Example 18.6-2 reproduced from Ref. 1

The diffusivity of the gas pair O2-CCl4 is being determined by observing the steady-state evaporation of carbon tetrachloride into a tube containing oxygen, as shown in the Figure below. The distance between the CCl4 liquid level and the top of the tube is z2 − z1 = 17.1 cm. The total pressure on the system is 755 mmHg , and the temperature is 0 °C . The vapor pressure of CCl4 at that temperature is 33 .0 mmHg and its liquid density is 1 .629 g∕cm3 . The cross-sectional area of the diffusion tube is 0.82 cm2 . It is found that 0 .0208 cm3 of liquid CCl4 evaporates in a 10-hour period after steady state has been attained. It may be assumed that the partial pressure of CCl4 at z=z2 is zero. What is the diffusivity of the gas pair O2 - CCl4 ? We consider O2 as stagnant since it is insoluble in liquid CCl4.
​​TheArnoldcell
Vapor pressure of CCl4 at 0 °C
Antoine Equation where T in K and Psat in bar
In[]:=
A1=4.02291;B1=1221.781;C1=-45.739;
In[]:=
10^(A1-B1/(C1+T))/.T->273.15
Out[]=
0.0447036
In[]:=
%760/1.01325(*vaporpressureofCCl4at0°CexpressedinmmHg*)
Out[]=
33.5304
The molar flux of CCl4
◼
  • 0.0208 cm3 of CCl4 evaporates during 10 hours
    • ◼
  • liquid density of CCl4 is 1.629 g/cm3
    • ◼
  • cross-section area is 0.82 cm2
    • ◼
  • 10 hours is 3.6 10^4 seconds
    • ◼
  • Molecular weight of CCl4 is equal to 153.82 g/mol
    • In[]:=
    MWA=153.82;
    In[]:=
    NAz=0.02081.629/MWA/0.82/(3.610^4)
    Out[]=
    7.462×
    -9
    10
    The diffusion of CCl4 in stagnant O2 without neglecting the convection term is governed by:
    In[]:=
    DIFF1=NAz17.1×82.06273/P/Log[755/722](*dz=17.1cm*)
    Out[]=
    0.0639602
    P
    The diffusion of CCl4 in stagnant O2 if we neglect the convection term is governed by:
    In[]:=
    DIFF2=NAz17.182.06/P273(33/755)^-1
    Out[]=
    0.0654001
    P
    Estimation of the diffusivity of CCl4 in O2 using the relationship of Ref. 2:
    In[]:=
    Clear[A,B,C1,D1,E1,F,G,H,R,S,W,P]
    In[]:=
    OMEGA11=A/TS^B+C1/Exp[D1TS]+E1/Exp[FTS]+G/Exp[HTS](*collisionintegralbyNeufeld(seeRef.3)*)
    Out[]=
    C1
    -D1TS
    
    +
    -FTS
    
    E1+
    -HTS
    
    G+A
    -B
    TS
    In[]:=
    A=1.06036;B=0.15610;C1=0.19300;D1=0.47635;E1=1.03587;F=1.52996;​​G=1.76474;H=3.89411;
    In[]:=
    sigmaA=5.881;​​sigmaB=3.433;​​sigmaAB=1/2(sigmaA+sigmaB)
    Out[]=
    4.657
    In[]:=
    EPSILONsurKappaA=327.;​​EPSILONsurKappaB=113;​​EPSILONsurKappaAB=Sqrt[EPSILONsurKappaAEPSILONsurKappaB]
    Out[]=
    192.226
    In[]:=
    T=273;​​P=755/760;(*totalpressureinatm*)
    In[]:=
    DIMENTIONLESStemperature=T/EPSILONsurKappaAB(*dimensionlesstemperature*)
    Out[]=
    1.4202
    In[]:=
    OMEGAD=OMEGA11/.TS->DIMENTIONLESStemperature(*collisionintegral*)
    Out[]=
    1.22691
    In[]:=
    MWB=32;
    In[]:=
    DIFF3=0.001858T^1.5/P/sigmaAB^2/OMEGAD(1/MWA+1/MWB)^0.5(*unit:cm2/s*)
    Out[]=
    0.0616023
    Relative errors : we consider DIFF1 as the exact value of the diffusivity obtained using experimental data and without dropping the convection term
    In[]:=
    DIFF2-DIFF1
    Out[]=
    0.00144946
    In[]:=
    %100/DIFF1(*approximately2%relativeerror*)
    Out[]=
    2.25128
    In[]:=
    Abs[DIFF3-DIFF1]
    Out[]=
    0.0027815
    In[]:=
    %100/DIFF1(*approximately4%relativeerror*)
    Out[]=
    4.32018

    References

    ◼
  • [1] R. B. Bird, W. E. Stewart, E. N. Lightfoot and D. J. Klingenberg, Introductory Transport Phenomena, NY: Wiley, 2015.
    • ◼
  • [2] J. O. Hirschfelder, R. B. Bird, and E. L. Spotz, Chem. Rev., 44, 205 (1949).
    • ◼
  • [3] P. D. Neufeld, A. R. Janzen, and R. A. Aziz, J. Chem. Phys., 57, 1100 (1972).

    • CITE THIS NOTEBOOK

    Diffusivity of carbon tetrachloride into oxygen​
    by Housam Binous & Ahmed Bellagi
    Wolfram Community, STAFF PICKS, March 13, 2025
    ​https://community.wolfram.com/groups/-/m/t/3415906