UNIT: 8.7 Relationship Between pH and pKa

Relationship Between pH and pKa

Introduction

  • This subunit explores the relationship between the pH of an environment and the pKa of a system.
  • The key tool for understanding this relationship is the Henderson-Hasselbalch equation.

Henderson-Hasselbalch Equation

  • The Henderson-Hasselbalch equation is provided on formula sheets, so memorization is not required.
  • It is applicable specifically to buffer systems, which consist of:
    • A weak acid and its conjugate base, or
    • A weak base and its conjugate acid.
  • The equation allows you to determine the ratio of the concentrations of the two parts of your buffer system (conjugate base to weak acid, or weak base to conjugate acid) given the pH of the environment and the pKa of the buffer system.

Using pH and pKa to Determine Relative Concentrations

  • The Henderson-Hasselbalch equation is: pH = pKa + log\frac{[A^-]}{[HA]}, where A^- is the conjugate base and HA is the weak acid.
  • If pH < pKa, the acid form (HA) has a higher concentration.
    • This avoids the need to perform the full calculation; the denominator (acid form) of the fraction will be larger.
  • If pH > pKa, the conjugate base form has a higher concentration.
    • In this case, the numerator (conjugate base form) of the fraction will be larger.

Weak Base and Conjugate Acid Buffer Systems

  • The same principles apply to buffer systems made of a weak base and its conjugate acid, but the wording changes slightly.
  • If pH < pKa, then the conjugate acid form is in higher concentration.
  • If pH > pKa, then the weak base form is in higher concentration.

Indicators

Definition

  • Indicators are used to visually signal the equivalence point in a titration, especially since most acids and bases are colorless in solution.
  • The endpoint is when the indicator changes color.

Nature of Indicators

  • Indicators are weak acids themselves.
  • They possess the unique property of having different colors in their protonated (acid) and deprotonated (conjugate base) forms.
  • The general equilibrium reaction for an indicator (In) is: HIn(red) \rightleftharpoons H^+ + In^-(yellow)
  • The pH of the environment controls the equilibrium and thus the observed color.

Selecting Indicators

  • Not every indicator is suitable for every titration.
  • Indicators have a "useful range", which is a pH range where they are most effective at signaling the equivalence point.

Determining the Useful Range

  • Each indicator has its own Ka value, and thus a pKa value.
  • The useful range of an indicator is its pKa ± 1.
  • For example, if an indicator has pKa = 4.0, its useful range is 3.0 to 5.0.

Choosing the Best Indicator

  • The ideal indicator is one whose useful range includes or is closest to the pH at the equivalence point of the titration.

Example of Indicators

  • Phenolphthalein has a useful range of approximately 8 to 10 and changes from colorless to pink.
    • It is suitable for titrations where the pH at equivalence falls within this range.
  • Thymol blue is a diprotic acid, meaning it has two hydrogens to donate and, thus, two different useful ranges.

Example Problem: Titration of Hydrochloric Acid (HCl) with Sodium Hydroxide (NaOH)

Problem Setup

  • The problem involves a titration between HCl and NaOH, requiring multiple analyses based on a given graph.

Part A: Identifying the Analyte

  • The analyte is the solution initially in the beaker.
  • In this case, the analyte is the acid because the initial pH is 1 (acidic range).
  • Alternatively, the pH increases as titrant is added, indicating the titrant is a base and the analyte is an acid.

Part B: Identifying the Equivalence Point

  • The equivalence point is at a pH of approximately 7 on the curve.

Part C: Calculating Moles of Titrant at Equivalence Point

  • Given the volume and molarity of NaOH added at the equivalence point, the number of moles can be calculated.
  • If the volume of NaOH is 40.0 mL and the molarity is 0.100 M, then the moles of NaOH are (0.040 L) * (0.100 mol/L) = 0.00400 mol.

Part D: Selecting the Best Indicator

  • The goal is to choose the indicator whose useful range is closest to the pH at the equivalence point (pH 7).
  • Among the given options (methyl orange, methyl red, and phenolphthalein), methyl red is the best choice because its color change occurs closest to pH 7.

Part E: Sketching the Reverse Titration Curve

  • If the solutions in the beaker and burette are reversed (i.e., the acid is the titrant and the base is the analyte):
    • The pH at the equivalence point remains the same (pH 7).
    • However, the initial pH is now in the basic range and decreases as the acidic titrant is added.
    • The shape of the curve is essentially the reverse of the original curve.