# Strength of Acids and Bases The strength of an acid or a base refers to the degree to which it can donate or accept protons, respectively, in a solution. * A **strong acid** readily donates protons. For example, hydrochloric acid ($HCl$) is stronger than acetic acid ($CH_3COOH$). * A **strong base** readily accepts protons. For example, ammonia ($NH_3$) is stronger than water ($H_2O$) in accepting protons. ## 3.1 Strength of Acids and Bases ### 3.1.1 Strong and Weak Acids The strength of an acid is quantitatively expressed by its **acid dissociation constant**, $K_a$. Consider the ionization of a general acid $HX$ in water: $$ HX_{(aq)} + H_2O_{(l)} \rightleftharpoons H_3O^+_{(aq)} + X^-_{(aq)} $$ The equilibrium constant $K$ for this reaction is: $$ K = \frac{[H_3O^+][X^-]}{[HX][H_2O]} $$ Since water is the solvent and its concentration remains essentially constant, we can incorporate $[H_2O]$ into the equilibrium constant to define the acid dissociation constant, $K_a$: $$ K_a = K[H_2O] = \frac{[H_3O^+][X^-]}{[HX]} $$ * $K_a$ is a measure of the extent to which an acid ionizes or dissociates at equilibrium. * The value of $K_a$ is temperature-dependent, so temperature should always be specified. For instance, the $K_a$ of acetic acid in water at $25^\circ C$ is $1.8 \times 10^{-5}$. * **The greater the value of $K_a$, the stronger the acid.** To express $K_a$ values in a more convenient format, we use the **$pK_a$ scale**: $$ pK_a = -\log K_a $$ * Since $pK_a$ is the *negative* logarithm of $K_a$, **the lower the $pK_a$ value, the stronger the acid**, as a lower $pK_a$ corresponds to a higher $K_a$ value. **Table 3.1: Ionization Constants ($K_a$) and $pK_a$ of Some Common Acids in Water at $25^\circ C$** | Name of Acid | Formula | $K_a$ | $pK_a$ | | :-------------- | :---------------------------------------- | :--------------------- | :----- | | Perchloric acid | $HClO_4$ | $1.0 \times 10^{10}$ | -10.0 | | Hydroiodic acid | $HI$ | $1.0 \times 10^{10}$ | -10.0 | | Hydrobromic acid | $HBr$ | $1.0 \times 10^{9}$ | -9.0 | | Hydrochloric acid | $HCl$ | $1.0 \times 10^{6}$ | -6.0 | | Sulphuric acid | $H_2SO_4$ (first dissociation) | $1.0 \times 10^{3}$ | -3.0 | | Hydrofluoric acid | $HF$ | $7.2 \times 10^{-4}$ | +3.1 | | Formic acid | $HCOOH$ | $1.8 \times 10^{-4}$ | +3.75 | | Benzoic acid | $C_6H_5COOH$ | $6.3 \times 10^{-5}$ | +4.2 | | Acetic acid | $CH_3COOH$ | $1.8 \times 10^{-5}$ | +4.7 | | Phenol | $C_6H_5OH$ | $1.3 \times 10^{-10}$ | +8.9 | | Water | $H_2O$ | $1.8 \times 10^{-16}$ | +15.7 | From the table: * The strongest acid listed is Perchloric acid ($HClO_4$) or Hydroiodic acid ($HI$), with the highest $K_a$ and lowest $pK_a$. * The weakest acid listed (excluding water as a solvent) is Phenol ($C_6H_5OH$), with the lowest $K_a$ and highest $pK_a$. * Comparing $HCl$ ($K_a = 1.0 \times 10^6$, $pK_a = -6.0$) and $HF$ ($K_a = 7.2 \times 10^{-4}$, $pK_a = +3.1$), $HCl$ is a significantly stronger acid than $HF$. ### 3.1.2 Strong and Weak Bases The strength of a base is its ability to accept a proton, usually from a solvent like water. * **Strong bases** such as hydroxides of alkali metals (e.g., sodium hydroxide, $NaOH$, and potassium hydroxide, $KOH$) ionize *completely* in aqueous solution: $$ NaOH_{(aq)} \longrightarrow Na^+_{(aq)} + OH^-_{(aq)} $$ $$ KOH_{(aq)} \longrightarrow K^+_{(aq)} + OH^-_{(aq)} $$ The hydroxide ion ($OH^-$) itself is a strong Bronsted base because it readily accepts a proton: $$ OH^- + H^+ \longrightarrow H_2O $$ * For **weak bases**, the ability to accept a proton from water is described by the **base ionization constant**, $K_b$. For a general base $B$: $$ B_{(aq)} + H_2O_{(l)} \rightleftharpoons BH^+_{(aq)} + OH^-_{(aq)} $$ The base ionization constant $K_b$ is derived as: $$ K_b = \frac{[BH^+][OH^-]}{[B]} $$ * A large $K_b$ value indicates a high degree of ionization and thus a strong