0.13 Reaction equilibrium in the gas phase

Foundation

In beginning our study of the reactions of gases, we will assume a knowledge of the physical properties ofgases as described by the Ideal Gas Law and an understanding of these properties as given by the postulates and conclusions of the Kinetic Molecular Theory . We assume that we have developed a dynamic model of phase equilibrium in terms of competing rates. We willalso assume an understanding of the bonding, structure, and properties of individual molecules.

Goals

In performing stoichiometric calculations, we assume that we can calculate the amount of product of a reactionfrom the amount of the reactants we start with. For example, if we burn methane gas, $C{H}_4\left(g\right)$ , in excess oxygen, the reaction

occurs, and the number of moles of $C{O}_2\left(g\right)$ produced is assumed to equal the number of moles of $C{H}_4\left(g\right)$ we start with.

From our study of phase transitions we have learned the concept of equilibrium. We observed that, in thetransition from one phase to another for a substance, under certain conditions both phases are found to coexist, and we refer to thisas phase equilibrium. It should not surprise us that these same concepts of equilibrium apply to chemical reactions as well. In the reaction , therefore, we should examine whether the reaction actually producesexactly one mole of $C{O}_2$ for every mole of $C{H}_4$ we start with or whether we wind up with an equilibrium mixture containing both $C{O}_2$ and $C{H}_4$ . We will find that different reactions provide us with varyinganswers. In many cases, virtually all reactants are consumed, producing the stoichiometric amount of product. However, in manyother cases, substantial amounts of reactant are still present when the reaction achieves equilibrium, and in other cases, almost noproduct is produced at equilibrium. Our goal will be to understand, describe and predict the reaction equilibrium.

An important corollary to this goal is to attempt to control the equilibrium. We will find that varying theconditions under which the reaction occurs can vary the amounts of reactants and products present at equilibrium. We will develop ageneral principle for predicting how the reaction conditions affect the amount of product produced at equilibrium.

Observation 1: reaction equilibrium

We begin by analyzing a significant industrial chemical process, the synthesis of ammonia gas, $N{H}_3$ , from nitrogen and hydrogen:

If we start with 1 mole of $N_2$ and 3 moles of $H_2$ , the balanced equation predicts that we will produce 2 moles of $N{H}_3$ . In fact, if we carry out this reaction starting with thesequantities of nitrogen and hydrogen at 298K in a 100.0L reaction vessel, we observe that the number of moles of $N{H}_3$ produced is 1.91 mol. This "yield" is less than predicted by the balanced equation, but the difference is not dueto a limiting reagent factor. Recall that, in stoichiometry, the limiting reagent is the one that is present in less than the ratioof moles given by the balanced equation. In this case, neither $N_2$ nor $H_2$ is limiting because they are present initially in a 1:3 ratio, exactly matching the stoichiometry. Note also that this seemingdeficit in the yield is not due to any experimental error or imperfection, nor is it due to poor measurements or preparation.Rather, the observation that, at 298K, 1.91 moles rather than 2 moles are produced is completely reproducible: every measurement ofthis reaction at this temperature in this volume starting with 1 mole of $N_2$ and 3 moles of $H_2$ gives this result. We conclude that the reaction achieves reaction equilibrium in which all three gases are present in the gas mixture. We can determine the amountsof each gas at equilibrium from the stoichiometry of the reaction. When $n_{N{H}_3}=1.91\mathrm{mol}$ are created, the number of moles of $N_2$ remaining at equilibrium is $n_{N_2}=0.045\mathrm{mol}$ and $n_{H_2}=0.135\mathrm{mol}$ .