Composition and Action of Buffered Solutions

Buffered solutions or buffers are solutions which resist a change in pH when small amounts of acid or base are added.

Buffers contain an acidic species to neutralize $OH-$ ions and a basic species to neutralize $H+$ ions. However, these two species must be able to coexist in a solution, without completely neutralizing each other. Buffers are therefore made of weak acid-base conjugate pairs, such as $HC$₂H₃O₂ and $C$₂H₃O₂^-.

If we have a weak acid, HX, and its conjugate base, $X-$, the following equilibrium occurs:

$HX\; (aq)$ H⁺ (aq) + X^- (aq)

For this reaction,

If an amount of $H+$ ions are added, the above reaction will shift to the left. This will cause the $[H+]$ to decrease, to close to what it was before, and thus the pH will stay fairly constant.

If $OH-$ ions are added they will remove $H+$ ions to form water, thus increasing the pH. However, the equilibrium reaction will shift to the right as $H+$ ions are removed. The $[H+]$ will therefore remain fairly constant, as will the pH.

The most effective buffering solutions are those which have similar concentrations of HX and $X-$, because then the buffer has the capacity to absorb both acid and base, with the same effectiveness in either direction.

When choosing an appropriate conjugate acid-base pair to form a buffer at a specific pH, the most effective buffers have the desired pH within 1.0 of the conjugate acid's pKa.

Ways to make a buffer

• Adding a conjugate base to a weak acid
• Adding a strong acid to a weak base
• Adding a strong base to a weak acid

Buffering Capacity and pH

The buffering capacity is the amount of acid or base a buffer can accept without the pH changing appreciably. The greater the amounts of the conjugate acid-base pair, the more resistant they are to change in pH.

If we solve the acid-dissociation-constant expression for $[H+]$ we get:

assuming that the amount of added acid or base is less than 5% of the conjugate acid / base molarity.

We can use this to determine the pH of a buffer:

We first take the negative log of both sides:

We know -log [$H+$] = pH and -log $K$_a = $pK$_a.

In general:

This is known as the Henderson-Hasselbalch equation.

Additions of Acids or Bases to Buffers

EXAMPLE

STEP 1: Stoichiometry calculation:

The $OH-$ will react completely with the weak acid $HC$₂H₃O₂:

$HC$₂H₃O₂ (aq) + OH^- (aq) H₂O (l) + C₂H₃O₂^- (aq)

STEP 2: Equilibrium calculation:

The solution contains the weak acid and its conjugate base. We shall therefore use their equilibrium equation, and create an I.C.E. table :

$HC$₂H₃O₂ (aq) H⁺ (aq) + C₂H₃O₂^- (aq)

Applications of Buffer Calculations

In many systems, such as biological applications, there is extreme sensitivity to minute pH changes. To study these systems, the pH must be controlled by a buffer that is effective within given limits. How does one determine what the buffer concentration is?

EXAMPLE

What must the minimum concentration of $HC$₂H₃O₃ be in a one litre buffer solution of $HC$₂H₃O₃-C₂H₃O₃^- (pH = 4.74) if the pH changes by less than 0.1 if 0.050 moles of HCl are added?

STEP 1: Stoichiometry calculation:

The amount of HCl added will react completely with the conjugate base, $C$₂H₃O₃^-:

$C$₂H₃O₃^- + H⁺ HC₂H₃O₃

The pH of the buffered solution, 4.74, matches the $pK$_a of acetic acid, so from the Henderson-Hasselbach equation, we know that there are originally equal concentrations of acid and conjugate base, which we denote as x:

For a complete derivation

Because there is one litre of solution, [H₂H₃O₃] = (x + 0.050)M and [C₂H₃O₃^-] = (x - 0.050)M.

STEP 2: Calculate the equilibrium concentration that will produce the desired pH:

Having added acid, the pH will decrease. However, the tolerance given is 0.1, so the lowest pH that the final solution can have is 4.64.

The hydronium concentration is thus:

STEP 3: Equilibrium calculation:

I.C.E. table:

$HC$₂H₃O₃ H⁺ + C₂H₃O₃^-

Thus, the molarity of both [HC₂H₃O₂] and [C₂H₃O₂^-] must be equal to or greater than 0.417M to produce the required effectiveness.