Chemical Education Today
Letters Exception to the Le Châtelier Principle In “The Ammonia Synthesis Reaction: An Exception to the Le Châtelier Principle and Effects of Nonideality”, published in this Journal (1), the authors assert that “With T and P held fixed, Le Châtelier’s principle predicts that the addition of more nitrogen into the reaction vessel will cause the [ammonia synthesis] reaction to shift to the right, that is, more ammonia will be produced.” It is true as the authors demonstrate that the reaction actually shifts to the left instead if the initial mole fraction of nitrogen exceeds 0.5 when additional nitrogen is added to a system initially at equilibrium and with T and P constant. However, in my view this is not an exception to Le Châtelier’s principle but rather a situation to which this principle is not applicable. The authors define Le Châtelier’s principle as follows: “In a system at equilibrium, a change in one of the variables that determines the equilibrium will shift the equilibrium in the direction counteracting the change in that variable. (emphasis added)” All versions of this principle of which I am aware define it in terms of a change in a single variable, and none impose the constraint of constant pressure. However, it is not applicable to the addition of nitrogen gas to the ammonia synthesis reaction equilibrium under conditions of constant P as this addition changes not just the initial partial pressure of nitrogen but the initial partial pressures of hydrogen and ammonia gas as well. This result occurs owing to Dalton’s law of partial pressure and the ideal gas law. When the total chemical amount of gas increases owing to addition of nitrogen to the system at equilibrium, given PV = nRT the only way for both T and P to remain constant is for V to increase proportionately to the increase in n. Since the chemical amounts of both hydrogen and ammonia are initially unchanged, this volume increase causes the partial pressures of both of these gases to decrease. Thus, in P = PN2 + PH2 + PNH3, holding P fixed while adding moles of nitrogen means that PN2 increases but
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both PH2 and PNH3 decrease. While I have assumed ideal behavior of the gases in this argument, the same result would hold qualitatively for nonideal gases as well as if one used activity or fugacity instead of pressure. Therefore, adding nitrogen gas to the equilibrium mixture for the ammonia synthesis reaction under the constraint of constant pressure necessarily changes the initial partial pressures of all three gases present. Le Châtelier’s principle does not apply to this situation as it is premised upon a single variable, for example, the pressure of a single gas, changing. This conclusion is true for any equilibrium mixture that contains more than one gaseous species when the constraint of constant pressure is present; that is, it is impossible to change the pressure of only one gas in the mixture under this constraint. If this constraint (which is not part of Le Châtelier’s principle) is removed, then Le Châtelier’s principle does apply to the ammonia synthesis reaction, and it behaves as the principle predicts. Thus, while I agree with the authors that Le Châtelier’s principle cannot be used to predict qualitatively the direction the ammonia synthesis reaction will shift when ammonia is added at constant pressure, I disagree with their description of this phenomenon as an exception to the principle when actually this is a situation to which the principle does not apply. While this is a semantic distinction rather than a scientific one, it is an important distinction nonetheless. Literature Cited 1. Uline, M. J.; Corti, D. S. J. Chem. Educ. 2006, 83, 138– 144. Thomas R. Herrinton Department of Chemistry and Biochemistry University of San Diego San Diego, CA 92110
[email protected] Vol. 84 No. 9 September 2007
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Journal of Chemical Education
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