Ionic Equilibrium and Acid-Base Theories

The Ionic Product of Water and pH Scale

The ionic product of water, denoted as $K_w$, represents the product of the molar concentrations of oxonium cations ($H_3O^+$) and hydroxide anions ($OH^-$). Under standard conditions, this value is constant, though it is dependent on temperature. In pure water, the molar concentrations of these ions are equal, with both $[H_3O^+]$ and $[OH^-]$ measuring exactly $1.0 \times 10^{-7}\,mol\,dm^{-3}$.

The process known as the autoprotolysis of water is described by the chemical equation $2H_2O \rightleftharpoons H_3O^+ + OH^-$. The equilibrium constant for this acid-base reaction is significantly shifted toward the formation of water molecules. The derivation of the water constant starts with the equilibrium constant expression $K = \frac{[H_3O^+][OH^-]}{[H_2O]^2}$. By multiplying both sides by the concentration of water square, we obtain $K \times [H_2O]^2 = [H_3O^+][OH^-]$. This leads to the definition of the ionic product: $K_w = [H_3O^+][OH^-] = 1.0 \times 10^{-14}\,mol^2\,dm^{-6}$.

The acidity and basicity of substances are measured using the pH scale, which is defined as the negative logarithm of the oxonium cation concentration: $pH = -\log([H_3O^+])$. Furthermore, the relationship between pH and pOH is expressed as $pH + pOH = 14$. Solutions are categorized based on their pH values: an acidic solution has a $pH < 7$ and $[H_3O^+] > [OH^-]$, a neutral solution has a $pH = 7$ and $[H_3O^+] = [OH^-]$, and a basic (alkaline) solution has a $pH > 7$ and $[H_3O^+] < [OH^-]$.

Indicators are substances that change color at different pH values. A universal indicator typically appears red or orange in acidic solutions, yellow in neutral solutions, and green or blue in basic solutions. Specific indicators include Methyl Violet (red to yellow, pH range $2.9-4.0$), Methyl Orange (red to yellow-orange, pH range $3.1-4.4$), Litmus (red to blue, pH range $5.0-8.0$), Thymol Blue (yellow to blue, pH range $8.0-9.6$), and Phenolphthalein (colorless to red-violet, pH range $8.0-9.8$). For more precise measurements, pH-meters are used.

Acid-Base Theories

Acid-base reactions, also known as protolytic reactions, occur between acids and bases. Arrhenius theory defines acids as substances that release a hydrogen cation ($H^+$) in an aqueous environment ($HB \rightarrow H^+ + B^-$), and bases as substances that release a hydroxide anion ($OH^-$) in an aqueous environment ($BOH \rightarrow B^+ + OH^-$). Examples of Arrhenius acids include $HCl \rightarrow H^+ + Cl^-$, $HNO_3 \rightarrow H^+ + NO_3^-$, and $CH_3COOH \rightarrow H^+ + CH_3COO^-$. Examples of Arrhenius bases include $KOH \rightarrow K^+ + OH^-$, $Ca(OH)_2 \rightarrow Ca^{2+} + 2OH^-$, and $Fe(OH)_3 \rightarrow Fe^{3+} + 3OH^-$. The combination of released protons with water forms the oxonium cation: $H^+ + H_2O \rightarrow H_3O^+$.

Neutralization is the mutual reaction of an acid and a base, producing water and the salt of the given acid. For instance, $KOH + HCl \rightarrow KCl + H_2O$ or $NaOH + HNO_3 \rightarrow NaNO_3 + H_2O$. Looking at the ionic level, the core of neutralization is the reaction $H^+ + OH^- \rightarrow H_2O$, while the remaining ions ($K^+$ and $Cl^-$) form the dissolved salt ($KCl$).

Brønsted-Lowry theory expands these definitions by stating that acids are particles (molecules or ions) capable of donating a hydrogen cation (proton), while bases are particles capable of accepting a proton. The general transformations are $Acid \rightarrow H^+ + Base$ and $Base + H^+ \rightarrow Acid$. Examples of Brønsted acids include $HBr \rightarrow H^+ + Br^-$ and $H_2SO_4 \rightarrow H^+ + HSO_4^-$. Examples of Brønsted bases include $NH_3 + H^+ \rightarrow NH_4^+$ and $CO_3^{2-} + H^+ \rightarrow HCO_3^-$.

