pH and Human Buffering Systems

Introduction to pH and Related Definitions

• $pK_a$: The negative base-10 logarithm of the acid dissociation constant (Ka) of a solution.
  • Formula: $- ext{log}<em>{10}K</em>a$
  • Significance: A lower $pK_a$ indicates a stronger acid.
• Isoelectric point ($pI$): The pH at which the net charge of a molecule (e.g., a protein) is zero, meaning it is neutral.
• $pH$: The negative base-10 logarithm of the concentration of hydrogen ions ($H^+$) in a solution.
  • Formula: $- ext{log}_{10}[H^+]$
  • Significance: A lower pH indicates a more acidic solution, meaning a higher concentration of $H^+$ions.

Equations for pH and Water Dissociation

• The fundamental equation for pH is: $pH = - ext{log}_{10}[H^+]$
• The ionic product of water ($K<em>w$) at $25^ ext{o}C$ is given by: $K</em>w = [H^+][OH^-] = 10^{-14} M^2$
  • This constant is related to the equilibrium constant $K<em>{eq}$, specifically $K</em>w = 55.5 K_{eq}$.
• The relationship between pH, pOH, and $pK<em>w$ (negative logarithm of $K</em>w$) is: $pK_w = pH + pOH = 14$

The pH Scale and Common Fluid pH Values

• The pH scale demonstrates a reciprocal relationship between $H^+$ and $OH^-$ concentrations.
• Hydrogen ion and hydroxyl ion concentrations are typically given in moles per liter at $25^ ext{o}C$.
• Examples of pH values for common fluids:
  • Battery acid: $0.35$
  • Gastric juice: $1.2-3.0$
  • Lemon juice: $2.3$
  • Soft drinks: $2.8$
  • Vinegar: $2.9$
  • Grapefruit juice: $3.2$
  • Orange juice: $4.3$
  • Beer: $4.5$
  • Boric acid: $5.0$
  • Urine: $5-8$
  • Muscle intracellular fluid: $6.1$
  • Saliva: $6.6$
  • Liver intracellular fluid: $6.9$
  • Blood plasma: $7.4$
  • Seawater: $7.5-8.4$
  • Pancreatic fluid: $7.8-8.0$
  • Baking soda: $8.4$
  • Milk of magnesia: $10.3$
  • Household ammonia: $11.4$
  • Bleach: $12.6$
  • Household lye: $13.6$
• Example: Battery acid's acidic component is Sulfuric Acid ($H<em>2SO</em>4$), also known as 'Oil of Vitriol'. The term 'vitriol' comes from the Latin word vitriolum, meaning "glassy," because the crystals of various metallic sulfates resemble pieces of colored glass.

The Henderson-Hasselbalch Equation

• This equation describes the dissociation of a weak acid in the presence of its conjugate base.
• For the ionization of a weak acid, HA, with an acid dissociation constant, $K_a$:
  $HA <br /> ightleftharpoons H^+ + A^-$
• The acid dissociation constant ($K<em>a$) is defined as: Ka = rac{[H^+][A^-]}{[HA]}
• Rearranging this expression to solve for $[H^+]$: [H^+] = rac{K_a[HA]}{[A^-]}
• Taking the base-10 logarithm of both sides gives: ext{log}{10}[H^+] = ext{log}{10}Ka + ext{log}{10}rac{[HA]}{[A^-]}
• By changing the signs and defining $pK<em>a = - ext{log}</em>{10}K<em>a$, the equation becomes: pH = pKa - ext{log}_{10}rac{[HA]}{[A^-]}
• This is typically written as the Henderson-Hasselbalch equation:
  pH = pKa + ext{log}{10}rac{[A^-]}{[HA]}

