CEE 680 Lecture #25 3/4/2020 Print version Updated: 4 March 2020 - - PDF document

CEE 680 Lecture #25 3/4/2020 1

Lecture #25 Dissolved Carbon Dioxide: Open & Closed Systems VI

(Stumm & Morgan, Chapt.4 )

Benjamin; Chapter 7

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Updated: 4 March 2020

Print version  Lake Erie

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 Lake Taihu

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 algae

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 Algal cells

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Photosynthesis Problem

 Principles of conservation of Alk and CT

 From Stumm & Morgan (example 4.8, pg. 174)

 Approach

 General: assume that system is closed  Simplified: treat alkalinity as constant  Alternative: allow alkalinity to vary in accordance with

reaction stoichiometry

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Problem Statement

 Photosynthesis with nitrate assimilation

 106 CO2 + 16 NO3

‐ + HPO4 ‐2 + 122 H2O + 18 H+

= C106H263O110N16P + 138 O2

 Conditions

 Initial

 Alk = 0.85 meq/L  pH = 9.0

 Final (3 hours later)

 pH = 9.5

 What is the net rate of carbon fixation?

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Simplified Solution: (const. alk.)

 Use standard alkalinity equation

 So initially:

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 

] [ ] [ 2

2 1   

   H OH C Alk

T

  M x x H OH Alk CT

4 9 5 4 2 1

10 017 . 8 ) 0477 . ( 2 9523 . 10 10 10 5 . 8 2 ] [ ] [

     

           0477 . 1 1 1 1

3 . 10 9 2 2 1 2

10 10 ] [ ] [ 2

     

   

K H K K H

 9523 . 1 1 1 1

9 3 . 10 2 1

10 10 ] [ ] [ 1

     

   

H K K H



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Simplified Solution: (const. alk.)

 And 3 hours later

 So the rate is:

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M x x H OH Alk CT

4 5 . 9 5 . 4 4 2 1

10 199 . 7 ) 1368 . ( 2 8632 . 10 10 10 5 . 8 2 ] [ ] [

     

           1368 . 1 1 1 1

3 . 10 5 . 9 2 2 1 2

10 10 ] [ ] [ 2

     

   

K H K K H

 8632 . 1 1 1 1

5 . 9 3 . 10 2 1

10 10 ] [ ] [ 1

     

   

H K K H

 hr M x hr M x M x t CT / 10 7 . 2 3 10 199 . 7 10 017 . 8

5 4 4     

  

Alternative Solution

 Allow alkalinity to vary in accordance with reaction

stoichiometry

 106 CO2 + 16 NO3

‐ + HPO4 ‐2 + 122 H2O + 18 H+

= C106H263O110N16P + 138 O2

 Now, incorporating this into the final alkalinity value:  And the rate becomes:

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C Alk Alk



 

106 18

    

  

5 5 4 5 . 4 106 18 4 2 1 2 1

10 1 . 7 10 2995 . 9 3066 . 1 10 017 . 8 136 . 1 10 10 5 . 8 2 ] [ ] [ ] [ 2

            

              x C x C C x C x C C OH Alk H OH C Alk

T T T T T T f f f T

i

   

hr M x hr M x t CT / 10 4 . 2 3 10 1 . 7

5 5    

 

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Buffer Intensity & Closed System

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From: Butler, 1991; pg 67

 

2 1 1

] [ ] [ 303 . 2     

T T

C C H OH    

 

Buffer Intensity & Open System

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From: Butler, 1991; pg 68

 

] [ 4 ] [ ] [ ] [ 303 . 2

2 3 3    

    CO HCO H OH 

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To next lecture

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DAR