acid/base buffering reginald stanton, phd september 2009
TRANSCRIPT
Acid/Base Buffering
Reginald Stanton, PhD
September 2009
Acids are electrolyte compounds, and electrolytes dissociate in water into their respective cations and anions. A generic representation for an acid is HA. Here the H represents a dissociable hydrogen; a hydrogen bound to a strongly electronegative atom that detaches from the substance in aqueous solution to become H+(aq). The A represents an anion; the negatively charged segment of the molecule that is A-(aq) in water. The hydrogen is attached to the anion; hence, HA.
HA >>> H+(aq) + A-(aq) H2O
Vinegar (acetic acid), is CH3COOH. Acetate ,CH3COO-, is the anion of acetic acid.
HClHCl is hydrogen chloride. Chloride ion, Cl-, is the anion. HCl(aq) is hydrochloric acid.
C
O
When HA is dissolved in water it dissociatesinto H+ and A-.
HA ↔ H+(aq)+ A-(aq)If the dissociation is complete (i.e. more than 90% of all HA is converted into H+ and A-) the substance is called a strong acid. Otherwise, it is called a weak acid.
The anion of a weak acid is called a conjugate base. The cation of a weak base is called a conjugate acid. A weak acids with it’s conjugate bases or weak bases with it’s conjugate acids are called conjugates.
The dissociation of hydrogen from weak acid in aqueous solution occurs when H+ levels are low enough. Further, that process is a statistical function associated with bond strength.
For example, dissociation of dissociable hydrogen from acetic acid molecules takes place when the [H+] ≥ 1.8x10-5M. When hydrogen content is at that level, the pH of the solution is equal to the pKa for the dissociation of acetic acid {pH = pKa (pK for short)} and [HA] = [A-].
So the pK of the acid is a measure of the strength of the bond between hydrogen and the anion; the larger the pK, the stronger the bond!
The strength of the bond between the anion and it’s hydrogen varies from anion to anion. For example chloride ion, Cl-, barely holds onto hydrogen at all. Acetate, CH3COO-, on the other hand, holds hydrogen rather tightly. And then ammonium ion, NH4
+, holds onto hydrogen for dear life!
The stronger the bond between the hydrogen and the anion, the greater the probability the anion will hold the hydrogen for a longer period of time.
HCl
CH3COOH
Weak Bond
Stronger Bond
H.Cl
CH3COOH
Weak Bond
Stronger Bond
H..Cl
CH3COOH
Weak Bond
Stronger Bond
H+...Cl-
CH3COOH
Weak Bond
Stronger Bond
H+....Cl-
CH3COO.H
Weak Bond
Stronger Bond
H+ Cl-
CH3COO.H
Weak Bond
Stronger Bond
H+ Cl-
CH3COO..H
Weak Bond
Stronger Bond
H+ Cl-
CH3COO..H
Weak Bond
Stronger Bond
The pK of the compound is thus an indicator of the strength of the bond between the anion and its hydrogen. The larger the pK, the greater the bond strength.
Compound : pK Values HA1 : pK1~0.53 HA2 : pK2~1.13 HA3 : pK3~0.07 HA4 : pK4~0.21
Here we see that the 3rd compound, HA3, has the lowest pK and the 2nd compound, HA2, has the highest pK. Therefore, HA2, has the greatest bond strength between the hydrogen and the anion and HA3 has the lowest.
If the bond between the anion and the hydrogen is substantial, and [H+] is high, there is a low probability that the anion will lose the hydrogen.
H+
A- HA
HA
HA
HA
H+
H+
H+
H+
H+
H+
H+
H+
H+
H+
H+
H+
H+
H+H+
H+
H+
H+
H+
That’s because the environment is full of H+. Every time the anion loses a hydrogen, it immediately picks up another one.
If the bond between the anion and the hydrogen is substantial, and [H+] is low, there is a high probability that the anion will lose the hydrogen.
A-HA
H+
H+
That’s because the environment has little H+. If the anion loses a hydrogen, it is unlikely to get another one quickly.
A-
A-
Under conditions of low pH (high H+ concentrations) an acidic solution of a weak acid consists mostly of undissociated acid; HA. At high pH (low H+ concentrations) acidic solutions of weak acids consists mostly of free anion, A-. For intermediate pH values, the solutions are mixtures of the acid and the anion.
Low pH Intermediate pH
High pH
H+
H+
HA
H+
H+
H+
H+
H+
H+
H+
H+
H+
H+
HA
H+
H+
H+
H+
H+
H+
H+
H+
H+
H+
H+
H+
HA
HA
HA
HA
H+
A-
H+
H+
H+ H+
A-
H+
H+
H+
H+
H+
H+
HA
A-
HA
HA
H+
A-
H+
A-
A-
H+
A-
A-
A-
To be sure, the bond between the anion and the hydrogen is a game of catch-n-release!
H+HA + A-
The anion releases the hydrogen periodically, no matter what! The amount of time it holds the hydrogen depends on the strength of the bond between the anion and the hydrogen. The stronger the bond, the longer the hydrogen is held.
H+
H+
H+
Once the hydrogen is released, the anion can re-bind that hydrogen or bind to a different one altogether.
H+HA A-
H+
H+
H+
The amount of H+ in solution determines how long it takes the anion to bind to another hydrogen!
H+
H+
H+
If the amount of H+ in solution is great, the anion will get another hydrogen fairly quickly.
H+HA A-H+
H+
H+
H+ H+
H+H+
H+
H+
H+H+
If the amount of H+ in solution is low, the anion may have to wait a long time to get another hydrogen.
