Buffer Solution Notes

Buffer Solutions

Objectives

• Define "Buffer solution."
• Understand the chemistry of a "buffer solution."
• Illustrate how to make a buffer solution.
• Illustrate applications of a buffer.
• Illustrate how to calculate pH of a buffer.

What is a Buffer Solution?

• A buffer solution is an aqueous solution consisting of a mixture of a weak acid and its conjugate base or a weak base and its conjugate acid.
• It has the property that the pH of the solution changes very little when a small amount of acid or base is added to it.
• Buffer solutions are used as a means of keeping pH at a nearly constant value in a wide variety of chemical applications.

The Chemistry of a Buffer Solution

• In a buffer solution, there is an equilibrium between a weak acid, HA, and its conjugate base, A-.
  $HA \leftrightarrow H^+ + A^−$
• When $H^+$ are added to the solution, the equilibrium shifts to the left, according to Le Chatelier's principle.
• When $OH^−$ are added, the equilibrium shifts to the right as $H^+$ are removed in the reaction.
• Thus, some of the added reagent is consumed in shifting the equilibrium, and the pH changes by less than it would if the solution were not buffered.

The Acid Dissociation Constant ($K_a$)

• The acid dissociation constant ($K<em>a$) for the weak acid, HA, is defined as: $K</em>a = \frac{[H^+][A^-]}{[HA]}$
• Rearranging to find $[H^+]$:
  $[H^+] = K_a \times \frac{[HA]}{[A^-]}$
• Since $pH = -\log[H^+]$, taking the negative logarithm of both sides:
  $-log [H^+] = -log K_a - log \frac{[HA]}{[A^-]}$

Henderson-Hasselbalch Equation

• Which is the same as:
  $-log [H^+] = -log K_a + log \frac{[A^-]}{[HA]}$
• OR
  $pH = pK_a + log \frac{[A^-]}{[HA]}$
• OR
  $pH = pK_a + log \frac{[conjugate base or salt]}{[acid]}$
• This is known as the Henderson-Hasselbalch equation.

Creating a Buffer Solution at a Specific pH

• Use the Henderson-Hasselbalch equation:
  $pH = pK_a + log \frac{[A^-]}{[HA]}$

Calculating the pH of a Buffer

• Example: Calculate the pH of a 0.20M $CH<em>3COOH$ and 0.30M $CH</em>3COONa$ solution, given $K_a = 1.8 \times 10^{-5}$.
• Answer: 4.9
• What would be the pH of a 0.20M $CH_3COOH$ solution?
• $pH = 2.72$

Factors Determining Buffer pH

• The $pK_a$ of the weak acid you are using.
• The RATIO of the concentration of the acid and the salt that you add to the solution.
• The pH of the buffer does not depend on the actual concentration of the buffer, but on the ratio of the two parts.
• The pH you want your buffer to be depends on these two things.

Buffer Capacity

• Buffer capacity is a measure of the efficiency of a buffer in resisting changes in pH.
• It indicates the amount of acid or base that can be added before a buffer loses its ability to resist the change in pH.
• Buffer capacity depends on:
  • How close the pH of the buffer is to the $pK_a$ (should be within 1-2 pH units).
  • The total concentration of the buffer.

Concentration Effect on Buffer Capacity

• A buffer consisting of 0.001M $CH<em>3COOH$ and 0.001M $CH</em>3COONa$ will have the same pH as a buffer made with 0.1M $CH<em>3COOH$ and 0.1M $CH</em>3COONa$ (ratio is 1:1, $pH = pK_a = 4.76$).
• However, the 0.1M buffer will have a much larger buffer capacity and will better resist changes in pH upon the addition of a strong acid or base.

Applications of Buffers

• Resistance to changes in pH makes buffer solutions very useful for chemical manufacturing and many biochemical processes.
• The ideal buffer for a particular pH has a $pK_a$ equal to that pH, since such a solution has maximum buffer capacity.

Buffers in Biological Systems

• Many enzymes work only under very precise conditions; if the pH strays too far out of the margin, the enzymes slow or stop working and can denature, thus permanently disabling its catalytic activity.
• A buffer of carbonic acid ($H<em>2CO</em>3$) and bicarbonate ($HCO_3^−$) is present in blood plasma to maintain a pH between 7.35 and 7.45.
• Buffer solutions are necessary to keep the correct pH for enzymes in many organisms to work.

Industrial and Research Applications of Buffers

• Industrially, buffer solutions are used in fermentation processes and in setting the correct conditions for dyes used in coloring fabrics.
• They are also used in chemical analysis and calibration of pH meters.
• The majority of biological samples used in research are made in buffers, especially PBS (phosphate buffer saline) at pH 7.4.

Demonstration of Buffer Action

• Calculate the pH of 100ml buffer solution containing 0.2 mol $K<em>2HPO</em>4$ and 0.1 mol $KH<em>2PO</em>4$, given $K_a = 6.2 \times 10^{-8}$.
• What is the pH after adding to the entire buffer solution:
  • 20.0 ml of 0.035M NaOH?
  • 20.0 ml of 0.035M HCl?
• Answers: 7.51, 7.51, 7.50