Question

Equilibrium data from batch studies for the sorption of paranitrophenol (MW = 139 g/mol) from aqueous solution at 25 C by activated charcoal are given below.

PNP absorbed, q (mmol/g)	PNP concentration in solution, C (mM)
0.9	0.006
1.1	0.011
1.4	0.023
1.6	0.045
1.9	0.18
2.1	0.33

(a) Convert the data to units of mg/g for q and mg/L for C.

(b) Determine the coefficients for these data assuming a Freundlich isotherm q = K*C^1/n applies. You may want to use the linear form log(q) = (1/n)log(C) + log(K).

(c)  Determine the coefficients for these data assuming a Langmuir isotherm q = q_max(bC/1+bC) applies.

(d) Which isotherm model provides a better fit to the data? Why?

Answer 1

The solution is attached herewith. Please go through.

	1mg/g of PNP = 139 mg/mmol * 1 mmol/g and 1mg/L = 139 *1 mM
PNP absorbed, q (mmol/g)	PNP concentration in solution, C (mM)	PNP absorbed, q (mg/g)	PNP concentration in solution, C (mg/L)
0.9	0.006	125.1	0.834
1.1	0.011	152.9	1.529
1.4	0.023	194.6	3.197
1.6	0.045	222.4	6.255
1.9	0.18	264.1	25.02
2.1	0.33	291.9	45.87

For friendlich isotherm,

logc (mg/L)	logq (mg/g)
-0.078833949	2.09725731
0.184407485	2.184407485
0.504742636	2.289142836
0.796227314	2.347134783
1.398287305	2.421768401
1.66152874	2.465234095

From graph, Intercept = log K = 2.15

so K = 141.25

Slope =1/n =0.2

Therefore n =5

For finding coefficient b for langmuir,

Its seen that the plot is mostly linear for Friendlich whereas different points give very different coefficient in case of Langmuir. Hence Friendlich is preferred.