pH , Buffering

• Clinical and Biological Significance in Dentistry:

  • Tooth Structure Preservation: Acidic environments lead to the dissolution of hydroxyapatite, causing tooth erosion and caries.

  • Anaesthetic Efficacy: Local anaesthetics depend on tissue $pH$ to remain in un-ionised forms capable of penetrating nerve membranes.

  • Enzymatic and Protein Regulation: Catalytic efficiency and structural stability of enzymes and proteins across the body are strictly regulated by $pH$.

  • Oral Biology and Material Science: Understanding molecular and ionic behavior provides a foundational framework for oral physiology and dental materials (e.g., restorative fillings).

Fundamental Concepts of pH and Free Hydrogen Ions

• Definition of pH:

  • $pH$ quantifies the concentration of free hydrogen ions ($[H^+]$) in an aqueous solution, defining its relative acidity or alkalinity.

  • Etymologically, "$pH$" stands for "potential of hydrogen" or "exponent (power) of hydrogen ion concentration."

  • Mathematical formulation:         $10^{-pH} = [H^+]$         where concentration is expressed in moles per liter ($M$ or $mol\,dm^{-3}$).

• Free vs. Bound Hydrogen Ions:

  • Acidity is determined exclusively by free hydrogen ions ($[H^+]$) present in solution.

  • Protons bound to anions or weak bases (such as proteins, chemical buffers, or un-dissociated water molecules) do not contribute directly to measured $pH$.

• Water Content across Human Life Stages:

  • Infant: Approximately $75\%$

  • Young Adult Male: Approximately $60\%$

  • Young Adult Female: Approximately $50\%$

  • Older Person: Approximately $45\%$

• Ionisation of Water:

  • Pure water has a molar concentration of $55.6\,M$ ($55.6\,mol\,dm^{-3}$).

  • Water molecules undergo auto-ionisation to a minimal degree:         $H_2O \rightleftharpoons H^+ + OH^-$

  • At exact neutrality ($pH = 7$), the concentrations of hydrogen and hydroxide ions are equal:         $[H^+] = [OH^-] = 10^{-7}\,M$

  • Ionic Product of Water ($K_w$): At all $pH$ values in aqueous solution, the product of $[H^+]$ and $[OH^-]$ remains constant:         $K_w = [H^+] \times [OH^-] = 10^{-14}\,M^2$

  • Example Calculation: If $[H^+] = 10^{-4}\,M$, then $[OH^-] = 10^{-10}\,M$.

• Logarithmic pH Scale and Calculations:

  • $pH$ formula:         $pH = -\log_{10}([H^+])$

  • A shift of $1$ $pH$ unit corresponds to a tenfold ($10\times$) change in free hydrogen ion concentration.

  • The logarithm used in $pH$ calculations is base-10 ($\log_{10}$), not the natural logarithm (base-$e$).

  • Sample Calculation for Blood $pH$: At blood $pH = 7.4$:         $10^{-7.4}\,M = 3.98 \times 10^{-8}\,M$         This corresponds to an extremely low proton concentration of less than one ten-millionth of a mole per liter.

Physiological Spectrum of pH and Acid Sources

• Blood pH Homeostasis and Physiological Limits:

  • Blood maintains intimate contact with nearly every cell in the body; therefore, precise systemic $pH$ regulation is essential.

  • Normal Blood pH Range: Strictly regulated between $7.35$ and $7.45$ (representing a total allowable variance of approximately $\pm 25\%$

  • Absolute Viable Physiological Limits: $pH = 6.8$ to $pH = 7.8$

  • Acidosis (Acidaemia): Blood $pH < 7.35$

  • Alkalosis (Alkalaemia): Blood $pH > 7.45$

  • Uncompensated severe acidosis or alkalosis can result in mortality.

• Origins of Acidic Species in the Body:

  • Exogenous Sources: Ingestion of acidic foods and beverages (note: culinary spiciness is distinct from acidity).

  • Endogenous Sources (Primary Origin):

    • Metabolic breakdown and oxidation of dietary and structural proteins.

    • Oxidation of metabolic fats and carbohydrates.

    • Dissolution of metabolic carbon dioxide ($CO_2$) in systemic blood circulation.

  • Etymological Note: "Oxy" originates from the Greek oxys meaning "acid." The German word for oxygen is Sauerstoff ("sour substance"). Fermented foods produce acids that define flavor profiles.

