Thermodynamics

The differential of the Gibbs function (G H TS) at constant temperatureand pressure isGChapter 16 | 795(16–3)From Eqs. 16–2 and 16–3, we have (dG) T,P 0. Therefore, a chemical reactionat a specified temperature and pressure proceeds in the direction of adecreasing Gibbs function. The reaction stops and chemical equilibrium isestablished when the Gibbs function attains a minimum value (Fig. 16–4).Therefore, the criterion for chemical equilibrium can be expressed as(16–4)A chemical reaction at a specified temperature and pressure cannot proceedin the direction of the increasing Gibbs function since this will be a violationof the second law of thermodynamics. Notice that if the temperature orthe pressure is changed, the reacting system will assume a different equilibriumstate, which is the state of the minimum Gibbs function at the newtemperature or pressure.To obtain a relation for chemical equilibrium in terms of the properties ofthe individual components, consider a mixture of four chemical componentsA, B, C, and D that exist in equilibrium at a specified temperature and pressure.Let the number of moles of the respective components be N A , N B , N C ,and N D . Now consider a reaction that occurs to an infinitesimal extentduring which differential amounts of A and B (reactants) are converted to Cand D (products) while the temperature and the pressure remain constant(Fig. 16–5):The equilibrium criterion (Eq. 16–4) requires that the change in the Gibbsfunction of the mixture during this process be equal to zero. That is,or1dG2 T,P dH T dS S dT→0 1dU P dV V dP2 T dS S dT→0 dU P dV T dS1dG2 T,P 0dN A A dN B B ¡ dN C C dN D D1dG2 T,P a 1dG i 2 T,P a 1g idN i 2 T,P 0gCdN C g DdN D g AdN A g BdN B 0(16–5)(16–6)where the g – ’s are the molar Gibbs functions (also called the chemical potentials)at the specified temperature and pressure and the dN’s are the differentialchanges in the number of moles of the components.To find a relation between the dN’s, we write the corresponding stoichiometric(theoretical) reaction100%reactantsdG < 0 dG > 0dG = 0Violation ofsecond lawEquilibriumcomposition100%productsFIGURE 16–4Criteria for chemical equilibrium for afixed mass at a specified temperatureand pressure.REACTIONCHAMBERT, PN A moles of AN B moles of BN C moles of CN D moles of DdN A A + dN B B → dN C C + dN D DFIGURE 16–5An infinitesimal reaction in a chamberat constant temperature and pressure.n A A n B B ∆ n C C n D D(16–7)where the n’s are the stoichiometric coefficients, which are evaluated easilyonce the reaction is specified. The stoichiometric reaction plays an importantrole in the determination of the equilibrium composition of the reacting