Thermodynamics

798 | ThermodynamicsEXAMPLE 16–1Equilibrium Constant of a Dissociation ProcessUsing Eq. 16–14 and the Gibbs function data, determine the equilibriumconstant K P for the dissociation process N 2 → 2N at 25°C. Compare yourresult to the K P value listed in Table A–28.Solution The equilibrium constant of the reaction N 2 → 2N is listed inTable A–28 at different temperatures. It is to be verified using Gibbs functiondata.Assumptions 1 The constituents of the mixture are ideal gases. 2 The equilibriummixture consists of N 2 and N only.Properties The equilibrium constant of this reaction at 298 K is ln K P 367.5 (Table A–28). The Gibbs function of formation at 25°C and 1 atm isO for N 2 and 455,510 kJ/kmol for N (Table A–26).Analysis In the absence of K P tables, K P can be determined from the Gibbsfunction data and Eq. 16–14,where, from Eq. 16–11,Substituting, we findor¢G* 1T2 n N g * N1T2 n N2g *N21T2 122 1455,510 kJ>kmol2 0 911,020 kJ>kmol911,020 kJ>kmolln K P 18.314 kJ>kmol # K21298.15 K2367.5K P e ¢G*1T2>R uTK P 2 10 160The calculated K P value is in agreement with the value listed in Table A–28.The K P value for this reaction is practically zero, indicating that this reactionwill not occur at this temperature.Discussion Note that this reaction involves one product (N) and one reactant(N 2 ), and the stoichiometric coefficients for this reaction are n N 2 andn N2 1. Also note that the Gibbs function of all stable elements (such as N 2 )is assigned a value of zero at the standard reference state of 25°C and 1 atm.The Gibbs function values at other temperatures can be calculated from theenthalpy and absolute entropy data by using the definition of the Gibbs function,g , where h 1T 2 h*f hT * 1T 2 h 1T 2 Ts * 1T 2h298 K. EXAMPLE 16–2Dissociation Temperature of HydrogenDetermine the temperature at which 10 percent of diatomic hydrogen (H 2 )dissociates into monatomic hydrogen (H) at a pressure of 10 atm.Solution The temperature at which 10 percent of H 2 dissociates into 2H isto be determined.Assumptions 1 The constituents of the mixture are ideal gases. 2 The equilibriummixture consists of H 2 and H only.