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38. The equations and constants for the dissociation of three different acids are given below.

HCO3- H+ + CO3-2               Ka = 4.2 x 10-7

H2PO4- H+ + HPO4-2            Ka = 6.2 x 10-8

HSO4- H+ + SO4-2                 Ka = 1.3 x 10-2
    

a. From the systems above, identify the conjugate pair that is best for preparing a buffer with a pH of 7.2. Explain your choice.
   
pKa = - log Ka 

pKa HCO3 - = - log 4.2 x 10 -7 = 6.38

pKa H2PO4 - = - log 6.2 x 10 -8 = 7.21

pKa HSO4 - = - log 1.3 x 10 -2 = 1.89

Pick as the acid in the acid-base conjugate pair, the species with the pKa closest to the desired pH.

H2PO4 -  is the acid  and HPO4 -2  is the conjugate base.   The conjugate base will have one less H+ than the acid.

   
    
b. Explain briefly how you would prepare the buffer solution described in (a) with the conjugate pair you have chosen.
   
Because the desired pH is the same as the pKa, the buffer solution should have equal concentrations of  H2PO4 -  and HPO4 -2  .  Higher concentrations create solutions with greater buffer capacities.  If the desired pH was not the same as the pKa, pick a concentration for one of the species, and solve for the other species using the pH to get the [H +].

H2PO4 -    HPO4 -2  +  H + 

   

         [HPO4 -2 ]] H + ]
Ka = ------------------------
             [H2PO4 - ]
    

                Ka x [H2PO4 - ]
] H + ] = -----------------------   equal concentration give pH = pKa
                    [HPO4 -2 ]

    
   
c. If the concentrations of both the acid and the conjugate base you have chosen were doubled, how would the pH be affected? Explain how the capacity of the buffer is affected by this change in concentrations of acid and base.
   
H2PO4 -    HPO4 -2  +  H + 

   

         [HPO4 -2 ]] H + ]
Ka = ------------------------
             [H2PO4 - ]
    

                Ka x [H2PO4 - ]
] H + ] = -----------------------  
                    [HPO4 -2 ]
    

Doubling both concentrations would not change ratio of concentrations or [H +].  The pH would be unchanged.

The buffer capacity would be doubled by doubling the concentrations.

H2PO4 - reacts with any base added to form HPO4 -2  .  When the H2PO4 - is used up, the pH begins to change rapidly and the buffer capacity has been exceeded.  Doubling the [H2PO4 - ] doubles the amount of base that can be added before this occurs.

HPO4 -2 reacts with any acid added to form H2PO4 -  .  When the HPO4 - is used up, the pH begins to change rapidly and the buffer capacity has been exceeded.  Doubling the [HPO4 - ] doubles the amount of acid that can be added before this occurs.

    
    
d. Explain briefly how you could prepare the buffer solution in (a) if you had available the solid salt of only one member of the conjugate pair and solutions of a strong acid and a strong base.
    
         H2PO4 -   +  OH -  -->  HPO4 -2 
i           2X              X               0
/\           X               X               X
f           X                0               X
    

If  2X moles of H2PO4 -  are added to X moles of OH - , the solution will end up with equal moles of H2PO4 -   and HPO4 -2

This will create the same buffer solution as starting with equal moles of the two chemicals.