Question

Question 3 Phenol adsorbs to powdered activated carbon (PAC) according to the following Langmuir isotherm: 0.45Ce S = 1+5.7C where S is expressed in g/g and Ce is expressed in mg/L. (a) What is the maximum concentration of phenol that can be adsorbed to this PAC? (b) If 5 kg of PAC is added to 100 L of wastewater that initially contains 25 mg/L of phenol, what will be the concentration of phenol in the wastewater once equilibrium has been reached?

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Answer 1

The adsorbed concentration of Phenol is given by the relation,

S = 0.45C 1 +5.7C

Here, S is in g/g and C_e is in mg/L. In Langmuir isotherm, for maximum adsorption, C_e will tend to infinity. Thus, we have,

0.45C Smar = lim C+01+5.7C 0.45 Smar = lim C+ + +5.7 67 0.45 Dividing by Cal = Smar = 57 [At limĆ +0] Smar = 0.079

Thus, maximum adsorption will be 0.079 g Phenol per g of PAC

b)

Total mass of Phenol = Concentration * Volume = 25 mg/L * 100 L = 2500 mg = 2500 mg * (0.001g/mg) = 2.5 g

Let at equilibrium, x mg/L of Phenol remains. Then

Total mass of phenol remaining = Concentration * Volume = x mg/L * 100 L = 100x mg = 100x mg * (0.001g/mg) = 0.1x g

Mass of Phenol adsorbed = Initial - Mass Remaining = (2.5 - 0.1x) g

Mass of PAC = 5kg = 5kg * (1000g/kg) = 5000 g

Thus at equilibrium S will be

S= Mass of Phenol adsorbed Mass of PAC 2.5 -0.1.2 5000

Further, C_e that is the equilibrium concentration will be x mg/L

Thus,

S = 0.45. 1 +5.7.0

Equation both expressions of S, we have,

2.5 -0.1.2 0.45.0 5000 1+5.7.0 0.00111814 Solving for positive x

Thus, the concentration of Phenol remaining will be 1.12 x 10^-3 mg/L