In 1922 Donald D. van Slyke (J. Biol. Chem., 52, 525) defined a quantity known as the buffer index: β = dc_b/d(pH), where d_cb represents the increment of moles of strong base to one liter of the buffer. For the addition of a strong acid, he wrote β = -dc_a/d(pH). By applying this idea to a monoprotic acid and its conjugate base, we can derive the following expression:

where c is the total concentration of monoprotic acid and conjugate base.

(a) Use the above expression to calculate the buffer index for the acetic acid buffer with a total acetic  acid and acetate ion concentration of 2.0 x 10^-2 and a pH = 5.0.

(b) Use the buffer index from part (a) and calculate the pH of the buffer after the addition of of a strong acid.

(c) Make a plot of β versus pH for a 0.1 M acetic acid buffer system. Locate the maximum buffer index as well as the minimum buffer indices.

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B = 2.303 Kw [H3O+] + [H3O+] + cKa[H3O+] (Ka+ [H3O+])2/