Lecture 2: Water, pH, pKa, and Buffers

Acetic Acid and Acid Strength

• Acetic acid is a good acid because…

  • It can give up a proton

  • It can stabilize the resulting negative charge through resonance

    • This stabilization is crucial for its acidic properties

• Acetic acid resonance stabilization significantly contributes to its acidity

  • It does this by delocalizing the negative charge on the acetate ion.

• A stronger acid is able to stabilize its deprotonated form more effectively than a weaker acid

  • The stability of the conjugate base is a key determinant of acid strength.

• A good base readily accepts a proton

  • Results in a stable, positively charged species

  • The ability to stabilize this positive charge influences basicity

    • Stronger bases will have structural features that can delocalize the charge effectively, leading to a greater tendency to accept protons

    • This can include the presence of electronegative atoms or resonance structures that can distribute the charge across a larger area

    • Overall stability of the base is enhanced, thereby increasing its strength and its ability to interact with protons during acid-base reactions.

• The relative stability of the protonated versus deprotonated forms dictates acid/base strength

  • The more stable the deprotonated form, the stronger the acid, and vice versa.

• Resonance stabilization is particularly important in amino acids

  • It influences the properties of alpha complexes and C-termini on polypeptides, especially carboxylic acids.

Ka - Acid Dissociation Constant

• $Ka$ is a quantitative measure of acid strength, indicating the extent of acid dissociation in water.

• A generalized $Ka$ equation: $Ka = \frac{[A^-][H_3O^+]}{[HA]}$

  • $[A^-]$ is the concentration of the conjugate base at equilibrium.

  • $[H_3O^+]$ is the concentration of hydronium ions at equilibrium.

  • $[HA]$ is the concentration of the acid at equilibrium.

• A higher $Ka$ value indicates a stronger acid because it signifies a greater formation of $A^-$ and $H_3O^+$

  • Shifts the equilibrium towards the products.

pKa - Relationship to Acidity

• $pKa$ is the negative base-10 logarithm of $Ka$. It provides a convenient scale for expressing acid strength.

• $pKa = -log(Ka)$

• A lower $pKa$ value indicates a stronger acid, corresponding to a higher $Ka$ value.

• When $pH = pKa$, the concentrations of $[HA]$ and $[A^-]$ are approximately equivalent, representing the point of maximum buffering capacity.

• If a weak acid has a $pKa$ of 1.75 (three $pH$ units lower than acetic acid), it will deprotonate in an environment with 1000 times more hydronium ions, illustrating the impact of $pKa$ on ionization.

• An acid with a $pKa$ of 8 requires a high hydroxide concentration to remove a proton, indicating it is a very weak acid.

Proving $[HA] = [A^-]$ when $pH = pKa$

• If $pH = pKa$, then $[H_3O^+] = Ka$, demonstrating a direct relationship between hydronium ion concentration and the acid dissociation constant.

• If $pKa = 4.75$, then $Ka = 10^{-4.75}$, illustrating the calculation of $Ka$ from $pKa$.

• $Ka = \frac{[A^-][H_3O^+]}{[HA]} = 10^{-4.75}$

• If $[H_3O^+] = 10^{-4.75}$, then:
  

$10^{-4.75} = \frac{[A^-] \times 10^{-4.75}}{[HA]}$

• The only way for this equation to hold true is if $[A^-] = [HA]$, confirming that at $pH = pKa$, the concentrations of the acid and its conjugate base are equal.

• If $[A^-] = [HA]$, then the equilibrium is balanced, indicating optimal buffering capacity.

• More hydronium favors protonation (more $HA$), while more hydroxide favors deprotonation (more $A^-$.), illustrating Le Chatelier's principle in acid-base equilibria.

• At a $pH$ of 4.75 for acetic acid, the concentrations of acetate and acetic acid are balanced, resulting in maximum buffering effectiveness.

Buffer Systems

• A buffer system contains similar concentrations of a conjugate acid and a conjugate base, enabling it to resist changes in $pH$.

• When a strong base (hydroxide) is added, it reacts with the acid ($HA$) to form the conjugate base ($A^-$) and water, neutralizing the base before it affects the overall $pH$:
  

$HA + OH^- \rightarrow A^- + H_2O$

• Similarly, a strong acid reacts with the conjugate base to prevent it from altering the hydronium/hydroxide balance, thus maintaining a stable $pH$.

• Biological systems (cells, blood, organs) rely on buffer systems to maintain homeostasis, which is essential for their proper function.

Impact of pH on Proteins

• Proteins have various functional groups with different $pKa$ values, each influencing the protein's overall charge and behavior.

• Changes in $pH$ alter the charges on these functional groups, which can affect protein folding, stability, and interactions.

• Enzymes (protein catalysts) depend on specific functional group charges for their mechanisms, and any disruption can impair their catalytic activity.

• Disrupting $pH$ can disrupt these charges and impair enzyme function, leading to a loss of enzymatic activity or altered substrate binding.

• Acidosis and alkalosis are examples of conditions with imbalanced $pH$, leading to various symptoms ranging from mild discomfort to life-threatening complications.

Bicarbonate Buffer System in Blood

• The blood uses a carbonic acid/bicarbonate buffer system to maintain a stable $pH$ essential for physiological processes.

• $CO2$ from cellular respiration reacts with $H2O$ to form carbonic acid ($H2CO3$):
  

$CO2 + H2O \rightleftharpoons H2CO3$

• Carbonic acid dissociates into hydronium ($H3O^+$) and bicarbonate ($HCO3^-$):
  

$H2CO3 \rightleftharpoons H3O^+ + HCO3^-$

• The balance between $H2CO3$ and $HCO_3^-$ buffers external acidic or basic perturbations, ensuring that blood $pH$ remains within a narrow range.

