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1. Below shows the application of the Langmuir equation to calculate the amount adsorbed gram carbon: 9 = q = qmax. TA = qmax KACA 1+KA.CA 0.000004 x 100.11 x 2.259 1100.11 x 2.259 Eq 1 = 3.98 × 10-6 mg/g = q = amount adsorbed per unit mass mg/g qmax = maximum adsortion capacity mg/g TA = Fraction of occupied sites K₁ = adsorption equilibrium constant L/mg CA = concentration of the adsorbant in solution mg/L 2. Calculating total capacity: Total capacity = q x mass of GAC = 3.98 × 10-6 mg/g x 100,000g = 3.98 mg 3. Calculation of the lifespan of the GAC: Assumed flow rate: 1,000,000L/day with 0.000004mg/L (1ppb) PFAS per day = 0.000004 × 1,000,000 = 1000mg/day Dividing the total capacity by the daily load gives: lifespan = 3.98 1000 = 3.98 x 10-3 days 5.73 minutes 3.98 × 10-3 x 24 x 60 Table 1: screenshot from research paper listing and corresponding K₁ values (Wang L., 2024) GAC MGAC PFOA PFNA PFOA PFNA single single in mixture in mixture PFOA PFNA single single PFOA in mixture mixture PFNA in Qmax (mg/g) 100.11 67.09 92.64 54.34 104.25 81.68 93.49 49.18 KL 2.259 0.019 1.05 0.041 2.272 0.074 3.485 0.027 (L/mg) R² 0.987 0.964 0.951 0.974 0.991 0.956 0.952 0.956

1. Below shows the application of the Langmuir equation to calculate the amount adsorbed gram carbon: 9 = q = qmax. TA = qmax KACA 1+KA.CA 0.000004 x 100.11 x 2.259 1100.11 x 2.259 Eq 1 = 3.98 × 10-6 mg/g = q = amount adsorbed per unit mass mg/g qmax = maximum adsortion capacity mg/g TA = Fraction of occupied sites K₁ = adsorption equilibrium constant L/mg CA = concentration of the adsorbant in solution mg/L 2. Calculating total capacity: Total capacity = q x mass of GAC = 3.98 × 10-6 mg/g x 100,000g = 3.98 mg 3. Calculation of the lifespan of the GAC: Assumed flow rate: 1,000,000L/day with 0.000004mg/L (1ppb) PFAS per day = 0.000004 × 1,000,000 = 1000mg/day Dividing the total capacity by the daily load gives: lifespan = 3.98 1000 = 3.98 x 10-3 days 5.73 minutes 3.98 × 10-3 x 24 x 60 Table 1: screenshot from research paper listing and corresponding K₁ values (Wang L., 2024) GAC MGAC PFOA PFNA PFOA PFNA single single in mixture in mixture PFOA PFNA single single PFOA in mixture mixture PFNA in Qmax (mg/g) 100.11 67.09 92.64 54.34 104.25 81.68 93.49 49.18 KL 2.259 0.019 1.05 0.041 2.272 0.074 3.485 0.027 (L/mg) R² 0.987 0.964 0.951 0.974 0.991 0.956 0.952 0.956

Introduction to Chemical Engineering Thermodynamics
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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  1. b) Explain the key features of the Langmuir adsorption model 

 - Drawing a diagram with empty and occupied sites. Show how new molecules would adsorb.

drawing the diagram, showing free and empty sites, and their number (to use for next section)

 - Define the capacity and binding affinity parameters in terms of things shown on the diagram

Defining the capacity and binding affinity parameters in terms of bound, free sites, and free molecules

 - Plot what would be a typical breakthrough curve and give an explanation approximately when breakthrough would occur

plotting a typical sigmoidal breakthrough curve and saying it would certainly occur by the time capacity is used, but also could be much earlier if the affinity is low

 

 

 

 

 

 

 

1. Below shows the application of the Langmuir equation to calculate the amount adsorbed gram carbon: 9 = q = qmax. TA = qmax KACA 1+KA.CA 0.000004 x 100.11 x 2.259 1100.11 x 2.259 Eq 1 = 3.98 × 10-6 mg/g = q = amount adsorbed per unit mass mg/g qmax = maximum adsortion capacity mg/g TA = Fraction of occupied sites K₁ = adsorption equilibrium constant L/mg CA = concentration of the adsorbant in solution mg/L
Transcribed Image Text:1. Below shows the application of the Langmuir equation to calculate the amount adsorbed gram carbon: 9 = q = qmax. TA = qmax KACA 1+KA.CA 0.000004 x 100.11 x 2.259 1100.11 x 2.259 Eq 1 = 3.98 × 10-6 mg/g = q = amount adsorbed per unit mass mg/g qmax = maximum adsortion capacity mg/g TA = Fraction of occupied sites K₁ = adsorption equilibrium constant L/mg CA = concentration of the adsorbant in solution mg/L
2. Calculating total capacity: Total capacity = q x mass of GAC = 3.98 × 10-6 mg/g x 100,000g = 3.98 mg 3. Calculation of the lifespan of the GAC: Assumed flow rate: 1,000,000L/day with 0.000004mg/L (1ppb) PFAS per day = 0.000004 × 1,000,000 = 1000mg/day Dividing the total capacity by the daily load gives: lifespan = 3.98 1000 = 3.98 x 10-3 days 5.73 minutes 3.98 × 10-3 x 24 x 60 Table 1: screenshot from research paper listing and corresponding K₁ values (Wang L., 2024) GAC MGAC PFOA PFNA PFOA PFNA single single in mixture in mixture PFOA PFNA single single PFOA in mixture mixture PFNA in Qmax (mg/g) 100.11 67.09 92.64 54.34 104.25 81.68 93.49 49.18 KL 2.259 0.019 1.05 0.041 2.272 0.074 3.485 0.027 (L/mg) R² 0.987 0.964 0.951 0.974 0.991 0.956 0.952 0.956
Transcribed Image Text:2. Calculating total capacity: Total capacity = q x mass of GAC = 3.98 × 10-6 mg/g x 100,000g = 3.98 mg 3. Calculation of the lifespan of the GAC: Assumed flow rate: 1,000,000L/day with 0.000004mg/L (1ppb) PFAS per day = 0.000004 × 1,000,000 = 1000mg/day Dividing the total capacity by the daily load gives: lifespan = 3.98 1000 = 3.98 x 10-3 days 5.73 minutes 3.98 × 10-3 x 24 x 60 Table 1: screenshot from research paper listing and corresponding K₁ values (Wang L., 2024) GAC MGAC PFOA PFNA PFOA PFNA single single in mixture in mixture PFOA PFNA single single PFOA in mixture mixture PFNA in Qmax (mg/g) 100.11 67.09 92.64 54.34 104.25 81.68 93.49 49.18 KL 2.259 0.019 1.05 0.041 2.272 0.074 3.485 0.027 (L/mg) R² 0.987 0.964 0.951 0.974 0.991 0.956 0.952 0.956
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