Lewis theory is based on electronic structure. A Lewis base is a substance with a free electron pair (e.g., $NH_3$, where the nitrogen has a lone pair), while a Lewis acid is a substance with an empty (vacant) orbital (e.g., $AlCl_3$, $BF_3$, $FeCl_3$, $H^+$, $Cd^{2+}$, $Ag^+$). Neutralization in Lewis theory results in the formation of a coordinate covalent bond between the acid and the base.

Proton Transfer and Dissociation

A conjugate pair consists of two substances that differ by a single proton ($H^+$). In the reaction $HCl + H_2O \rightleftharpoons H_3O^+ + Cl^-$, $HCl$ and $Cl^-$ form one conjugate pair, while $H_2O$ and $H_3O^+$ form another. Acid dissociation is the process where acids split into ions in an aqueous environment. Examples include the stepwise dissociation of sulfuric acid: first $H_2SO_4 + H_2O \rightleftharpoons H_3O^+ + HSO_4^-$, then $HSO_4^- + H_2O \rightleftharpoons H_3O^+ + SO_4^{2-}$. Other examples include $HNO_3 + H_2O \rightleftharpoons H_3O^+ + NO_3^-$ and the reaction of ammonia as a base: $NH_3 + H_2O \rightleftharpoons NH_4^+ + OH^-$.

The categorization of a substance as an acid or a base is relative and depends on the partner it reacts with. Autoprotolysis can occur between identical molecules of a protic solvent, creating a new acid and base. Substances that exhibit this dual character (capable of both donating and accepting a proton) are called ampholytes or amphoteric substances. Water ($H_2O + H_2O \rightleftharpoons H_3O^+ + OH^-$) and acetic acid ($2CH_3COOH \rightleftharpoons CH_3COOH_2^+ + CH_3COO^-$) serve as primary examples.

Strength of Acids and Bases

The strength of an acid is determined by how easily it can donate a proton, whereas the strength of a base is determined by how easily it can accept one. For oxygen-containing acids ($H_nXO_m$), strength can be categorized by the number of oxygen atoms relative to hydrogen atoms. Very weak acids occur when $m=n$ (e.g., $HClO$, $H_3BO_3$, $H_4SiO_4$). Weak acids occur when $m=n+1$ (e.g., $H_2CO_3$, $H_3PO_4$, $HNO_2$, $H_2SO_3$). Strong acids occur when $m=n+2$ (e.g., $H_2SO_4$, $HNO_3$, $HClO_3$). Very strong acids occur when $m=n+3$ (e.g., $HClO_4$).

Among binary (oxygen-free) acids, the hydrohalic acids are notably strong. Acidity generally increases moving down a group and to the right across a period in the periodic table. For example, in group 15, 16, and 17: $NH_3 < H_2O < HF$, $PH_3 < H_2S < HCl$, $AsH_3 < H_2Se < HBr$, and $SbH_n < H_2Te < HI$. Consequently, ammonia ($NH_3$) is the weakest in this comparison, while hydroiodic acid ($HI$) is the strongest.

Hydrolysis of Salts

Hydrolysis of salts involves the reaction of salt ions with water, affecting the final pH of the solution. If a salt is formed from a strong acid and a strong base (e.g., $NaCl$, $KNO_3$, $Na_2SO_4$, $KBr$, $KClO_4$), the resulting solution is neutral ($pH = 7$). If the salt comes from a strong acid and a weak base (e.g., $NH_4Cl$, $CuSO_4$, $FeCl_3$, $NH_4NO_3$, $Pb(NO_3)_2$), the solution is acidic ($pH < 7$) due to cation hydrolysis: $M^+ + 2H_2O \rightleftharpoons MOH + H_3O^+$.

Conversely, solutions of salts derived from weak acids and strong bases (e.g., $Na_2CO_3$, $Na_2SO_3$, $K_3PO_4$, $KCN$, $(NH_4)_2S$) react alkalinely ($pH > 7$) due to anion hydrolysis:$B^- + H_2O \rightleftharpoons HB + OH^-$. Specific examples include$NaCl$, which yields$Na^+$and$Cl^-$for a neutral solution,$NH_4Cl$, which yields$NH_4^+$and$Cl^-$for an acidic solution, and$Na_2CO_3$, which yields$2Na^+$and$CO_3^{2-}$$ for a basic solution.