base. * A small $K_b$ value indicates a low degree of ionization and thus a weak base. Similar to acids, the **$pK_b$ scale** is used for convenience: $$ pK_b = -\log K_b $$ * **The lower the $pK_b$ value, the stronger the base**, as a lower $pK_b$ corresponds to a higher $K_b$ value. **Table 3.2: $K_b$ and $pK_b$ Values of Some Common Bases in Water at $25^\circ C$** | Name of Base | Formula | $K_b$ | $pK_b$ | | :------------ | :------------------------------------------------ | :-------------------- | :----- | | Diethylamine | $(\mathrm{C}_2\mathrm{H}_5)_2\mathrm{NH}$ | $9.6 \times 10^{-4}$ | 3.02 | | Ethylamine | $\mathrm{C}_2\mathrm{H}_5\mathrm{NH}_2$ | $5.6 \times 10^{-4}$ | 3.25 | | Methylamine | $\mathrm{CH}_3\mathrm{NH}_2$ | $4.5 \times 10^{-4}$ | 3.34 | | Ammonia | $\mathrm{NH}_3$ | $1.7 \times 10^{-5}$ | 4.76 | | Pyridine | $\mathrm{C}_5\mathrm{H}_5\mathrm{~N}$ | $5.6 \times 10^{-9}$ | 8.25 | | Aniline | $\mathrm{C}_6\mathrm{H}_5\mathrm{NH}_2$ | $4.3 \times 10^{-10}$ | 9.37 | From the table: * Diethylamine is the strongest base among those listed ($pK_b = 3.02$, lowest $pK_b$). * Aniline is the weakest base among those listed ($pK_b = 9.37$, highest $pK_b$). * Ammonia is stronger than pyridine and aniline but weaker than methylamine and ethylamine, as indicated by their respective $pK_b$ values. ## Worked Examples ### Example 3.1: Calculating $[H^+]$ for a Weak Acid Calculate the concentration of $H^+$ ions in a solution that contains $1.0\,M\,HF$ ($K_a = 7.2 \times 10^{-4}$). 1. **Write the given values:** * Initial concentration of $HF = 1.0\,M$ * $K_a$ for $HF = 7.2 \times 10^{-4}$ 2. **Apply the formula and set up ICE table:** The ionization of $HF$ in water is: $$ HF_{(aq)} \rightleftharpoons H^+_{(aq)} + F^-_{(aq)} $$ Let $x$ be the change in concentration of $HF$ that ionizes at equilibrium. | | $HF$ | $\rightleftharpoons$ | $H^+$ | $+$ | $F^-$ | | :------------- | :------------ | :------------------- | :------------ | :-- | :------------ | | **Initial** | $1.0\,M$ | | $0$ | | $0$ | | **Change** | $-x$ | | $+x$ | | $+x$ | | **Equilibrium** | $1.0 - x\,M$ | | $x\,M$ | | $x\,M$ | The $K_a$ expression is: $$ K_a = \frac{[H^+][F^-]}{[HF]} $$ Substitute equilibrium concentrations: $$ 7.2 \times 10^{-4} = \frac{(x)(x)}{1.0 - x} = \frac{x^2}{1.0 - x} $$ 3. **Show calculation with proper formatting:** Since $K_a$ is small, $x$ will be very small compared to $1.0$. Therefore, we can approximate $1.0 - x \approx 1.0$. $$ 7.2 \times 10^{-4} \approx \frac{x^2}{1.0} $$ $$ x^2 = 7.2 \times 10^{-4} $$ $$ x = \sqrt{7.2 \times 10^{-4}} $$ $$ x \approx 0.0268\,M $$ Thus, at equilibrium: $$ [H^+] = x = 0.0268\,M $$ ## Possible Questions/Answers * **Q:** What is the relationship between $K_a$ and acid strength? **A:** The *greater* the value of $K_a$, the *stronger* the acid. * **Q:** How does $pK_a$ relate to acid strength? **A:** The *lower* the value of $pK_a$, the *stronger* the acid. * **Q:** Is $HNO_3$ a strong or weak acid given its $pK_a$ is approximately -1.4? **A:** $HNO_3$ is a strong acid because its $pK_a$ value is negative and very low. * **Q:** Which is a stronger base: methylamine ($pK_b = 3.34$) or ammonia ($pK_b = 4.76$)? **A:** Methylamine is a stronger base than ammonia because it has a lower $pK_b$ value. ## Factors Affecting Acidity in Organic Compounds In organic chemistry, specifically for carboxylic acids, the strength is influenced by the stability of the conjugate base (carboxylate ion) and inductive effects. ### Inductive Effect * **Electron Withdrawing Groups (EWGs):** Groups like $-Cl$, $-F$, or $-NO_2$ pull electron density away from the carboxyl group, stabilizing the negative charge on the carboxylate ion and increasing acidity. * **Electron Donating Groups (EDGs):** Alkyl groups ($R-$) push electron density toward the carboxyl group, destabilizing the carboxylate ion and decreasing acidity.