Entropy Changes in Gaseous Reactions

Submitted by ChemPRIME Staff on Thu, 12/16/2010 - 15:21

Knowing what factors affect the magnitude of the entropyA thermodynamic state function, symbol S, that equals the reversible heat energy transfer divided by temperature; higher entropy corresponds to greater dispersal of energy on the molecular scale. See also standard entropy. often enables us to predict whether the entropy of the products will be greater or less than that of the reactants in a given chemical reactionA process in which one or more substances, the reactant or reactants, change into one or more different substances, the products; chemical change involves rearrangement, combination, or separation of atoms. Also called chemical change.. This is particularly true for gaseous reactions. In a dissociationThe breaking apart of one species into two or more smaller species; often applied to ions in a crystal lattice, which dissociate when the ionic solid dissolves in water. Dissociation refers to separation of particles that already exist; ionization refers to the formation of ions from neutral species, as in the ionization of a weak acid in aqueous solutoin. reaction like

N2O4(g) → NO2 + NO2      ΔSm°(298 K) = +176 J K–1 mol–1

for instance, it is easy to see that ΔS should be positive. The two halves of the N2O4 moleculeA set of atoms joined by covalent bonds and having no net charge. are forced to move around together before dissociation, but they can move around independently as NO2 molecules once dissociation has occurred. A similar argument applies to reactions like

2O3 → 3O2      ΔSm°(298 K) = +137 J K–1 mol–1

In the form of O3, O atomsThe smallest particle of an element that can be involved in chemical combination with another element; an atom consists of protons and neutrons in a tiny, very dense nucleus, surrounded by electrons, which occupy most of its volume. are constrained to move around in groups of three, but in the form of O2, only two atoms need move around together, a lesser restriction. Accordingly we expect ΔS to be positive for this reaction.

A further extension of this argument leads us to the general conclusion that in any reaction involving gases if the amount of substanceA material that is either an element or that has a fixed ratio of elements in its chemical formula. in the gaseous phase increases, ΔS will be positive, while if it decreases, so will ΔS. For example, in the reaction

2CO(g) + O2(g) → 2CO2(g)

The amount of gas decreases from 3 to 2 mol (i.e., Δn = –1 mol). The entropy change should thus be negative for this reaction. From the Table of Standard Molar Entropies we can readily find that ΔSm°(298 K) has the value –173 J K–1 mol–1.