Dinitrogen oxide, N₂O, colloquially called “laughing gas,” was first used as an anesthetic in dentistry in 1844. Suppose that you are a chemist attempting to prepare N₂O from N₂ and O₂; you might want to know the expected equilibrium composition. You plan to transfer a mixture of 0.482 mol N₂ and 0.933 mol O₂ to a reaction vessel of volume 10.0 L, where it will form N₂O at 800. K; at this temperature, K = 3.2 * 10^–28 for the reaction 2 N₂(g) + O₂(g) ⇌ 2 N₂O(g). Calculate the partial pressures of the gases in the equilibrium mixture.

ANTICIPATE Because the equilibrium constant is so small, you should expect that equilibrium will be reached when only a very small amount of product has formed.

PLAN Use the procedure in Toolbox 5I.1. Because data are in liters and pressures are expected in bar, use the value of R that matches these units (namely, L · bar · K^–1 · mol^–1).

What should you assume? Assume that all the gases are ideal and, because the value of K is so small, that the amount of product formed will be so small that the change in partial pressures of the reactants is negligible.

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Toolbox 51.1 HOW TO SET UP AND USE AN EQUILIBRIUM TABLE CONCEPTUAL BASIS The composition of a reaction mixture tends to adjust until the molar concentrations of solutes or partial pressures of gases ensure that Q = K. A change in the abundance of any one component is linked to changes in the others by the reaction stoichiometry. PROCEDURE Step 1 Write the equilibrium expression for the balanced chemical equation. Then set up an equilibrium table as shown here, with columns labeled by the species taking part in the reaction. If K, is given for a reaction involving gases (Topic 5H), then proceed in the same way, but with molar concentrations for all the species. The first line in the table shows how the reaction system was pre- pared before reaction began. As always, use molar concentrations (in moles per liter) and partial pressures (in bar), but strike out the units. Omit pure solids and liquids, as they do not appear in the equilibrium expression. initial composition change in composition equilibrium composition Species 1 Species 2 Species 3 ***