Stoichiometry, Ionic Equilibria and Titrations for the Chemistry Olympiad — NSEC and INChO

Weightage: This is the quantitative backbone of chemistry, and it is where careful arithmetic wins marks. It underlies the experimental component at the later stages, so check the current HBCSE notice for the format. The method is the same throughout: write the balanced equation, convert to moles, then apply the equilibrium or titration relation.

1. The mole and stoichiometry

Everything starts with the balanced equation. Convert masses to moles ($n=m/M$), use the mole ratio, and convert back. Concentrations are molarity (mol per litre of solution), molality (mol per kg of solvent) and mole fraction.

The limiting reagent runs out first and fixes the yield.

Worked example. $2{\text{H}}_2+{\text{O}}_2\to 2{\text{H}}_2\text{O}$. With $4$ g of ${\text{H}}_2$ ($2$ mol) and $16$ g of ${\text{O}}_2$ ($0.5$ mol), the oxygen would need $1$ mol of hydrogen, so oxygen is limiting and gives $1$ mol of water, $18$ g. Hydrogen is in excess by $1$ mol.

Empirical formulas come from percentage composition by dividing by atomic masses and taking the simplest ratio. For a gas, $PV=nRT$ links volume to moles, and at STP ($273$ K, $1$ bar) one mole occupies about $22.7$ L.

2. Acids, bases and pH

For a weak acid HA with initial concentration $C$ and dissociation constant $K_a$, if the dissociation is small:

$[{\text{H}}^{+}]=\sqrt{K_{a}C},\text{pH}=\frac{1}{2}(\text{p}{K}_a-\log C)$

Worked example. For $0.1$ M acetic acid ($K_a=1.8\times 10^{-5}$), $[{\text{H}}^{+}]=\sqrt{1.8\times 10^{-6}}=1.34\times 10^{-3}$, so $\text{pH}=2.87$.

Check the approximation: it holds if less than about $5\%$ dissociates. Otherwise solve the quadratic. For water, $K_w=10^{-14}$ at $298$ K, so $\text{p}{K}_a+\text{p}{K}_b=14$ for a conjugate pair. Very dilute solutions need the contribution of water. Salts hydrolyse: a salt of a weak acid and strong base is basic.

3. Buffers

A buffer resists change in pH. The Henderson-Hasselbalch equation is:

$\text{pH}=\text{p}{K}_a+\log \frac{[{\text{A}}^{-}]}{[\text{HA}]}$

Worked example. A litre containing $0.1$ mol acetic acid and $0.1$ mol acetate has $\text{pH}=4.76$. After adding $0.01$ mol HCl, acetate falls to $0.09$ and acetic acid rises to $0.11$, so $\text{pH}=4.76+\log (0.09/0.11)=4.67$, a change of only $0.09$.

A buffer works best when the ratio is near $1$, so $\text{pH}\approx \text{p}{K}_a\pm 1$, and its capacity rises with total concentration.

4. Solubility and precipitation

For a sparingly soluble salt, the solubility product $K_{sp}$ is the product of ion concentrations at saturation.

Worked example. For AgCl, $K_{sp}=1.8\times 10^{-10}$, so $s=\sqrt{K_{sp}}=1.34\times 10^{-5}$ M. For a salt ${\text{AB}}_2$ with $s$ mol per litre dissolved, $K_{sp}=4s^3$.

The common ion effect lowers solubility: in $0.1$ M NaCl, $s(\text{AgCl})=K_{sp}/0.1=1.8\times 10^{-9}$ M. A precipitate forms when the ion product $Q$ exceeds $K_{sp}$. Complex formation raises solubility, as AgCl dissolves in ammonia. Compare precipitation order by the ion that reaches its $K_{sp}$ first.

5. Titrations

A titration finds an unknown concentration from the volume of a standard solution that reacts completely.

Acid-base: at the equivalence point the moles are in the stoichiometric ratio, $n_1{M}_1{V}_1=n_2{M}_2{V}_2$ with $n$ the number of moles reacting per mole. The pH at equivalence depends on the salt formed: neutral for strong-strong, basic for weak acid and strong base. An indicator is chosen with a colour change that falls within the steep part of the curve, such as phenolphthalein for weak acid and strong base. At the half-equivalence point of a weak acid, $\text{pH}=\text{p}{K}_a$.

Redox: potassium permanganate in acid takes $5$ electrons (${\text{MnO}}_4^{-}\to {\text{Mn}}^{2+}$) and acts as its own indicator, with a faint pink end point.

Worked example. $25.0$ mL of $0.100$ M Fe${}^{2+}$ contains $2.5$ mmol. Each MnO${}_4^{-}$ oxidises $5$ Fe${}^{2+}$, so $0.5$ mmol is needed, which is $25.0$ mL of $0.0200$ M permanganate.

Other methods: iodometric titrations use thiosulfate with starch near the end point, complexometric titrations use EDTA with a metal indicator, and gravimetric analysis weighs a precipitate, requiring a pure, stoichiometric, filterable product.

6. Experimental habits that earn marks

• Rinse the burette with the solution it will hold, and the pipette likewise. Do not rinse the conical flask with titrant.
• Read the burette at eye level, at the bottom of the meniscus, to $0.05$ mL.
• Concordant readings: repeat until two readings agree within $0.10$ mL, and average only those.
• Add the last drops carefully, swirling, and note the first permanent colour change.
• Record every reading in a table with units, and give the answer to the correct significant figures.
• Think about sources of error: indicator choice, a bubble in the tip, parallax and a contaminated standard.

Common traps

• Using the weak-acid approximation without checking that it is valid.
• Forgetting the volume change when mixing solutions.
• Calling a weak-acid titration neutral at equivalence.
• Using the wrong electron count for permanganate or dichromate.
• Treating $K_{sp}$ as solubility without the stoichiometric power.

Memory aids

• "Half equivalence: pH equals pKa."
• "Five electrons for permanganate in acid."
• "Equation, moles, ratio, answer": the stoichiometry routine.

Summary

Stoichiometry starts from a balanced equation and moles, and the limiting reagent sets the yield. Weak acids and buffers follow the approximations and Henderson-Hasselbalch, and solubility follows $K_{sp}$ with the common ion effect.

Titrations convert measured volumes into concentrations at an end point, and good technique and error awareness protect the result.

Exam protocol

• Balance the equation before any calculation.
• Check an approximation against its validity condition.
• Keep units and significant figures to the end.
• Confirm the syllabus and format with HBCSE.