• Spectrum of Common Substance pH Values:

*   $pH = 1.0$: $0.1\,M$ Sulfuric acid ($H_2SO_4$) or any strong acid
*   $pH = 2.0$: Gastric juice, lemon juice
*   $pH = 2.5$: Coca-Cola and Pepsi
*   $pH = 3.0$: Grapefruit juice
*   $pH = 3.5$: Sauerkraut
*   $pH = 4.2$: Tomato juice
*   $pH = 5.0$: Black coffee
*   $pH = 5.0 - 8.0$: Urine (wide functional range strictly managed by renal exretion)
*   $pH = 6.5$: Human saliva, milk
*   $pH = 7.0$: Pure distilled water ($[H^+] = [OH^-] = 10^{-7}\,M$)
*   $pH = 7.5 - 8.4$: Seawater, toothpaste
*   $pH = 8.0$: Egg white
*   $pH = 9.0$: Baking soda (Sodium bicarbonate)
*   $pH = 10.0$: Milk of magnesia
*   $pH = 11.0$: Ammonia solution
*   $pH = 12.0$: Soapy water
*   $pH = 11.0 - 13.0$: Household bleach
*   $pH = 14.0$: Drain cleaner, oven cleaner

Mechanisms of Acid-Base Regulation and Chemical Buffering

• Systemic Regulators of Acid-Base Balance:

  • The Lungs: Respiratory control of blood $pH$ via rate-controlled elimination of gaseous carbon dioxide ($CO_2$).

  • The Kidneys: Renal regulation via variable reabsorption and excretion of hydrogen ions ($H^+$) and bicarbonate ions ($HCO_3^-$).

  • Chemical Buffers: Circulating aqueous systems in blood, interstitial fluid, and intracellular fluid that act instantaneously.

• Functional Definition of Chemical Buffers:

  • Buffers are aqueous solutions containing a weak acid and its conjugate base that resist drastic or rapid fluctuations in $pH$.

  • Response to Increasing pH (Addition of Base/Removal of Protons): The buffer releases free $H^+$ ions (acting as an acid) to neutralize added hydroxide ($OH^-$) ions.

  • Response to Decreasing pH (Addition of Acid): The buffer binds free $H^+$ ions (acting as a base) to prevent excess proton accumulation.

• Definitions of Acids and Bases:

  • Brønsted-Lowry Acid: A chemical species that donates protons ($H^+$).

  • Brønsted-Lowry Base: A chemical species that accepts protons ($H^+$).

  • Strong Acids: Dissociate completely in aqueous solution:         $HCl \rightarrow H^+ + Cl^-$         $H_2SO_4 \rightarrow 2H^+ + SO_4^{2-}$

  • Weak Acids: Dissociate incompletely in aqueous solution, establishing a dynamic equilibrium:         $H_2CO_3 \rightleftharpoons H^+ + HCO_3^-$

  • Strong Bases: Bind $H^+$ ions with high affinity and dissociate completely in water.

  • Weak Bases: Bind $H^+$ ions reversibly with moderate affinity.

Acid-Base Titrations, pKa, and the Henderson-Hasselbalch Equation

• Titration Principles:

  • Titration involves the step-by-step addition of a standardized base (alkali) or acid to a solution to characterize its dissociation profile across a range of concentration increments.

• Titration Curve of Ethanoic Acid (Acetic Acid, $CH_3COOH$):

*   *Experimental Setup:* Titration of $50\,ml$ of $0.1\,M$ ethanoic acid with $0.1\,M$ Sodium Hydroxide ($NaOH$).
*   **Midpoint:** Occurs where $pH = pKa = 4.75$. At this precise point, exactly half of the ethanoic acid is dissociated, yielding equal concentrations of acid and conjugate base:

        $[CH_3COOH] = [CH_3COO^-] = 0.05\,M$ * Equivalence Point: Occurs when an equal molar quantity of base has been added ($50\,ml$ of $NaOH$), completely neutralizing the starting acid to form $0.1\,M$ conjugate base ($CH_3COO^-$). * The plateau region (shallow slope) surrounding the midpoint defines the region of maximum buffering efficiency.

• Titration Curve of Phosphoric Acid ($H_3PO_4$) — Polyprotic Acid:

*   *Experimental Setup:* Titration of $50\,ml$ of $0.1\,M$ Phosphoric Acid ($H_3PO_4$) with $0.1\,M$ Potassium Hydroxide ($KOH$).
*   Phosphoric acid possesses three ionisable protons, yielding three distinct midpoints and equivalence points:
    1.  **First Dissociation Step:** $H_3PO_4 \rightleftharpoons H_2PO_4^- + H^+$
        *   First Midpoint ($pKa_1 = 2.12$): $[H_3PO_4] = [H_2PO_4^-]$
        *   First Equivalence Point: Complete conversion to $H_2PO_4^-$
    2.  **Second Dissociation Step:** $H_2PO_4^- \rightleftharpoons HPO_4^{2-} + H^+$
        *   Second Midpoint ($pKa_2 = 7.21$): $[H_2PO_4^-] = [HPO_4^{2-}]$
        *   Second Equivalence Point: Complete conversion to $HPO_4^{2-}$
    3.  **Third Dissociation Step:** $HPO_4^{2-} \rightleftharpoons PO_4^{3-} + H^+$
        *   Third Midpoint ($pKa_3 = 12.67$): $[HPO_4^{2-}] = [PO_4^{3-}]$
        *   Third Equivalence Point: Complete conversion to $PO_4^{3-}$

