Barium Gas-Phase Equilibrium Model

Knowns:

   5.21      Ei           eV        ionization energy of Ba 
   4.7       Ed           eV        dissociation energy of BaOH                   
   17        Mx           amu       Molecular weight of OH               
   137.3     Mm           amu       Atomic weight of Ba      
   154.3     Mmx          amu       Molecular weight of BaOH                 
   1E9       ntotal       cm-3      number density of Ba in all forms 
   1E11      ne           cm-3      number density of electrons   
   1E17      nx           cm-3      number density of species OH radicals  

Unknowns: number density of Ba, Ba+, and BaOH.

Equation 7-1
    Kd=nm*nx/nmx 
Equation 7-2 
    log(Kd)=20.274+(3/2)*log(Mx*Mm/Mmx)+log(Zx*Zm/Zmx)+(3/2)*log(T)-5040*Ed/T  
Mass balance
    ntotal=nm+nmx+ni
Saha equation 7-4
    log(Ki)=15.6844+log(Zi/Zm)+(3/2)*log(T)-5040*Ei/T
Definition of Ki (Equation 7-3)
    Ki=ni*ne/nm
Definition of degree of ionization (Equation 7-10)                              
    alphai=ni/(nm+ni)
Free atom fraction (Equation 7-5)
    betaa=nm/(nm+nmx+ni)
Ideal gas law (top of page 197, right column)  
    nm=7.34e21*pm/T                                                               
    ni=7.34e21*pi/T                                                               
    nx=7.34e21*px/T                                                               
    nmx=7.34e21*pmx/T                                                             
    ne=7.34e21*pe/T 

[RETURN] to Chem 623 home page.