9. Assume all of the following will fully dissolve in water at the indicated con

Question

9. Assume all of the following will fully dissolve in water at the indicated concentrations. Which of the following buffers will have the greatest buffering capacity at pH = 5.8 D
          a) 0.150 M phosphate buffer, pKa 6.82;             
          b) 150 mM phosphate buffer, pKa 6.82;
          c) 150 mM carbonate buffer, pKa 6.4;                
          d) 150 mM histidine buffer, (pKa%u2019s 2.12, 6.0, 8.99)
          e) 0.150 mM acetate buffer, pKa 4.76.                     
          f) 0.015 M histidine buffer, (pKa%u2019s 2.12, 6.0, 8.99)

Explanation / Answer

let B(beta) be the buffer capacity

according to van slyke equation we have buffer capacity =

B = 2.3*C*Ka*[H]/(Ka + [H])^2

C = total buffer concentration (acid + salt)

Ka = 10^-pKa

H =10^-pH

a.Ba = 2.3*0.15*10^(-6.82-5.8)/(10^-6.82 + 10^-5.8)^2

b.Bb = 2.3 *0.15(150mM=0.15M)*10^(-6.82-5.8)/(10^-6.82 + 10^-5.8)^2

Ba=Bb

c.Bc = 2.3*0.15*10^(-6.4-5.8)/(10^-6.4 + 10^-5.8)^2

Bc>Bb>Ba

d.150mM =0.15M pKa is low hence Bd is greater than Bc

Bd>Bc>Bb>Ba

e.0.15x10^-3 M pKa => low Be but pKa =4.76(negligible effect)

=> Be<Ba

Bd>Bc>Bb>Ba>Be

f.similarly Bd>Bf

therefore the order is

Bd>Bf>Bc>Bb>Ba>Be

Thus option D has the greatest buffer capacity

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