Acid and bases 2

Acid Strength and Molecular Structure

• Acidic compounds are broadly categorized into two major divisions based on their molecular composition:
      * Binary Acids: These contain hydrogen ($H$) and only one other nonmetal element ($Y$), represented by the general formula $H-Y$.
      * Oxyacids: These contain hydrogen bonded to an oxygen atom, which is in turn bonded to another element ($Y$), represented by the structural arrangement $H-O-Y$. Element $Y$ may also be bonded to additional atoms.

• Key investigative questions regarding acid strength include:
      * Why is $H_2S$ considered acidic while $CH_4$ is not?
      * Why is $HF$ classified as a weak acid while $HCl$ is a strong acid?

Binary Acids: Factors Influencing Acidity

• The acidity of a binary acid $H-Y$ is determined by the ease with which the hydrogen atom can be donated as a proton ($H^+$). This is governed by two primary factors: bond polarity and bond strength.

• Bond Polarity:
      * For a molecule $H-Y$ to be acidic, the bond must be polarized such that the hydrogen atom serves as the positive pole ($ext{H}^{\boldsymbol{ ext{\delta}}+} - ext{Y}^{\boldsymbol{ ext{\delta}}-}$).
      * Lithium Hydride ($LiH$): This is an ionic compound where the hydrogen atom carries a negative charge ($H^-$). Consequently, $LiH$ is not acidic.
      * Methane ($CH_4$): The bond between carbon and hydrogen ($C-H$) is essentially nonpolar because the electronegativities of carbon and hydrogen are very similar. Because the hydrogen is not significantly positive, $CH_4$ is not acidic.
      * Hydrogen Fluoride ($HF$): The $H-F$ bond is highly polar, with the positive charge residing on the hydrogen atom, which facilitates acidity.

• Bond Strength:
      * The strength of the $H-Y$ bond inversely relates to acid strength. A stronger bond holds the hydrogen atom more tightly, making it less likely to dissociate.
      * Hydrogen Halide Comparison: While $HF$ has the greatest bond polarity among the halides, it also has a very strong bond. This high bond strength makes $HF$ a weak acid. In contrast, $HCl$ and $HBr$ have weaker bonds and are categorized as strong acids.

Trends in Binary Acid Strength

• Left to Right across a Period: The hydrides become more acidic as the electronegativity of element $Y$ increases, causing the $H-Y$ bond to become more polar.

• Top to Bottom down a Group: The hydrides become more acidic as the size of element $Y$ increases, causing the $H-Y$ bond to become weaker.

• The combined effect of these trends results in acidity increasing as one moves right and down the periodic table for binary acids.

Oxyacids: Factors Influencing Acidity

• The acidity of oxyacids ($H-O-Y$) is influenced by the electronegativity of the central element $Y$ and the number of oxygen atoms attached to $Y$.

• The Electronegativity of Y:
      * An increase in the electronegativity of element $Y$ weakens and polarizes the $H-O$ bond. As $Y$ pulls electron density toward itself, the oxygen atom in turn pulls electron density away from the hydrogen atom.
      * Experimental Evidence: Comparing oxyacids where $Y$ is a halogen shows that higher electronegativity correlates with a higher acid ionization constant ($K_a$). For example, Chlorine ($Cl$) is more electronegative than Bromine ($Br$). Although they may have the same oxidation number ($+5$), chloric acid is stronger than bromic acid because the $O-H$ bond in chloric acid is more polar and ionizes more readily.

• The Number of Oxygen Atoms Bonded to Y:
      * Additional oxygen atoms attached to the central atom $Y$ are highly electronegative. They draw electron density away from $Y$, which subsequently draws density away from the $H-O$ bond.
      * This effect further weakens and polarizes the bond, leading to increased acidity.
      * Predictive Comparisons:
          * Sulfuric acid ($H_2SO_4$) is a stronger acid than sulfurous acid ($H_2SO_3$).
          * Nitric acid ($HNO_3$) is stronger than nitrous acid ($HNO_2$).
      * Cl Oxoacid Series: Within a group of oxoacids containing the same central atom, acid strength increases as the oxidation number of that atom increases. The capacity to draw electrons away from the $OH$ group increases with more oxygen atoms. The acid strength decreases in the following order: $HClO_4 > HClO_3 > HClO_2 > HClO$.

The Common Ion Effect

• Definition: The common ion effect occurs when two solutes are dissolved in a solution and share a common cation or anion. The presence of this common ion suppresses the ionization of a weak acid or a weak base.