H+H+
HA A- H+
Therefore two factors determine whether or not an anion will be bound to a dissociable hydrogen:
1) the strength of the bond between the hydrogen and the anion, and
2) the amount of hydrogen ion in solution.
Can you tell how each is related to binding of the hydrogen to the anion (each factor separately and in conjunction with the other)?
Buffers are entities that resist change. In biochemistry, the reference to buffers is almost always to compounds called acid-base buffers.
The aqueous solution of these compounds resist changes in [H+], hydronium ion.
Compounds that are capable of buffering are weak acids or weak bases. This is because they have a reasonably strong hold on the dissociable hydrogen (or hydroxide).
The bond between the anion of a strong acid and it’s hydrogen is too weak for buffering to take place.
Assume HA is a weak acid. At pH values lower than the pK of the acid, there is a great deal of H+ and since the bond between the anion and the hydrogen is fairly strong, very little of the acid will lose hydrogen and not quickly gain another one.
H+HA
H+
H+
H+
H+
H+
H+
H+
H+
H+
H+
H+H+
H+
H+
H+
H+
H+
H+H+
If a small amount of OH- is added, a small amount of H+ will be converted into H2O. Furthermore, the pH of the solution is increased since some H+ is removed.
H2O HAH+
H+
H+
H+
H+
H+
H2O
OH-
H+
H+
H+H+
H+
H+
H+
H+
H2O
H+
H+
Yet, there is still enough H+ to keep a hydrogen attached to the anion.
However, once enough OH- has been added, a significant amount of H+ will have been converted into H2O.
H2O H+....A-
H2O
H+
H+
OH-
OH-
H2O
OH-
H+
H+
H2O
H2O
H+
H2O
At that point, if the anion loses a hydrogen, it is unlikely it will pick up another one.
H2O
H2O
H2O
H2O
Under these circumstances if you add another OH- it reacts with H+ to produce H2O.
HA > H+ + A-
OH-...H+ > H2OSo the pH would be expected to increase, however, at the same time the anion loses an H+, restoring the amount of [H+].
So the pH Does Not Change Significantly!
That’s Buffering! The solution is resisting a change in pH!
This does NOT happen until [H+] is low enough that the attraction between the anion and hydrogen ion is not a factor. [H+] is very low and the collision frequency isn’t high enough to produce HA when pH ~ pK.
Some fraction of anions donate hydrogen as the added OH- takes them away; but the ratio is not 1:1, so the pH just rises slower than it did outside the buffering zone (1 pH unit of the pK)!
The acid dissociation expression is:
Ka = [H+][A-]/[HA]
Which can be rearranged to:
1/[H+] = [A-]/[HA]·Ka so [H+] = Ka·[HA]/[A-]
Taking the –log of each side yields:
-log([H+]) = -log(Ka·[HA]/[A-])-log([H+]) = -log(Ka)-log([HA]/[A-])
andpH = pKa + log([A-]/[HA])
This is the Henderson-Hasselbalch Equation:
pH = pK + log([A-]/[HA])
Compounds buffer best when the pH of the solution is close to the pK of the compound:
pH = pK
This occurs when log([A-]/[HA]) = 0
(when [A-] = [HA])
So weak acids/bases buffer best when the concentration of the conjugates is equal.
Adding a known amount of an entity to determine the unknown amount of some other entity is called titration. The titration of a weak acid with OH- shows a lot about its acid/base behavior.
Consider a weak acid in a highly acidic solution (i.e. low pH).
The stepwise addition of OH- can be used to produce a titration curve; a graph of the solution pH as a function of OH- added.
pH
[OH-]
mostlyHA
At the low pH, the solution consists mostly of H+ and HA.
Titration curves are sigmoid.
pH
[OH-]
pH Increases
As OH- is added, H+ reacts with it to produce H2O and the pH goes up.
pH
[OH-]
Eventually enough H+ is removed and HA starts to lose H+ (regenerating H+) and the pH doesn’t increase significantly.
Buffer
ing Re
gion
pH
[OH-]
Here, all of the HA is gone; no more H+ is generated to stabilize the pH. pH increases again.
Region of Buffering
pH
[OH-]
pH = pK
mostlyHA
mostlyA-
pH of titrant
[HA] = [A-]
The titration curve shows how HA responds to the addition of OH-.
Since the compound buffers best around the point where pH = pK, and [HA] ~ [A-] at that point, we can make a solution that buffers at a particular pH just by combining approximately equal proportions of the appropriate conjugates if that compound’s pK is close to the target pH.
For example, acetic acid has a pK of ~ 4.7. We can make a solution that buffers around that pH by combining equal amounts of acetic acid and acetate.
And since the concentration of a buffer is the sum of the concentrations of the buffer’s conjugates, to make a 1.0M solution of pH 4.7 acetate buffer, I’d mix equal amounts (volumes) of 1.0M acetic acid and 1.0M acetate.
AceticAcid
Acetate
pH
AceticAcid
Acetate
pH
AceticAcid
Acetate
pH
AceticAcid
Acetate
pH
AceticAcid
Acetate
pH
AceticAcid
Acetate
pH
If you wanted to make a 1M solution that buffers around pH = 5.0, you could still use acetic acid/acetate. But you can’t use equal amounts of equimolar solutions.
Since the target is 5.0:pH = pK + log(A-/HA)5.0 = 4.7 + log(A-/HA)A-/HA = 10(5.0-4.7) = 100.3 = 1.9953
The ratio of acetate/acid should be 1.9953!
You’d need to use almost twice as much acetate as acetic acid (i.e. 199.5mL of 1M acetate with 100.0mL of 1M acetic acid) to make the buffer.