• Increased $CO2$ shifts the equilibrium towards acidity (acidosis), while decreased $CO2$ shifts it towards alkalinity (alkalosis), impacting respiratory and metabolic functions.

• Rapid breathing (a symptom of acidosis) helps remove excess $CO_2$, partially counteracting the problem by shifting the equilibrium back towards normal $pH$.

Titration Curves

• Titration curves graphically represent the relationship between a weak acid and a strong base across different $pH$ values, illustrating the buffering capacity of the weak acid.

• Starting with a weak acid ($HA$), titrating in a strong base (e.g., $NaOH$) increases the $pH$, with the curve's shape reflecting the acid's buffering behavior.

• The strong base reacts with the acid:
  

$HA + OH^- \rightarrow A^- + H_2O$

• The buffer region is where significant quantities of both $HA$ and $A^-$ exist, resulting in minimal $pH$ change upon addition of small amounts of acid or base.

• Half Equivalence Point:

  • The point where half as much hydroxide has been added as there was uric acid to start with, indicating that half of the weak acid has been converted to its conjugate base.

  • The point at which the base is equal to one half as a: this refers to the concentration of the added base being half of the initial concentration of the weak acid.

  • 1 L of a 1 M solution contains one mole: this explains the molar quantity at a specified concentration and volume, relating to the amount of substance.

  • At the half equivalence point = A-.

  • In this process, we reacted away all the hydroxide we added, which brought us to the half equivalence point, demonstrating the stoichiometry of the reaction.

  • At the half equivalence point, $[HA] = [A^-]$, signifying equal concentrations of the weak acid and its conjugate base.

• Equivalence Point: The point where a full quantity of strong base has been added.

  • A point where we have fully deprotonated and removed the starting weak acid, leaving only the conjugate base in the solution.

Titration Curve Stages

1. Increase: Initial addition of strong base increases $pH$ rapidly, reflecting the initial consumption of hydronium ions.

2. Buffer Region: $pH$ flatlines due to buffering action, as the weak acid and its conjugate base neutralize added acid or base.

3. Half Equivalence Point: $pH = pKa$, $[HA] = [A^-]$, indicating optimal buffering capacity.

4. Exiting Buffer Region: Runs out of $HA$, causing $pH$ to increase sharply as the buffering capacity is exhausted.

5. Equivalence Point: Weak acid is fully deprotonated (only $A^-$ remains), resulting in a rapid $pH$ increase.

• During titration, the primary reaction is $HA + OH^- \rightarrow A^- + H_2O$, illustrating the neutralization of the weak acid by the strong base.

Acetic Acid Titration

• At the beginning of titration, there is 100% acetic acid ($HA$) and 0% acetate ($A^-$), as no base has been added yet.

• As $pH$ increases, acetic acid concentration decreases, and acetate concentration increases, reflecting the conversion of the acid to its conjugate base.

• At 50% acetic acid and 50% acetate, the half equivalence point is reached, where the solution has maximum buffering capacity.

Buffer Boundaries

• Buffer boundaries are approximately $pKa \pm 1$, defining the effective range over which the buffer can resist $pH$ changes.

• For acetic acid ($pKa = 4.75$), the buffer range is 3.75 to 5.75, indicating its optimal buffering range.

Henderson-Hasselbalch Equation

• Used for estimating the $pH$ of a buffer solution based on the concentrations of the weak acid and its conjugate base.

• $pH = pKa + log(\frac{[A^-]}{[HA]})$

• If $[A^-] = [HA]$, then $log(\frac{[A^-]}{[HA]}) = 0$, and $pH = pKa$, demonstrating that at equal concentrations, the $pH$ equals the $pKa$.

• If [A^-] > [HA], then the $pH$ is above the $pKa$, log is positive, indicating a more basic solution.

• If [HA] > [A^-], then the $pH$ is below the $pKa$, log is negative, indicating a more acidic solution.

Buffer Ratios and pH

• Buffer region boundaries can also be defined by the ratio of $[A^-]$ to $[HA]$, reflecting the effective buffering range.

• The effective buffer range is where the ratio of $[A^-]$ to $[HA]$ is between 1:10 and 10:1, indicating the range of useful buffering action.

• At a $pH$ one unit above the $pKa$, the ratio of $[A^-]$ to $[HA]$ is 10:1, indicating a more basic condition within the buffering range.

• At a $pH$ one unit below the $pKa$, the ratio of $[A^-]$ to $[HA]$ is 1:10, indicating a more acidic condition within the buffering range.

Polyprotic Acids

• Amino acids are polyprotic acids, capable of donating more than one proton and exhibiting multiple ionization states.

• Each deprotonation has its own $pKa$ and buffer region, resulting in multiple buffering ranges within the same molecule.

• The conjugate base of one deprotonation becomes the conjugate acid for the next, illustrating stepwise ionization.

• Phosphoric acid (H3PO4) has three deprotonations with $pKa$ values of 2.12, 7.2, and 12.3, each corresponding to a different ionization state.

• The predominant forms change as $pH$ increases: $H<em>3PO</em>4 \rightarrow H<em>2PO</em>4^- \rightarrow HPO<em>4^{2-} \rightarrow PO</em>4^{3-}$, illustrating the sequential deprotonation of phosphoric acid.