• Example: Acetic Acid and Sodium Acetate:
      * When sodium acetate ($CH_3COONa$) and acetic acid ($CH_3COOH$) are in the same solution, both produce acetate ions ($CH_3COO^-$).
      * $CH_3COONa$ is a strong electrolyte and dissociates completely.
      * $CH_3COOH$ is a weak acid and ionizes only slightly.
      * According to Le Châtelier’s principle, the high concentration of $CH_3COO^-$ from the salt shifts the acetic acid equilibrium to the left: $CH_3COOH(aq) <br>ightleftharpoons H^+(aq) + CH_3COO^-(aq)$.
      * This shift suppresses the ionization of the acid, decreasing the concentration of hydrogen ions ($H^+$). Consequently, the solution is less acidic (has a higher pH) than a solution of pure acetic acid at the same concentration.

• Mathematical Application (Example Calculation):
      * Part A: Calculate pH of $0.20M$ $CH_3COOH$ ($K_a = 1.83 imes 10^{-5}$).
      * Part B: Calculate pH of a solution with $0.20M$ $CH_3COOH$ and $0.30M$ $CH_3COONa$.
      * Initial Concentrations: $[CH_3COOH] = 0.20M$, $[H^+] = 0$, $[CH_3COO^-] = 0.30M$ (from salt).
      * Change: $-x$ for acid, $+x$ for products.
      * Equilibrium Expression: $1.8 imes 10^{-5} = rac{(x)(0.30 + x)}{0.20 - x}$.
      * Assuming $x$ is small: $1.8 imes 10^{-5} imes rac{0.20}{0.30} = x$, resulting in $x = [H^+] = 1.2 imes 10^{-5}M$.
      * Final pH: $-log(1.2 imes 10^{-5}) = 4.92$.

• Weak Bases: The effect also applies to weak bases like ammonia ($NH_3$) combined with its salt ammonium chloride ($NH_4Cl$). The common ion $NH_4^+$ suppresses the ionization of $NH_3$, making the solution less basic.

Buffer Solutions: Mechanisms and Characteristics

• Definition: A buffer is a solution that resists changes in pH. It contains significant amounts of either:
      1. A weak acid and its conjugate base.
      2. A weak base and its conjugate acid.

• Functioning Mechanism (Acetic Acid/Sodium Acetate Buffer):
      * Adding Strong Base ($NaOH$): The weak acid ($HC_2H_3O_2$) neutralizes the added hydroxide ions ($OH^-$). As long as the amount of base added is less than the amount of acid available, the pH change is minimal.
      * Adding Strong Acid ($HCl$): The conjugate base ($NaC_2H_3O_2$ or $C_2H_3O_2^-$) neutralizes the added hydronium ions ($H^+$). As long as the amount of acid added is less than the amount of conjugate base available, the pH change remains small.

• Summary of Buffer Characteristics:
      * Buffers resist pH change.
      * They must contain significant quantities of the conjugate pair.
      * The weak acid component neutralizes added base.
      * The weak base component neutralizes added acid.

Quantitative Buffer Calculations

• Henderson-Hasselbalch Equation: This approach is frequently used to simplify buffer calculations.

• Example Calculations:
      * Calculate the pH of a buffer solution that is $0.100M$ in $HC_2H_3O_2$ and $0.100M$ in $NaC_2H_3O_2$.
      * Calculate the pH of a buffer solution that is $0.200M$ in $HC_2H_3O_2$ and $0.100M$ in $NaC_2H_3O_2$.
      * Benzoic Acid Example: For a solution containing $0.050M$ benzoic acid ($HC_7H_5O_2$) and $0.150M$ sodium benzoate ($NaC_7H_5O_2$) with a $K_a = 6.5 imes 10^{-5}$, the pH can be found using the Equilibrium (ICE) approach or the Henderson-Hasselbalch approach.

Calculating pH Changes in a Buffer Solution

• When an acid or base is added to a buffer, calculation of the resulting pH requires a two-step process:

    1. Stoichiometry Calculation: Calculate how the addition of the strong species changes the relative initial amounts of the weak acid and its conjugate base.
        * Added acid ($H^+$) reacts with the base ($A^-$) to produce more $HA$.
        * Example: Adding $0.025 ext{ mol}$ of $H^+$ to a $1.0 ext{ L}$ buffer of $0.100M$ $HA$ and $0.100M$ $A^-$ results in $A^-$ decreasing to $0.075M$ and $HA$ increasing to $0.125M$.

    2. Equilibrium Calculation: Calculate the pH based on the new concentrations of the acid and conjugate base using the $K_a$ expression.
        * $HA(aq) + H_2O(l) <br>ightleftharpoons H_3O^+(aq) + A^-(aq)$
        * $K_a = rac{[H_3O^+][0.075 + x]}{0.125 - x}$
        * Approximating $x$ as small: $x = [H_3O^+] = K_a imes rac{0.125}{0.075}$.

• Key Principles to Remember:
      * Adding a small amount of strong acid converts a stoichiometric amount of base to conjugate acid, causing a small decrease in pH.
      * Adding a small amount of strong base converts a stoichiometric amount of acid to conjugate base, causing a small increase in pH.