how to find qm and Kb constant in BET isotherm if:
qe = (qm*KB*Ce*Cs)/(Cs - Ce)[Cs + (KB - 1)Ce]
qe: is the amount adsorbed at equilibrium (mg/g) which can be found by
qe = {(Cs-Ce)V}/W
Cs, Ce: initial and final concentration
qm: maximum adsorption
KB: BET coefficient or equilibruim distributuion coffecient and presenting adsorption intensity
The BET constant is normally calculated from the intercept and slope of the plot of its linerized form.
KB = 1+ (slope/Intercept)
qm = 1/ (slope+Intercept)
Either do non-linear curve fitting or use the following linear form of the isotherm:
Ce/[qe(Cs - Ce)] = [1 + (KB - 1)Ce/Cs]/(qm*KB)
by trial and error method find an appropriate value for Cs. To do so, guess a value for Cs and using Excel software plot Ce/[qe(Cs - Ce)] versus Ce/Cs. Fit the above mentioned linear equation on the data and obtain the correlation coefficient (R2).
Now, change the Cs value (e.g. guess a lager (or smaller) value) and repeat the above procedure and obtain R2. Compare these two R2 to see which one is close to one. Increasing or decreasing Cs will lead to better R2 value. Further increase or decrease of Cs will lead to decrease R2. Chaining the Cs value by small increments can tune the Cs values.
When you find the best value for Cs, you can use the intercept and the slope of the linear line to obtain KB and qm.
I don't really understand the equation that you are trying to solve. It doesn't look like the Brunauer-Emmett-Teller adsorption isotherm (BET). BET should not have 'maximum' adsorption. Why there is initial and final concentration too?
BET (or any isotherm equation) should describe the dependence of adsorbed amount (qe in your case) as a function of concentration in equilibrium (Ce, in your case).
Perhaps you can give more information about your question, what are your unknowns and what are the parameters that you know... if you have experimental data... how you derived the equation... etc.
Forgive me if I'm mistaken in not understanding correctly. If no, I'll try to help more.
Regards
Does Cs indicate initial concentration or concentration at maximum solubility? Could anyone help me out.
thanks
Gentlemen, linearized form of BET gives you K from the slope and intercept.
How should one find the error of such estimation?
Using Propagation of uncertainty of indirect esimation?
Sk2 = (Sslope/slope)2 + (Sintercept/intercept)2 - 2S(interslope)/Intercept*Slope
Any reference or suggestion would help.
Hi Oleg Bolshakov ,
There is an excellent paper in Langmuir that addresses this exact topic:
"Analysis of Uncertainties in Manometric Gas-Adsorption Measurements. I: Propagation of Uncertainties in BET Analyses"
Langmuir, 2003, 19 (19), pp 7919–7928
DOI: 10.1021/la020985t
Slalm.. hello
Q/what is method to found Cs in BET isotherm?
Please helpe me to Cs
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