Buffer Intensity g Amount of strong 1 .2 1 .0 0 .8 0 .6 0 - - PDF document

CEE 680 Lecture #17 2/24/2020 1

Lecture #17 Acids/Bases and Buffers: Fundamentals & Buffer Intensity (Benjamin, Chapter 5)

(Stumm & Morgan, Chapt. 3 )

David Reckhow CEE 680 #17 1

Updated: 24 February 2020

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Buffer Intensity

 Amount of strong

acid or base required to cause a specific small shift in pH

David Reckhow CEE 680 #17 2

f

.2 .0 .2 .4 .6 .8 1 .0 1 .2

pH

2 3 4 5 6 7 8 9 1 1 1 1 2

g

.2 .0 .2 .4 .6 .8 1 .0 1 .2

p H 3 .3 5 p H 4 .7 p H 8 .3 5 S ta rtin g P

• in

t M id

• p
• in

t E n d P

• in

t

dpH dC dpH dC

A B

   

10-2M HAc

B

C



pH

 B

C



pH



Slope = 1/

CEE 680 Lecture #17 2/24/2020 2

Buffers: Acetic Acid with Acid/Base Addition

 1. List all species present



(use NaOH and HCl as acid/base)

 H+, OH‐, HAc, Ac‐, Na+, Cl‐

 2. List all independent equations

 equilibria

 Ka = [H+][Ac‐]/[HAc] = 10‐4.77  Kw = [H+][OH‐] = 10‐14

 mass balances

 CT = [HAc]+[Ac‐]

 electroneutrality: (positive charges) = (negative charges)

 Note: we can’t use the PBE because we’re essentially adding an

acid and its conjugate base

 [Na+] + [H+] = [OH‐] + [Ac‐] + [Cl‐]

David Reckhow CEE 680 #17 3

1 2 3 4 Six total

CA = [Cl-] CB = [Na+]

5 6

Acetic Acid with Acid/Base Addition (cont.)

 3. Use ENE, substitute & solve for CB‐CA

 [Na+] + [H+] = [OH‐] + [Ac‐] + [Cl‐]  CB + [H+] = Kw/[H+] + KaCT/{Ka+[H+]} + CA  CB ‐ CA = Kw/[H+] ‐ [H+] + KaCT/{Ka+[H+]}

 4. Take derivative

 with respect to [H+]

David Reckhow CEE 680 #17 4

4

Kw = [H+][OH-] [OH-] = Kw/[H+]

2 3 1,2,3,4,5,6

CT = [HAc]+[Ac-] [HAc]= CT - [Ac-] CA = [Cl-] CB = [Na+]

5 6 1 Ka = [H+][Ac-]/[HAc]

Ka = [H+][Ac-]/ {CT-[Ac-]} KaC-Ka[Ac-]= [H+][Ac-] KaC=[Ac-]{Ka+[H+]} [Ac-]=KaCT/{Ka+[H+]}

1+3

CEE 680 Lecture #17 2/24/2020 3

Acetic Acid with Acid/Base Addition (cont.)

 Take the derivative with respect to [H+] of:

 CB = CA + Kw/[H+] ‐ [H+] + KaCT/{Ka+[H+]}

 But this is not exactly what we want

 Factor out  equation  and recall:

David Reckhow CEE 680 #17 5

 

2 2

] [ 1 ] [ ] [

  

     H K K C H K H d dC

a a T w B

dpH H d H d dC dpH dC

B B

] [ * ] [

 

   ] [ 303 . 2 ] [ ] [ 303 . 2 ] [ 303 . 2 ] ln[ 303 . 2 ] ln[ ] log[

      

         H dpH H d H H d H d dpH H H pH

Acetic Acid with Acid/Base Addition (cont.)

 so:  and combining:

David Reckhow CEE 680 #17 6

] [ ] [ 303 . 2

 

  H d dC H

B



    

                        

       2 2 2

] [ ] [ ] [ ] [ 303 . 2 ] [ 1 ] [ ] [ 303 . 2 H K H K C H H K H K K C H K H

a a T w a a T w



 

1

] [ ] [ 303 . 2   

T

C H OH   

 

  

          

    2

] [ ] [ ] ][ [ ] [ ] [ 303 . 2 A HA A HA C H OH

T



] [ ] [ ] [

 

   H K H C HA

a T

 ] [ ] [

1  

   H K K C A

a a T



CEE 680 Lecture #17 2/24/2020 4

Example

 Trichlorophenol

 pKa = 6.00  CT = 10‐2

David Reckhow CEE 680 #17 7

f

0.0 0.2 0.4 0.6 0.8 1.0

pH

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

Log C

• 7
• 6
• 5
• 4
• 3
• 2
• 1

H+

OH-

Trichlorophenol Trichlorophenate ion

pH

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

g

0.0 0.2 0.4 0.6 0.8 1.0

pH 4 pH 6.0 pH 9 Starting Point Mid-point End Point

 See also

S&M fig 3.10

David Reckhow CEE 680 #17 8

pH

2 3 4 5 6 7 8 9 10 11 12

Buffer Intensity, B (M/pH)

0.000 0.001 0.002 0.003 0.004 0.005 0.006

Local Maximimum @ g=0.5 Local Min. @ g=0 Local Min. @ g=1

CEE 680 Lecture #17 2/24/2020 5

Equations for polyprotic acids

 Analogous to the monoprotic systems

 monoprotic  diprotic  triprotic

David Reckhow CEE 680 #17 9

 

1

] [ ] [ 303 . 2   

T

C H OH   

 

 

2 1 1

] [ ] [ 303 . 2     

T T

C C H OH    

 

 

3 2 2 1 1

] [ ] [ 303 . 2       

T T T

C C C H OH     

 

Buffer example

 Design a buffer using phosphate that will hold

its pH at 7.0 0.05 even when adding 10‐3 moles per liter of a strong acid or base

 first determine the required buffer intensity  Next look at the buffer equation and try to simplify

based on pH range of interest

David Reckhow CEE 680 #17 10

 

3 2 2 1 1

] [ ] [ 303 . 2       

T T T

C C C H OH     

 

02 . 05 . 10 3   



dpH dCB 

CEE 680 Lecture #17 2/24/2020 6

Buffer example (cont.)

 This gives us the simplified version that can be

further simplified

David Reckhow CEE 680 #17 11

 

       

 

M C

K H H K H K K H K K H H K K H K K H T

037 . 22 . 4 303 . 2 02 . 1 1 303 . 2 02 . 1 1 303 . 2 02 . 303 . 2

1 1 ] [ 1 ] [ 1 ] [ ] [ ] [ 1 ] [ ] [ ] [ 2 1

2 2 3 2 2 1 2 2 3 2 2 1

                        

    

       

  

Acid Neutralizing Capacity

 Net deficiency of protons

 with respect to a proton reference level

 when the reference level is H2CO3, the ANC=Alkalinity

 conservative, not affected by T or P  In a monoprotic system:

 [ANC] = [A‐] + [OH‐] ‐ [H+] 

= CT1 + [OH‐] ‐ [H+]

David Reckhow CEE 680 #17 12

 



 



x f n f

dpH ANC 

CEE 680 Lecture #17 2/24/2020 7

David Reckhow CEE 680 #17 13 David Reckhow CEE 680 #17 14

CEE 680 Lecture #17 2/24/2020 8

To next lecture

David Reckhow CEE 680 #17 15