Physical Chemistry

Adsorption Theory Modeling and Analysis Toth by Jozsef Toth

By Jozsef Toth

Bargains an outline of the new theoretical and sensible effects completed in gas-solid (G/S), liquid-solid (L/S), and gas-liquid (G/L) adsorption learn.

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172). If 0 < t < 1, Bx ¼ 0, and a ¼ 0 (heterogeneous surface, no interactions, immobile layer), then we have the To´th equation: P ¼ Pm ðwT À 1Þ1=t 6. 7. Y expðÀBF YÞ wF À Y Y ðwT À Yt Þ1=t See Eq. (199). If t > 0, Bx ¼ BFT , and a ¼ 0 (heterogeneous surface, interactions, immobile layer), then we have the FT equation:     B Y ÀBF Yt exp P ¼ Pm ðwF À 1Þ1=t exp F t ðwF À Yt Þ1=t t See Eq. 22). If t > 0, Bx ¼ 0, and a ¼ 1 (heterogeneous surface, no interactions, mobile layer), then we have the VT equation: & ' & ' 1 Y Yt P ¼ Pm ðwV À 1Þ1=t exp À exp tðwV À 1Þ ðwV À Yt Þ1=t tðwV À Yt Þ See Eq.

203). For the calculation of the total monolayer capacity, a four-parameter iteration may also be possible because Eq. (201) may also be written in this form: P¼ 1 ns t 1=t s ðKT Þ ½wT ðnm Þ À ðns Þt Š1=t ð211Þ However, for calculating nsm ; a general method is discussed in Section VI. The mathematically uniform and thermodynamically consistent interpretation of Eq. (199) is shown in Fig. 19, where the functions YðPÞ, cðPÞ, YðPr;m Þ, cðYÞ, Asr ðYÞ, and Asr ðPr;m Þ are plotted. The calculations of these functions have been made as follows: Top (left):  P¼ 1 KT 1=t Y ðwT À Yt Þ1=t ð212Þ or Y¼ ðwT Þ1=t P ½ð1=KT Þ þ Pt Š1=t ð213Þ Top (right): cT ðPÞ ¼ KT Pt þ 1 or the values of the function wT cT ðYÞ ¼ wT À Yt ð214Þ ð215Þ are conjugated with values of P caculated from Eq.

The parameters are as follows: KV ¼ 0:50 kPaÀ1 , wV ¼ 1:0, Pm ! 1 (solid line, original Volmer equation); KmV ¼ 0:50 kPaÀ1 , wV ¼ 1:3, Pm ¼ 186:9 kPa ð Á Á Á ÁÞ; KmV ¼ 0:30 kPaÀ1 , wV ¼ 1:4, Pm ¼ 101:5 kPa ð Þ; KmV ¼ 0:10 kPaÀ1 ; wV ¼ 1:5, Pm ¼ 147:8 kPa ð Á Á Þ. To´th 34 F. The Uniform and Consistent Interpretation of the Modified de Boer–Hobson Equation Both the mobility and the interactions are taken into account by the de Boer–Hobson (BH) equation [10], having the following explicit form:   1 Y À BB Y exp P¼ ð169Þ KB À Y 1ÀY The corresponding function cB ðYÞ is  2 1 ÀBB Y cB ðYÞ ¼ 1ÀY ð170Þ Equation (170) is also thermodynamical inconsistent because the limiting value is Y ¼ 1 if P !

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