Quantitative LeChâtelier’s Principle: From ICE Table to MICE table

ICE tables are useful for solving K_sp problems and Weak Acid-Base equilibrium problems, too.

Once students master the use of an ICE table, the next major lesson usually involves LeChâtelier’s Principle, LCP:

When any system at equilibrium for a long period of time is subjected to a change in concentration, temperature, volume, or pressure, (1) the system changes to a new equilibrium, and (2) this change partly counteracts the applied change.¹

We usually teach LCP from a qualitative prespective. A bunch of years ago, I came across the following problem in a most excellent book.²

sample2.png

This problem screams LeChâtelier . . . but it’s a quantitative scream.

Before beginning the quantitative problem solving, look at it qualitatively. If CO₂, a reactant, is removed from the system, the reverse reaction will predominate until equilibrium is re-established. This will result in a lower concentration of CO, which will be confirmed with a calculation . . .

To get the correct answer with minimal frustration, I recommend the use of a modified ICE table; my students call it a MICE table. In this instance, the first row—formerly [Initial], is

replaced with [Equilibrium]_initial. The next row allows us to account for the [stress], followed by a row for [response], ending with [Equilibrium]_final.

Fortunately for us—and thanks to Mother Nature—an equilibrium system at constant temperature has a constant K_eq value, regardless of whether its undergone a stress.⁴

We will solve Sample Problem 2 using a color-coded MICE table corresponding to the problem above. The given information is indicated in blue; the stress is shown in red. The initial response, calculated from the given information is in green, with the subsequent, stoichiometrically-derived responses in brown. [Equilibrium]_final as in black.

sample_2_ice.png

And so 0.5 mol of CO₂(g) would have to be removed from a 1.0-L bulb such that the [CO(g)], after equilibrium has been re-established at the same temperature, reduces to 0.5 mol. This answer makes sense qualitatively: if CO₂ is removed from the system

The MICE table can also be used to solve common-ion effect problems related to solubility and to weak acid-base equilibria. We will illustrate with another textbook example:⁵

sample_problem_3.png

This is a LCP problem; the HCl is a stress on the ionization equilibrium of acetic acid:

CH₃COOH(aq)  +  H₂O(l)  ⇄  H₃O⁺(aq)  +  CH₃COO^–(aq)

An increase in [H₃O⁺] will temporarily favour the reverse reaction, which will supress the ionization of acetic acid. This is the correct answer, qualitatively speaking.

Textbooks usually solve problems like these with an ICE table.

sample_3_ice_table_problem.png

There is nothing wrong with this problem-solving methodology. It’s easy-looking and its neat and clean.

But it does not pay homage to the stress-response manner in which we explain LCP.

Using a MICE table, we can see separate steps for stress and response: the 0.010 mol∙L^–1 HCl is the stress. As for the response, LCP tells us what will occur, just not how much. We denote this with a y. Take a look . . .

sample_3_mice_table.png

To the (initial) chagrin of some students, this appears to be a two-variable problem. It won’t take long for someone to point out that (x – y), itself an unknown, may be replaced with another unknown, such as q.

And so the final row of the MICE table reduces to the final row of Table 3, and hence will furnish the same answer.

The beauty of the MICE table is its pedagogical consistency with our original qualitative explanation of LCP. For solving Common Ion Effect problems, there are no smoke and mirrors. It’s straight forward: equilibrium-stress-response-equilibrium.

lcp_chart.png

Screenshot from Equilibrium PowerPoint SlideShow in Supporting Information

I humbly suggest that you consider giving this a try. I offer a PowerPoint presentation (to be used in SlideShow mode) that I use with my students in the Supporting Information. I hope you find it useful.

May peace be with you,

1. General Chemistry, 10th ed, Ebbing and Gammon, Brooks/Cole CENGAGE Learning, 2013, p 610 example 14.8

2. Wikipedia contributors. (2022, February 7). Le Chatelier's principle. In Wikipedia, The Free Encyclopedia. Retrieved 16:50, March 3, 2022, from https://en.wikipedia.org/w/index.php?title=Le_Chatelier%27s_principle&oldid=1070529824

3. Chemistry: Theory and Problems, Book 2, James A Hebden, McGraw-Hill Ryerson, 1980.

4. Unless the stress is a change in temperature

5. General Chemistry, 10th ed, Ebbing and Gammon, Brooks/Cole CENGAGE Learning, 2013, p 683 example 16.9