Acid Dissociation Constants ($K<em>a$) and $pK</em>a$ Values

• A table of $K<em>a$ (M) and $pK</em>a$ values for common weak electrolytes at $25^ ext{o}C$ includes:
  • Formic acid ($HCOOH$): $K<em>a 1.78 imes 10^{-4}$, $pK</em>a 3.75$
  • Acetic acid ($CH<em>3COOH$): $K</em>a 1.74 imes 10^{-5}$, $pK_a 4.76$
  • Propionic acid ($CH<em>3CH</em>2COOH$): $K<em>a 1.35 imes 10^{-5}$, $pK</em>a 4.87$
  • Lactic acid ($CH<em>3CHOHCOOH$): $K</em>a 1.38 imes 10^{-4}$, $pK_a 3.86$
  • Succinic acid ($HOOCCH<em>2CH</em>2COOH$):
    • $pK<em>{a1}$ ($K</em>a 6.16 imes 10^{-5}$): $4.21$
    • $pK<em>{a2}$ ($K</em>a 2.34 imes 10^{-6}$): $5.63$
  • Phosphoric acid ($H<em>3PO</em>4$):
    • $pK<em>{a1}$ ($K</em>a 7.08 imes 10^{-3}$): $2.15$
    • $pK<em>{a2}$ ($K</em>a 6.31 imes 10^{-8}$): $7.20$
    • $pK<em>{a3}$ ($K</em>a 3.98 imes 10^{-13}$): $12.40$
  • Imidazole ($C<em>3N</em>2H<em>5^+$): $K</em>a 1.02 imes 10^{-7}$, $pK_a 6.99$
  • Histidine-imidazole group ($C<em>6O</em>2N<em>3H</em>{11}^+$):
    • $pK<em>R$ refers to the imidazole ionization: $K</em>a 9.12 imes 10^{-7}$, $pK_R 6.04$
  • Carbonic acid ($H<em>2CO</em>3$):
    • $pK<em>{a1}$ ($K</em>a 1.70 imes 10^{-4}$): $3.77$
  • Bicarbonate ($HCO_3^-$):
    • $pK<em>{a2}$ ($K</em>a 5.75 imes 10^{-11}$): $10.24$
  • Tris-hydroxymethyl aminomethane (($HOCH<em>2)</em>3CNH<em>3^+$): $K</em>a 8.32 imes 10^{-9}$, $pK_a 8.07$
  • Ammonium ($NH<em>4^+$): $K</em>a 5.62 imes 10^{-10}$, $pK_a 9.25$
  • Methylammonium ($CH<em>3NH</em>3^+$): $K<em>a 2.46 imes 10^{-11}$, $pK</em>a 10.62$
• Note on notation: The pK values listed as $pK<em>1, pK</em>2$, or $pK<em>3$ are, in actuality, $pK</em>a$ values for respective dissociations.

What are Buffers?

• Definition: Buffers are solutions that resist significant changes in their pH upon the addition of acid or base.
• Composition: A buffer system typically consists of a weak acid and its conjugate base.
• Mechanism: In a buffered system:
  • The addition of $H^+$ has little effect because it is absorbed by the conjugate base ($A^-$-).
  • The addition of $OH^-$ has little effect because it is absorbed by the weak acid ($HA$).

Major Human Buffering Systems

The Phosphate Buffer System

• This is identified as a major intracellular buffering system.
• The titration curve for phosphoric acid illustrates its buffering capacities across different pH ranges, corresponding to its multiple $pK_a$ values.
• Calculation fragments related to the phosphate buffer system were shown, including:
  • 0.2 = ext{log}_{10} rac{[HPO_4^{2-}]}{[H_2PO_4^-]}
  • 10.2 = rac{[HPO_4^{2-}]}{[H_2PO_4^-]}, presented alongside an implied calculation segment involving $20-x$ and $x = 1.58$.

Histidine's Role in Buffering

• Histidine plays a minor role in intracellular buffering.
• This is due to the low concentration of free histidine within cells.
• Additionally, its imidazole $pK_a$ (which is approximately $6.04$ for the histidine-imidazole group) is more than 1 pH unit removed from the prevailing intracellular pH (which is typically around $7.2$).

"Good" Buffers for Physiological Use

• "Good" buffers are those that are effective within physiological pH ranges.
• Example: HEPES (4-(2-hydroxy)-1-piperazine ethane sulfonic acid).
  • $pK_a$ of its sulfonic acid group is approximately $3$.
  • $pK_a$ of its piperazine-$ext{N}^+ ext{H}$ group is $7.55$ at $20^ ext{o}C$, making it useful in biological research as a buffer near neutral pH.

The Bicarbonate Buffer System

• The bicarbonate buffer system of blood plasma is a crucial physiological buffering system.
• Further details on this system are provided in a required reading available in course materials.