accommodates” the constraint