• Titration Terminology Definitions:

  • Midpoint: The specific point on a titration curve where $pH = pKa$, representing $50\%$ dissociation of the acid or functional acidic group.

  • Equivalence Point: The point where an acid group is completely neutralized following the addition of a stoichiometrically equivalent quantity of base.

• Mathematical Derivation and Definition of pKa:

  • For any weak acid dissociation equilibrium:         $BH \rightleftharpoons H^+ + B^-$

  • The Acid Dissociation Constant ($K_a$) is defined as:         $K_a = \frac{[H^+][B^-]}{[BH]}$

  • Taking the negative logarithm of $K_a$ yields $pKa$:         $pKa = -\log_{10}(K_a)$

  • When $pH = pKa$, then $[H^+] = K_a$. Substituting this into the $K_a$ equation:         $K_a = \frac{K_a [B^-]}{[BH]} \implies \frac{[B^-]}{[BH]} = 1 \implies [B^-] = [BH]$

  • Key Relationship: The lower the $pKa$ value, the stronger the acid. $B^-$ represents the conjugate base of acid $BH$.

• The Henderson-Hasselbalch Equation:

*   **Derivation from $K_a$:**

        $K_a = \frac{[H^+][B^-]}{[BH]} \implies [H^+] = K_a \cdot \frac{[BH]}{[B^-]}$ * Taking negative logarithms of both sides:         $-\log_{10}([H^+]) = -\log_{10}(K_a) - \log_{10}\left(\frac{[BH]}{[B^-]}\right)$         $pH = pKa + \log_{10}\left(\frac{[B^-]}{[BH]}\right)$ * General Expression:         $pH = pKa + \log_{10}\left(\frac{[\text{conjugate base}]}{[\text{acid}]}\right)$

• Relationship Between pKa and Optimal Buffering Capacity:

  • A buffer solution consists of a mixture of a weak acid and its conjugate base.

  • Buffering efficiency reaches its maximum when $pH = pKa$, because equal concentrations of weak acid and conjugate base are available to neutralize added alkalis or acids, respectively.

  • The $pKa$ value indicates the exact $pH$ at which a buffering system offers its greatest buffering capacity.

Clinical and Physiological Buffer Systems

• Diagnostic Application of Henderson-Hasselbalch in Clinical Acidosis:

  • The equation $pH = pKa + \log_{10}\left(\frac{[HCO_3^-]}{[H_2CO_3]}\right)$ indicates that acidosis (low blood $pH$) can result from either a decrease in conjugate base ($[HCO_3^-]$) or an increase in acid ($[H_2CO_3]$).

  • The Carbonic Acid / Bicarbonate pair ($H_2CO_3 / HCO_3^-$) is the primary buffer system in extracellular fluid.

  • Metabolic Acidosis: Caused by low levels of $HCO_3^-$, often associated with uncontrolled diabetes mellitus due to ketone body production from lipid oxidation instead of carbohydrate metabolism.

  • Respiratory Acidosis: Caused by elevated levels of $H_2CO_3$, resulting from respiratory dysfunction and impaired $CO_2$ clearance (monitored via arterial $CO_2$ partial pressure, $PCO_2$).

• Primary Physiological Buffers in Blood, Saliva, and Fluids:

  1. Carbonic Acid System:         $H_2CO_3 \rightleftharpoons HCO_3^- + H^+ \quad (pKa = 6.1)$

  2. Phosphoric Acid System:         $H_2PO_4^- \rightleftharpoons HPO_4^{2-} + H^+ \quad (pKa = 6.8)$

  3. Protein Buffer Systems: Proteins act as buffers through proton-donating and proton-accepting amino acid side chains.

Amino Acid Buffering, Protein Structure, and Haemoglobin

• Titration and Buffering Limits of Free Amino Acids (e.g., Glycine):

  • Glycine contains two ionisable groups:

    • $\alpha$-Carboxyl group ($-COOH$): Stronger acid, $pKa_1 = 2.34$

    • $\alpha$-Amino group ($-NH_3^+$): Weaker acid, $pKa_2 = 9.66$

  • Zwitterion State: At physiological $pH$, glycine exists as a dipolar zwitterion ($H_3N^+-CH_2-COO^-$) and provides no buffering capacity.

