Acid/Base Reactions

Module 6 is the most heavily examined module, about 27 marks a year, and quantitative analysis (titrations and their calculations) is the single biggest inquiry question in the whole course at about 14 marks a year. Every paper has at least one multi-step titration calculation, so practise them until the setting-out is automatic.

• Properties of acids and bases: indicators, reactions of acids (with bases, carbonates and metals), enthalpy of neutralisation, and how definitions developed from Lavoisier to Brønsted–Lowry.
• Using Brønsted–Lowry theory: conjugate acid–base pairs, amphiprotic species, pH and pOH, strong versus weak and concentrated versus dilute, $K_a$ and $p{K}_a$, and the pH of salt solutions.
• Quantitative analysis: standard solutions and primary standards, titration technique, titration curves, choice of indicator, conductometric titrations, buffers, and titration and back-titration calculations.

Key data-sheet items: $K_w=1.0\times 10^{-14}$ at 25 °C, $\text{pH}=-{\log }_{10}[{\text{H}}^{+}]$ and $p{K}_a=-{\log }_{10}[K_a]$.

Typical reactions

Learn the general equations and be able to write balanced full and net ionic versions:

• Acid + base (metal hydroxide or oxide) → salt + water
• Acid + metal carbonate or hydrogen carbonate → salt + water + carbon dioxide
• Acid + reactive metal → salt + hydrogen
• Ammonia + acid → ammonium salt (no water forms)

The net ionic equation for any strong acid with a strong base is

which is why the enthalpy of neutralisation for any strong acid–strong base pair is about $-57\text{kJ}$ per mole of water formed. With a weak acid or base it is slightly less exothermic, because some energy is used to complete the ionisation of the weak species. In a calorimetry experiment, use $q=mc\Delta T$ with the mass of the combined solutions, then divide by the moles of water formed (from the limiting reagent).

Indicators

Indicators are weak acids whose acid form ($\text{HIn}$) and conjugate base (${\text{In}}^{-}$) are different colours. Know methyl orange (red to yellow, changes around pH 3.1–4.4), bromothymol blue (yellow to blue, about 6.0–7.6) and phenolphthalein (colourless to pink, about 8.3–10). Natural indicators such as red cabbage extract change through several colours over a wide pH range, which makes them useful for estimating pH but poor for titrations.

Development of acid–base theories

"Evaluate" or "assess" questions on this table want the limitations of each theory and how the next one fixed them, ending in a judgement.

An acid donates a proton (${\text{H}}^{+}$) and a base accepts one. When an acid donates its proton, what remains is its conjugate base; the two differ by exactly one ${\text{H}}^{+}$. For example, in

the pairs are $\text{HF}/{\text{F}}^{-}$ and ${\text{H}}_3{\text{O}}^{+}/{\text{H}}_2\text{O}$.

An amphiprotic species can donate or accept a proton: water, ${\text{HCO}}_3^{-}$, ${\text{HSO}}_4^{-}$, ${\text{H}}_2{\text{PO}}_4^{-}$ and ${\text{HPO}}_4^{2-}$ are examples. To show this, write two equations, one with the species acting as an acid and one as a base.

Strength versus concentration

• Strong acid: ionises completely in water (HCl, ${\text{HNO}}_3$, ${\text{H}}_2{\text{SO}}_4$ first proton). Equations use $\to$.
• Weak acid: ionises only partially, so an equilibrium exists (ethanoic, methanoic, citric acids). Equations use $\rightleftharpoons$.
• Concentrated or dilute describes how many moles of acid are in each litre, not how much it ionises.

So a dilute strong acid and a concentrated weak acid can have the same pH. The stronger the acid, the weaker its conjugate base: ${\text{Cl}}^{-}$ is a negligibly weak base, but ${\text{CH}}_3{\text{COO}}^{-}$ is a weak base.

pH and pOH

At 25 °C, $[{\text{H}}^{+}][{\text{OH}}^{-}]=K_w=1.0\times 10^{-14}$, so $\text{pH}+\text{pOH}=14.00$. $K_w$ increases with temperature (the ionisation of water is endothermic), so pure water at higher temperature has pH below 7 but is still neutral because $[{\text{H}}^{+}]=[{\text{OH}}^{-}]$.

A tenfold dilution of a strong acid raises the pH by 1. Give pH values to two decimal places unless told otherwise.

Quick examples. For $0.0040{\text{mol L}}^{-1}$ ${\text{HNO}}_3$, $\text{pH}=-{\log }_{10}0.0040=2.40$. For $0.0050{\text{mol L}}^{-1}$ KOH, $\text{pOH}=2.30$, so $\text{pH}=11.70$. For a diprotic strong acid such as ${\text{H}}_2{\text{SO}}_4$, HSC questions usually treat $[{\text{H}}^{+}]$ as twice the acid concentration; say so in your answer.

Ka and pKa

For a weak acid $\text{HA}\rightleftharpoons {\text{H}}^{+}+{\text{A}}^{-}$:

A larger $K_a$ (smaller $p{K}_a$) means a stronger acid. Water is left out of the expression.

Worked example. Calculate the pH of $0.10{\text{mol L}}^{-1}$ methanoic acid, given $K_a=1.8\times 10^{-4}$.

Let $x=[{\text{H}}^{+}]=[{\text{HCOO}}^{-}]$. Because the acid is weak, assume $x$ is small compared with 0.10, so $[\text{HCOOH}]\approx 0.10$:

Check the assumption: $x$ is 4.2% of 0.10, under 5%, so the approximation is fine (solving the quadratic exactly gives 2.38). The $p{K}_a$ of methanoic acid is $-{\log }_{10}(1.8\times 10^{-4})=3.74$.

