Calculation of the Viscosity coefficient and Potential Profile for HCl 

Follows derivations of L. Monchick and E.A. Mason, J.Chem. Phys. 9, 398 (1941) 

> restart;

Basic viscosity equation: 

> mu:= 5/16*(m*k*T/Pi)^(1/2)*fh/(sigma^2*Omega_[2,2]);

(Typesetting:-mprintslash)([mu := 5/16*(m*k*T/Pi)^(1/2)*fh/(sigma^2*Omega_[2, 2])], [5/16*(m*k*T/Pi)^(1/2)*fh/(sigma^2*Omega_[2, 2])]) 

Correction term: 

> fh:= 1 + 3/196*(8*E - 7)^2;

(Typesetting:-mprintslash)([fh := 1+3/196*(8*E-7)^2], [1+3/196*(8*E-7)^2]) 

For HCl at T= 0 C and 1 atm: 

> k:= 1.38066e-16*erg/K; T:= 273.15*K;

(Typesetting:-mprintslash)([k := 0.138066e-15*erg/K], [0.138066e-15*erg/K]) 

(Typesetting:-mprintslash)([T := 273.15*K], [273.15*K]) 

Mass of one HCl molecule 

> m:= ((35.45 + 1.01)*g/mol) / (6.0221e23/mol);

(Typesetting:-mprintslash)([m := 0.6054366417e-22*g], [0.6054366417e-22*g]) 

Dimensionless temperature term: 

> Tstar:= k*T/epsilon;

(Typesetting:-mprintslash)([Tstar := 0.3771272790e-13*erg/epsilon], [0.3771272790e-13*erg/epsilon]) 

Given values for HCl in Monchiek and Mason: 

where μd is the dipole moment, δ is polarity term, σ is minimum non-repulsive distance between two molecules,  

and ε is lowest parameter energy 

> mu_[d]:= 1.08*debye; delta:= .34; sigma:= 3.36*Angstrom; epsilon:= 328*K*k;

(Typesetting:-mprintslash)([mu_[d] := 1.08*debye], [1.08*debye]) 

(Typesetting:-mprintslash)([delta := .34], [.34]) 

(Typesetting:-mprintslash)([sigma := 3.36*Angstrom], [3.36*Angstrom]) 

(Typesetting:-mprintslash)([epsilon := 0.45285648e-13*erg], [0.45285648e-13*erg]) 

> Tstar;


Using the values for δ and T*, can find values for the collision integral and <E*> using tables in Monchiek and Mason: 

> Omega_[2,2]:= 1.780; E:= 0.901;

(Typesetting:-mprintslash)([Omega_[2, 2] := 1.780], [1.780]) 

(Typesetting:-mprintslash)([E := .901], [.901]) 

> fh;


> mu;


> erg:= g*cm^2/s^2; Angstrom:= 1e-08*cm;

(Typesetting:-mprintslash)([erg := g*cm^2/s^2], [g*cm^2/s^2]) 

(Typesetting:-mprintslash)([Angstrom := 0.1e-7*cm], [0.1e-7*cm]) 

> mu_[p]:= simplify(mu) assuming g::positive, cm::positive, s::positive;

(Typesetting:-mprintslash)([mu_[p] := 0.1326607197e-3*g/(cm*s)], [0.1326607197e-3*g/(cm*s)]) 

Accepted value is .000132 Poise - (from Air Liquide) 

Now to use the corrected non-polar model (based on Lennard-Jones potential and experimental evidence). 

> sigma_[lj]:= 3.305*Angstrom; epsilon_[lj]:= 360*K*k;

(Typesetting:-mprintslash)([sigma_[lj] := 0.3305e-7*cm], [0.3305e-7*cm]) 

(Typesetting:-mprintslash)([epsilon_[lj] := 0.49703760e-13*g*cm^2/s^2], [0.49703760e-13*g*cm^2/s^2]) 

> kTe:= k*T/epsilon_[lj];

(Typesetting:-mprintslash)([kTe := .7587500000], [.7587500000]) 

> Omega_[lj]:= 1.839;

(Typesetting:-mprintslash)([Omega_[lj] := 1.839], [1.839]) 

> mu_[lj]:= 5/16*sqrt(Pi*m*k*T)/(Pi*sigma_[lj]^2*Omega_[lj]);

(Typesetting:-mprintslash)([mu_[lj] := 0.2350735085e-3*(Pi*g^2*cm^2/s^2)^(1/2)/(Pi*cm^2)], [0.2350735085e-3*(Pi*g^2*cm^2/s^2)^(1/2)/(Pi*cm^2)]) 

> mu_[lj]:= simplify(%) assuming g::positive, cm::positive, s::positive;

(Typesetting:-mprintslash)([mu_[lj] := 0.1326260249e-3*g/(cm*s)], [0.1326260249e-3*g/(cm*s)]) 

Again, this value is closer to the given value than the corrected viscosity equation, although the difference is even less than with CH3Cl.  This  

only goes to show the advances in understanding of visosity.In recent years the omega terms have undoubtedly been corrected to give more 

accurate values, as the given value evidences.  We were unableto locate the more recent tables for polar viscosity, but the accuracy of the  

60 year-old model shows the benefits of applying the non-polar Chapman-Enskog theory over completely neglecting it.