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r sat K n C (1+ m ((q-1) C m-1 + q C rrrr Table 2. Pure Component Isotherm Equations Equation Form K1 4 n 2 M 4 4 Name a. Henry’s Law: b. Langmuir: c. Freundlich: d. Brunauer-Emmett-Teller: (Cr=C/Csat) e.BDDT (C =C/C ) n* = K nM C n* = K nMC /( 1 + K C ) n*=A CB n* = K nMCr /((1+(K-1) Cr )(1-Cr )) m n*=Mr r r r r m+1- (2q-1) C ( 1-C ) (1+ (K-1) C + K ( (q-1) C m - q C ) - C m m+1 )) f. Dual Mode Isotherm: g. Redlich-Peterson: h. Langmuir-Freundlich: i. Sips: j. Toth: k. UNILAN: l. Dubinin-Radushkevich3: m. Dubinin-Astakhov3: n. Dubinin-Stoeckli3: n* n* n* n* n* n* n* n* =K1 nM C/(1+K1 C)+K2 C = K nM C / ( 1 + K CB) =AnM CB /(1+ACB ) = nM [A C / ( 1 + A C ) ] B = K C / ( 1 + C B / A ) 1/B =nM ln D+Cexp(B) 2 B D+C exp( -B ) K1+K2 4 4 nM sinh(B) B D K A 1/B 1 2 3 n*=nM1 exp(-((k01g/$01)2)) +nM2 exp(-((k02g/$02)2)) 0 nM1+nM2 The Henry’s law coefficient, K, is traditionally defined as the initial slope of “fractional coverage” (or 2=n*/nM), versus concentration or partial pressure. That leads to awkward units. The maximum loading, nM, must be known before doing calculations. If saturation is not observed, it is not reasonable to assume a value for nM, so one has no choice but to plot n* versus C, and use that slope. Despite these aggravations, we will stick with tradition. nM corresponds to the “monolayer” loading for equations (a) through (e), while for the rest it represents a sort of “maximum” loading. Details go beyond the scope of this article. The adsorption capacity, n*, and maximum loading, nM, for this isotherm is expressed as the volume adsorbed per unit mass or volume of adsorbent. =nMexp(-((k0g/$0)2)) 0 nM =nMexp(-((k0g/$0)n)) 0 nM 12PDF Image | ADSORBENT SELECTION
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