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K. Zabielska, T. Aleksandrzak, E. Gabrus ́, Chem. Process Eng., 2018, 39 (3), 309–321 2.6. Langmuir–Freundlich equation In order to achieve greater flexibility, the equation of the Langmuir and Freundlich isotherms was com- bined into the form of an empirical relation which can be presented as (Paderewski, 1999, Thomas and Crittenden, 1998): b(T)· pn(T) q = qm(T)1+b(T)· pn(T) (7) In Equation (7) qm, b and n are characteristic coefficients for adsorbed component – adsorbent system and depend on the temperature T according to the relations: qm(T) = a0LF + a1LF + a2LF (8) TT2 (bb) b(T)=exp b0LF+ 1LF+ 2LF (9) n(T ) = n0LF + n1LF (10) TT2 T After substituting Eqs. (8)–(10) into Eq. (7) the mathematical form of multitemperature Langmuir–Freund- lich adsorption isotherm is obtained (Paderewski, 1999, Sarbak, 2000; Thomas and Crittenden, 1998): (( ))(n) b1LF b2LF n0LF + 1LF ( a1LF a2LF) exp b0LF+ T + T2 p q=a0LF++2 (( 2.7. Toth equation T ))(n1LF) (11) pn0LF+ T T T 1+ exp b0LF+b1LF+b2LF TT2 The Toth model is a semi-empirical equation which describes adsorption in a monolayer. The equation is related to the heterogeneity of the surface and interactions of the adsorbed molecules. Relation developed by Toth (Toth, 2001) has the following form: q=q p (12) m (b(T ) + pnT )1/nT In Eq. (12) the coefficient b depends on the temperature according to the formula: ( nT·∆H) b(T)=b0T ·exp − R·T (13) After substituting Eq. (13) into Eq. (12) the mathematical form of multitemperature Toth adsorption isotherm is obtained (Sarbak, 2000; Thomas and Crittenden, 1998; Toth, 2001): q = qm ( ( p ) )1/nT (14) b0T ·exp −nT ·∆H +pnT R·T Values of model parameters were calculated by nonlinear regression of experimental data using Statistica 13.1 (Statsoft).The average relative error ä, which is the measure of fitting quality was calculated as follows: δ=1∑N qexp−qsim100% (15) N i=1 qexp In addition the coefficients of determination R2 were calculated for each isotherm model. 314 http://journals.pan.pl/dlibra/journal/98834PDF Image | ADSORPTION EQUILIBRIUM OF CARBON DIOXIDE ON ZEOLITE
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