Chapter 13 Gas Mixtures Study Guide in PowerPoint to accompany Thermodynamics An Engineering Approach 8th edition by Yunus A engel and Michael A Boles 1 The discussions in this chapter are restricted to nonreactive ideal gas mixtures Those interested in real gas mixtures are encouraged to study carefully the material presented in Chapter 12 Many thermodynamic applications involve mixtures of ideal gases That is each of the gases in the mixture individually behaves as an ideal gas In this section we assume that the gases in the mixture do not react with one another to any significant degree We restrict ourselves to a study of only ideal gas mixtures An ideal gas is one in which the equation of state is given by PV mRT or PV NRu T Air is an example of an ideal gas mixture and has the following approximate composition Component N2 O2 Argon CO2 trace elements by Volume 78 10 20 95 0 92 0 03 2 Definitions Consider a container having a volume V that is filled with a mixture of k different gases at a pressure P and a temperature T A mixture of two or more gases of fixed chemical composition is called a nonreacting gas mixture Consider k gases in a rigid container as shown here The properties of the mixture may be based on the mass of each component called gravimetric analysis or on the moles of each component called molar analysis k gases T Tm P Pm V Vm m mm The total mass of the mixture mm and the total moles of mixture Nm are defined as k mm mi i 1 k and N m Ni i 1 3 The composition of a gas mixture is described by specifying either the mass fraction mfi or the mole fraction yi of each component i mf i Note that mi mm and yi k mf Ni Nm k 1 i and i 1 y i 1 i 1 The mass and mole number for a given component are related through the molar mass or molecular weight mi N i M i To find the average molar mass for the mixture Mm note k k mm mi N i M i N m M m i 1 i 1 Solving for the average or apparent molar mass Mm k k mm Ni Mm M i yi M i N m i 1 N m i 1 kg kmol 4 The apparent or average gas constant of a mixture is expressed as Rm Ru Mm kJ kg K Can you show that Rm is given as k Rm mf i Ri i 1 To change from a mole fraction analysis to a mass fraction analysis we can show that mf i yi M i k y M i i i 1 To change from a mass fraction analysis to a mole fraction analysis we can show that yi mf i M i k mf i Mi i 1 5 Volume fraction Amagat model Divide the container into k subcontainers such that each subcontainer has only one of the gases in the mixture at the original mixture temperature and pressure Amagat s law of additive volumes states that the volume of a gas mixture is equal to the sum of the volumes each gas would occupy if it existed alone at the mixture temperature and pressure k Amagat s law Vm Vi Tm Pm i 1 The volume fraction of the vfi of any component is and Vi Tm Pm vf i Vm k vf i 1 i 1 6 For an ideal gas mixture Vi N i Ru Tm Pm and Vm N m Ru Tm Pm Taking the ratio of these two equations gives Vi Ni vf i yi Vm N m The volume fraction and the mole fraction of a component in an ideal gas mixture are the same Partial pressure Dalton model The partial pressure of component i is defined as the product of the mole fraction and the mixture pressure according to Dalton s law For the component i Pi yi Pm k Dalton s law Pm Pi Tm Vm i 1 7 Now consider placing each of the k gases in a separate container having the volume of the mixture at the temperature of the mixture The pressure that results is called the component pressure Pi N i Ru Tm Pi Vm and N m Ru Tm Pm Vm Note that the ratio of Pi to Pm is Pi Vi Ni yi Pm Vm N m For ideal gas mixtures the partial pressure and the component pressure are the same and are equal to the product of the mole fraction and the mixture pressure 8 Other properties of ideal gas mixtures The extensive properties of a gas mixture in general can be determined by summing the contributions of each component of the mixture The evaluation of intensive properties of a gas mixture however involves averaging in terms of mass or mole fractions k k k U m U i mi ui N i ui i 1 i 1 i 1 k k k Hm Hi mi hi N i hi i 1 k i 1 i 1 k k Sm Si mi si N i si i 1 i 1 kJ kJ kJ K i 1 9 and k k um mf i ui and um yi ui i 1 i 1 k k hm mf i hi and hm yi hi i 1 kJ kg or kJ kmol kJ kg or kJ kmol i 1 k k sm mf i si and sm yi si i 1 kJ kg K or kJ kmol K i 1 k Cv m mf i Cv i k and i 1 i 1 k k C p m mf i C p i i 1 Cv m yi Cv i and C p m yi C p i i 1 10 These relations are applicable to both ideal and real gas mixtures The properties or property changes of individual components can be determined by using ideal gas or real gas relations developed in earlier chapters Ratio of specific heats k is given as km C p m Cv m C p m Cv m The entropy of a mixture of ideal gases is equal to the sum of the entropies of the component gases as they exist in the mixture We employ the Gibbs Dalton law that says each gas behaves as if it alone occupies the volume of the system at the mixture temperature That is the pressure of each component is the partial pressure For constant specific heats the entropy change of any component is 11 The entropy change of the mixture per mass of mixture is The entropy change of the mixture per mole of mixture is 12 In these last two equations recall that Pi 1 yi 1 Pm 1 Pi 2 yi 2 Pm 2 Example 13 1 An ideal gas mixture has the following volumetric analysis Component N2 CO2 by Volume 60 40 a Find the analysis on a mass basis For ideal gas mixtures the percent by volume is the volume fraction …