  • Free amino acids are ineffective physiological buffers because their $pKa$ values ($2.34$ and $9.66$) fall far outside the normal blood $pH$ range ($7.35 - 7.45$).

  • In intact proteins, backbone $\alpha$-amino and $\alpha$-carboxyl groups are covalently linked in peptide bonds, rendering them unavailable for proton exchange.

• Role of Amino Acid Side Chains (R-Groups) in Protein Buffering:

*   **Non-Polar R-Groups:** Glycine, Alanine, Valine, Leucine, Isoleucine, Methionine, Phenylalanine, Tryptophan, Proline (non-ionisable).
*   **Polar Uncharged R-Groups:** Serine, Threonine, Cysteine, Tyrosine, Asparagine, Glutamine (non-dissociating within normal physiological limits).
*   **Acidic R-Groups:** Aspartic acid ($pKa \approx 3.9$) and Glutamic acid ($pKa \approx 4.3$) have $pKa$ values too low for effective physiological buffering.
*   **Basic R-Groups:** Lysine ($pKa \approx 10.5$) and Arginine ($pKa \approx 12.5$) have $pKa$ values too high for physiological buffering.
*   **Histidine R-Group:** Free histidine possesses an imidazole ring with a $pKa = 6.0$, placing it closest to physiological $pH$ among all amino acids.

• Haemoglobin as the Primary Erythrocyte Buffer:

*   Haemoglobin contains abundant histidine residues.
*   The local chemical environment within the tertiary and quaternary structure of haemoglobin shifts the effective $pKa$ of its histidine residues upward compared to free histidine:
    *   **Free Histidine:** $pKa = 6.0$
    *   **Oxyhaemoglobin:** $pKa = 6.8$
    *   **Deoxyhaemoglobin:** $pKa = 7.8$
*   *Functional Advantage:* Deoxyhaemoglobin is more basic ($pKa = 7.8$) than oxyhaemoglobin. Upon releasing oxygen in metabolizing tissues, deoxyhaemoglobin binds free $H^+$ protons generated by metabolic carbon dioxide production, helping stabilize blood $pH$

Dental Applications: Critical pH, Stephan's Curve, and Local Anaesthesia

• Critical pH in Dental Enamel Demineralisation:

  • Definition: The threshold $pH$ below which dental enamel undergoes net mineral dissolution (decalcification).

  • Standard Value: Approximately $pH = 5.5$

  • Variability: The critical $pH$ is not fixed; it varies inversely with the concentration of dissolved calcium ($Ca^{2+}$) and phosphate ($PO_4^{3-}$) ions in saliva.

  • Salivary Ion Balance:

    • Higher salivary $Ca^{2+}$ and $PO_4^{3-}$ concentrations lower the critical $pH$ threshold, reducing enamel dissolution.

    • Conversely, high salivary calcium and phosphate levels increase the rate of dental calculus (tartar) deposition.

• Stephan's Curve:

*   **Description:** A graph plotting plaque/salivary $pH$ over time following exposure to fermentable carbohydrates (e.g., a sucrose rinse).
*   **Profile:** Following a carbohydrate challenge, oral $pH$ drops rapidly below the critical threshold ($5.5$) within $5\,min$, exposing enamel to demineralisation, before gradually returning to baseline over $20\,min$ via salivary buffering.
*   **Clinical Utility:** Used to evaluate the relative cariogenicity (cavity-causing potential) of different foodstuffs.

• Local Anaesthetic Action and Tissue pH:

  • Local anaesthetics (e.g., Lignocaine) are weak bases administered in aqueous solution, establishing an equilibrium between ionised ($BH^+$) and un-ionised ($B$) forms:         $BH^+ \rightleftharpoons B + H^+$

  • Mechanism of Entry: Only the un-ionised form ($B$) is lipid-soluble and capable of crossing the lipophilic nerve cell membrane. Once inside the axoplasm, the re-protonated ionised form ($BH^+$) binds voltage-gated sodium channels to block nerve conduction.

  • Lignocaine pKa: $7.9$

  • Clinical Co-injection of Bicarbonate:

    • Co-injecting sodium bicarbonate ($HCO_3^-$) with Lignocaine increases the local extracellular $pH$.

    • According to the Henderson-Hasselbalch equation, raising local $pH$ shifts the equilibrium toward the un-ionised form ($B$).

    • This increases the proportion of membrane-permeable anaesthetic molecules, accelerating the onset of anaesthesia and decreasing injection-related discomfort.