IB Chemistry: Acids and Bases

Acids and bases are among the most fundamental and practical concepts in chemistry, governing processes from digestion to industrial manufacturing. For IB Chemistry, mastery of this topic is non-negotiable, as it integrates quantitative calculation, conceptual theory, and hands-on experimental analysis. Your understanding will be tested through complex calculations, graphical interpretation, and explanations of chemical behavior in both biological and industrial contexts.

Bronsted-Lowry Theory and Acid Strength

The modern definition you must use is the Bronsted-Lowry theory. An acid is a proton ($H^{+}$) donor, while a base is a proton acceptor. This theory elegantly describes acid-base reactions as proton transfer processes. For example, when hydrochloric acid reacts with water: $$HCl+H_{2}O\to H_3{O}^{+}+C{l}^{-}$$ HCl donates a proton to $H_{2}O$, making HCl the acid and $H_{2}O$ the base. The resulting $H_3{O}^{+}$ is the conjugate acid (formed when a base gains a proton), and $C{l}^{-}$ is the conjugate base (formed when an acid loses a proton). Every acid has a conjugate base, and every base has a conjugate acid.

This leads directly to the crucial distinction between strong and weak acids and bases. Strength refers to the extent of dissociation in water. A strong acid, like HCl, $H_{2}S{O}_4$, or $HN{O}_3$, completely dissociates into ions in aqueous solution. A weak acid, like ethanoic acid ($C{H}_{3}COOH$), only partially dissociates, establishing a dynamic equilibrium between the molecules and their ions. The same logic applies to bases: strong bases (e.g., $NaOH$, $KOH$) dissociate completely, while weak bases (e.g., $N{H}_3$) only partially accept protons.

The pH Scale and Quantitative Calculations

The concentration of $H_3{O}^{+}$ ions determines acidity, measured using the pH scale, defined as $pH=-{\log }_{10}[H_3{O}^{+}]$. For a strong monoprotic acid at 0.10 mol dm${}^{-3}$, $[H_3{O}^{+}]$ is also 0.10 mol dm${}^{-3}$, so $pH=-{\log }_{10}(0.10)=1.0$.

This calculation relies on the ionic product of water ($K_w$). Even pure water undergoes self-ionization: $2H_{2}O(l)\rightleftharpoons H_3{O}^{+}(aq)+O{H}^{-}(aq)$. The equilibrium constant for this is $K_w=[H_3{O}^{+}][O{H}^{-}]$. At 298 K, $K_w=1.0\times 10^{-14}$ mol${}^2$ dm${}^{-6}$. In a neutral solution at 298 K, $[H_3{O}^{+}]=[O{H}^{-}]=1.0\times 10^{-7}$ mol dm${}^{-3}$, hence pH = 7. For any aqueous solution, knowing $[H_3{O}^{+}]$ allows you to find $[O{H}^{-}]$ using $K_w$, and vice-versa.

Buffer Solutions: Mechanism and Calculation (HL)

A buffer solution resists significant changes in pH upon addition of small amounts of acid or base. It is typically a mixture of a weak acid and its conjugate base (e.g., $C{H}_{3}COOH$ and $C{H}_{3}COONa$) or a weak base and its conjugate acid. The mechanism is a classic application of Le Châtelier’s principle. If you add $H^{+}$ ions, they are mopped up by the conjugate base ($C{H}_{3}CO{O}^{-}$). If you add $O{H}^{-}$ ions, they react with the weak acid ($C{H}_{3}COOH$) to form water and the conjugate base. It acts like a chemical sponge for excess $H^{+}$ or $O{H}^{-}$.

At Higher Level, you must calculate buffer pH using the acid dissociation constant, $K_a$. For a weak acid HA, $K_a=\frac{[H_3{O}^{+}][A^{-}]}{[HA]}$. The approximation for a buffer system leads to the Henderson-Hasselbalch equation: $pH=p{K}_a+{\log }_{10}(\frac{[salt]}{[acid]})$, where $p{K}_a=-{\log }_{10}{K}_a$. For a buffer made from 0.20 M $C{H}_{3}COOH$ ($K_a=1.8\times 10^{-5}$) and 0.10 M $C{H}_{3}COONa$, the pH is calculated as: $$p{K}_a=-{\log }_{10}(1.8\times 10^{-5})\approx 4.74$$ $$pH=4.74+{\log }_{10}(\frac{0.10}{0.20})=4.74+{\log }_{10}(0.50)=4.74-0.30=4.44$$ HL students also perform pH calculations for weak acids alone, which requires solving the equilibrium expression, often using the approximation $[H_3{O}^{+}]\approx \sqrt{K_a\times [HA{]}_{initial}}$ when the dissociation is small.

