Dear Peng-Yuan,

The change in the pH upon 10 times dilution stems from the buffer capacity and not as a result of the calcium ion nature:

Buffers, Buffer Capacity and Range

Buffers are aqueous systems that resist changes in pH when small amounts of

acid or base are added. Buffer solutions are composed of a weak acid (the proton

donor) and its conjugate base (the proton acceptor). Buffering results from two

reversible reaction equilibria in a solution wherein the concentration of proton

donor and its conjugate proton acceptor are equal. For example, in a buffer

system when the concentration of acetic acid and acetate ions are equal, addition

of small amounts of acid or base do not have any detectable influence on the pH.

This point is commonly known as the isoelectric point. At this point there is no

net charge and pH at this point is equal to pKa.

[CH3COO¯] pH = pKa + log ________________

[CH3COOH]

At isoelectric point [CH3COO¯] = [CH3COOH] hence, pH = pKa

Buffer capacity is a term used to describe the ability of a given buffer to resist

changes in pH on addition of acid or base. A buffer capacity of 1 is when 1 mol

of acid or alkali is added to 1 liter of buffer and pH changes by 1 unit. The buffer

capacity of a mixed weak acid-base buffer is much greater when the individual

pKa values are in close proximity with each other. It is important to note that the

buffer capacity of a mixture of buffers is additive.

Buffers have both intensive and extensive properties. The intensive property is a

function of the pKa value of the buffer acid or base. Most simple buffers work

effectively in the pH scale of pKa ± 1.0. The extensive property of the buffers is

also known as the buffer capacity. It is a measure of the protection a buffer offers

against changes in pH. Buffer capacity generally depends on the concentration

of buffer solution. Buffers with higher concentrations offer higher buffering

capacity. On the other hand, pH is dependent not on the absolute concentrations

of buffer components but on their ratio.

Using the above equation we know that when pH = pKa the concentrations of

acetic acid and acetate ion are equal. Using a hypothetical buffer system of HA

(pKa = 7.0) and [A–], we can demonstrate how the hydrogen ion concentration,

[H+], is relatively insensitive to external influence because of the buffering

action.

For example:

If 100 ml of 10 mM (1x 10-2 M) HCl are added to 1.0 liter of 1.0 M NaCl at pH 7.0,

the hydrogen ion concentration, [H+], of the resulting 1.1 liter of solution can be

calculated by using the following equation:

Buffers Booklet-2003.qxd 4/10/2003 2:04 PM Page 8

9

[H+] x Vol = [H+]

o x Volo

where

Volo = initial volume of HCl solution (in liters)

[H+]

o = initial hydrogen ion concentration (M)

Vol = final volume of HCl + NaCl solutions (in liters)

[H+] = final hydrogen ion concentration of HCl + NaCl solution (M)

Solving for [H+]:

[H+] x 1.1 liter = 1.0 x 10-2 x 0.1 = 1 x 10-3

[H+] = 9.09 x 10-4

or pH = 3.04

Thus, the addition of 1.0 x 10-3 mol of hydrogen ion resulted in a pH change of

approximately 4 pH units (from 7.0 to 3.04).

If a buffer is used instead of sodium chloride, a 1.0 M solution of HA at pH 7.0

will initially have:

[HA] = [A] = 0.5 M

[A] pH = pK + log ______

[HA]

0.5

pH = 7.0 + log ______ or pH = 7.0 0.5

When 100 ml of 1.0 x 10-2 M (10 mM) HCl is added to this system, 1.0 x 10-3 mol

of A– is converted to 1.0 x 10-3 mol of HA, with the following result:

0.499/1.1

pH = 7.0 + log _______________

0.501/1.1

pH = 7.0 - 0.002 or pH = 6.998

Hence, it is clear that in the absence of a suitable buffer system there was a pH

change of 4 pH units, whereas in a buffer system only a trivial change in pH was

observed indicating that the buffer system had successfully resisted a change in

pH. Generally, in the range from [A]/[HA] = 0.1 to [A]/[HA] = 10.0, effective

buffering exists. However, beyond this range, the buffering capacity may be

significantly reduced.

For more details, please see attached file.

Hoping this will be helpful,

Rafik

Ah I got the point. The buffer capacity works well only within pKa +/- 1. Since the pKa of Bistris is about 7.35, hence it happened. Meanwhile, I just found that solubility product of Ca(OH)2 is very low, but not under acidic condition. Thank you very much!