Graphical Approach Independent Variable pH: the master variable - - PDF document

SLIDE 1

CEE 680 Lecture #11 2/7/2020 1

Lecture #11 Acids & Bases: Graphical Solutions I

(Stumm & Morgan, Chapt.3 )

David Reckhow CEE 680 #11 1

Updated: 7 February 2020

Print version

(Benjamin, Chapt. 4)

Graphical Approach

 Independent Variable

 pH: “the master variable”

 Two types of graphs

 Distribution diagrams

 alpha values, independent of concentration

 Log concentration diagrams

 pC‐pH diagrams

David Reckhow CEE 680 #11 2

SLIDE 2

CEE 680 Lecture #11 2/7/2020 2

Monoprotic acids: calculations

 Start with C and Ka equations

David Reckhow CEE 680 #11 3

3 1 1+3

] [ ] [



  A HA C

] [ ] ][ [ HA A H Ka

 



] [ ] [ HA C A  



] [ ] [



  A C HA

 

] [ ] [ ] [ HA HA C H Ka  



] [ ] ][ [

  

  A C A H Ka ] [ ] ][ [ ] [

  

  H C H HA HA Ka ] [ ] [ ] [

 

  H K H C HA

a

1 1 ] [

] [

 



H Ka

C HA

0 1

] ][ [ ] [

   

 H A A K C K

a a

] [ ] [

 

  H K C K A

a a

a

K H

C A

] [

1 1 ] [



 



1+3

For LogC vs pH diagrams For distribution diagrams

Note: 0 + 1 = 1

David Reckhow CEE 680 #11 4

pH

1 2 3 4 5 6 7 8 9 10 11 12 13 14



0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0=NH4

+/C

1=NH3/C

1 1 ] [

] [

 



H Ka

C HA

a

K H

C A

] [

1 1 ] [



 



Distribution Diagram for Ammonia

pH

0 1

6 1 8.3 0.91 0.09 9.3 0.5 0.5 10.3 0.09 0.91 12 1

SLIDE 3

CEE 680 Lecture #11 2/7/2020 3

Preparing log C vs. pH Diagrams

 1. Draw [H+] line

 pH  ‐log[H+]  log[H+] = ‐pH

 2. Draw [OH‐] line

 Kw=[H+][OH‐]  log Kw= log[H+] + log[OH‐]  log [OH‐] = ‐log [H+] + log Kw  log [OH‐] = pH ‐ pKw

 3. Draw [HA] and [A‐] lines

 see next slide

David Reckhow CEE 680 #11 5

2

Calculations for log [HA] and log [A‐] lines

 If pH << pKa, or [H+] >> Ka  If pH >> pKa, or [H+] << Ka  If pH = pKa, or [H+] = Ka

David Reckhow CEE 680 #11 6

] [ ] [ ] [

 

  H K H C HA

a

] [ ] [

 

  H K C K A

a a

Log [HA]=log C Log [HA]=log C - pH + pKa Log [A-]=log C Log [A-]=log C + pH - pKa Log [A-]=log C - 0.3 Log [HA]=log C - 0.3 1+3 1+3

SLIDE 4

CEE 680 Lecture #11 2/7/2020 4

Blank Axes

David Reckhow CEE 680 #11 7

pH

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Log C

• 14
• 13
• 12
• 11
• 10
• 9
• 8
• 7
• 6
• 5
• 4
• 3
• 2
• 1

David Reckhow CEE 680 #11 8

pH

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Log C

• 14
• 13
• 12
• 11
• 10
• 9
• 8
• 7
• 6
• 5
• 4
• 3
• 2
• 1

H+

OH-

SLIDE 5

CEE 680 Lecture #11 2/7/2020 5

Log C vs. pH for 10‐3 HOCl

David Reckhow CEE 680 #11 9

pH

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Log C

• 14
• 13
• 12
• 11
• 10
• 9
• 8
• 7
• 6
• 5
• 4
• 3
• 2
• 1

H+

OH-

HOCl OCl-

1+3 2 4?

To next lecture

David Reckhow CEE 680 #11 10