Acid-Base Titrations and Curves

Titration is an experimental procedure to determine the concentration of an unknown solution by reacting it with a standard solution. The equivalence point is when the moles of acid equal the moles of base. Analyzing titration curves (pH vs. volume of titrant) is vital.

A strong acid-strong base curve (e.g., HCl vs. $NaOH$) starts at low pH, has a steep, vertical rise through pH 7 at the equivalence point, and levels off at high pH. A weak acid-strong base curve (e.g., $C{H}_{3}COOH$ vs. $NaOH$) starts at a higher pH (weak acid), shows a buffer region before the equivalence point, has an equivalence point above pH 7 (due to the conjugate base present), and a similar steep rise. The choice of indicator depends on the pH range of the equivalence point's vertical section. Phenolphthalein (range 8.2-10.0) is suitable for a weak acid-strong base titration, while methyl orange (range 3.1-4.4) is better for strong acid-strong base.

Titration Calculations

You must be proficient in titration calculations. The core formula is: $$n_A=n_B\text{at equivalence}$$ For monoprotic acids and bases, $c_A{V}_A=c_B{V}_B$, where $c$ is concentration and $V$ is volume. For polyprotic acids like $H_{2}S{O}_4$, you must account for the mole ratio (e.g., 1 mol $H_{2}S{O}_4$ reacts with 2 mol $NaOH$). A typical problem: "25.00 cm${}^3$ of $H_{2}S{O}_4$ required 31.25 cm${}^3$ of 0.100 mol dm${}^{-3}$ $NaOH$ for neutralization. Find the concentration of the acid."

1. Moles of $NaOH$ = $cV$ = $0.100\times 0.03125$ = $3.125\times 10^{-3}$ mol.
2. The equation is $H_{2}S{O}_4+2NaOH\to N{a}_{2}S{O}_4+2H_{2}O$. Moles of $H_{2}S{O}_4$ = $(3.125\times 10^{-3})/2=1.5625\times 10^{-3}$ mol.
3. Concentration of $H_{2}S{O}_4$ = $n/V$ = $(1.5625\times 10^{-3})/0.02500$ = $0.0625$ mol dm${}^{-3}$.

Common Pitfalls

1. Confusing Strength with Concentration: A dilute strong acid can have a higher pH (be less acidic) than a concentrated weak acid. Strength is about extent of dissociation; concentration is about amount in solution. You can have a 0.001 M strong acid (pH = 3) and a 1 M weak acid (pH ~ 2-3), showing similar pH despite vastly different concentrations.
2. Misapplying pH Calculations: For a 0.01 M $Ba(OH{)}_2$ solution, $[O{H}^{-}]$ is 0.02 M (because it provides 2 $O{H}^{-}$ per formula unit). A common error is using 0.01 M. Correctly: $pOH=-{\log }_{10}(0.02)\approx 1.70$, so $pH=14.00-1.70=12.30$.
3. Incorrect Indicator Selection: Choosing an indicator whose colour change range does not fall within the vertical section of the titration curve will give an inaccurate end-point. Always sketch or consider the curve's shape.
4. Buffer Composition Errors: A buffer must contain significant amounts of both a weak acid and its conjugate base. A solution of just $C{H}_{3}COOH$ is not a buffer; adding $C{H}_{3}COONa$ makes it one. Similarly, equimolar amounts provide the best buffer capacity, but not necessarily a pH of 7.

Summary

• The Bronsted-Lowry theory defines acids as proton donors and bases as proton acceptors, with strength determined by the degree of dissociation in water.
• The pH scale is logarithmic: $pH=-{\log }_{10}[H_3{O}^{+}]$, and the ionic product of water ($K_w=[H_3{O}^{+}][O{H}^{-}]=10^{-14}$ at 298 K) interrelates $H_3{O}^{+}$ and $O{H}^{-}$ concentrations.
• Buffer solutions resist pH change via equilibrium shifts and, at HL, their pH is calculated using the $K_a$ expression or Henderson-Hasselbalch equation.
• Titration curves graphically represent pH changes during neutralization; their shapes reveal acid/base strength and dictate appropriate indicator choice.
• Proficiency in stoichiometric titration calculations, including those for polyprotic species, is essential for both experimental and theoretical analysis.