Going backwards: from a measured pH, $[{\text{H}}^{+}]=10^{-\text{pH}}$, then

Salts in water

The ions of a salt can react with water (hydrolysis):

• Salt of a strong acid and strong base (NaCl, ${\text{KNO}}_3$): neutral.
• Salt of a weak acid and strong base (${\text{CH}}_3\text{COONa}$, ${\text{Na}}_2{\text{CO}}_3$): basic, because the anion accepts a proton from water and forms ${\text{OH}}^{-}$.
• Salt of a strong acid and weak base (${\text{NH}}_4\text{Cl}$): acidic, because ${\text{NH}}_4^{+}$ donates a proton to water.

Write the hydrolysis equation to justify your answer; that is usually where the mark is.

Standard solutions and technique

A primary standard is a substance pure enough, stable enough and with a high enough molar mass to weigh out and make a solution of accurately known concentration. Anhydrous sodium carbonate and potassium hydrogen phthalate are common; sodium hydroxide is not (it absorbs water and carbon dioxide from air), so NaOH solutions are standardised by titration against a primary standard.

Equipment and rinsing:

• Volumetric flask: to make up a standard solution; rinse with distilled water only.
• Pipette: delivers the aliquot; rinse with the solution it will deliver.
• Burette: delivers the titre; rinse with the solution it will hold.
• Conical flask: rinse with distilled water only (extra water doesn't change the moles in the aliquot).

Read the burette at the bottom of the meniscus at eye level, swirl continuously, add dropwise near the end point, and repeat until you have three concordant titres (within about 0.10 mL). Average the concordant titres only.

The equivalence point is where reactants have reacted in exactly the mole ratio of the equation; the end point is where the indicator changes colour. A good indicator has its end point at or very near the equivalence point.

Titration curves and indicator choice

On a titration curve, find the equivalence point at the middle of the steep vertical section. For a weak acid with a strong base the curve has a buffer region before equivalence, and at the half-equivalence point half the acid has been converted to its conjugate base, so $[\text{HA}]=[{\text{A}}^{-}]$ and $\text{pH}=p{K}_a$. This is how $p{K}_a$ is read from a curve.

Conductometric titrations

Conductivity depends on the number and the mobility of ions. ${\text{H}}^{+}$ and ${\text{OH}}^{-}$ are far more mobile than other ions. In a strong acid–strong base titration, conductivity falls as mobile ${\text{H}}^{+}$ is replaced by less mobile ${\text{Na}}^{+}$, reaches a minimum at equivalence, then rises as excess ${\text{OH}}^{-}$ builds up. With a weak acid, conductivity starts low and the graph shape is different, but the equivalence point is still where the line changes slope. Conductometric titrations work for coloured or cloudy solutions where an indicator can't be seen.

Buffers

A buffer is a solution of a weak acid and its conjugate base (or a weak base and its conjugate acid) in similar, reasonably large amounts. It resists changes in pH when small amounts of acid or base are added, because the added ${\text{H}}^{+}$ or ${\text{OH}}^{-}$ is consumed by one of the pair and the equilibrium shifts (Le Chatelier) to keep $[{\text{H}}^{+}]$ nearly constant. Blood is buffered mainly by carbonic acid and hydrogen carbonate, which keeps its pH near 7.4; oceans and lakes are also buffered by the carbonate system. Full answers include an equation for each direction.

Worked example: excess reagent

25.0 mL of $0.120{\text{mol L}}^{-1}$ NaOH is mixed with 20.0 mL of $0.100{\text{mol L}}^{-1}$ ${\text{H}}_2{\text{SO}}_4$. Find the pH (treat the acid as fully diprotic).

${\text{H}}^{+}$ is in excess by 0.00100 mol, in a total volume of 45.0 mL:

Worked example: back titration

A back titration is used when the sample doesn't dissolve or reacts slowly: add a known excess of acid, then titrate the leftover acid.

A 0.500 g antacid tablet containing calcium carbonate was added to 50.00 mL of $0.200{\text{mol L}}^{-1}$ HCl. When reaction stopped, the excess HCl needed 18.40 mL of $0.1000{\text{mol L}}^{-1}$ NaOH. Calculate the percentage by mass of ${\text{CaCO}}_3$ ($M=100.09{\text{g mol}}^{-1}$).

Step 1: total HCl added. $n=0.05000\times 0.200=0.01000$ mol.

Step 2: excess HCl (1 : 1 with NaOH). $n=0.01840\times 0.1000=0.001840$ mol.

Step 3: HCl that reacted with the tablet. $0.01000-0.001840=0.008160$ mol.

Step 4: moles and mass of CaCO₃ (1 : 2 ratio).

Step 5: percentage. $0.4084/0.500\times 100=81.7\%$.

Label every step; markers award a mark for each correct stage even if an earlier number is wrong.

Analysis by Aboriginal and Torres Strait Islander Peoples and industry

Questions may ask how acid–base chemistry is applied, for example using the properties of plant materials, ash and natural indicators, or industrial monitoring of pH with digital probes and data loggers in water treatment, food and agriculture. Link the technique to the chemistry it relies on.

• Confusing strong with concentrated, or weak with dilute.
• Forgetting the mole ratio (diprotic acids, carbonates react 1 : 2 with HCl).
• Using the volume of only one solution after mixing, or forgetting to convert mL to L.
• Including the rough titre or a non-concordant titre in the average.
• Rinsing the conical flask with the solution it will hold (this adds extra moles).
• Saying pH 7 means neutral at every temperature.
• Writing a weak acid's ionisation with a one-way arrow, or a strong acid's with an equilibrium arrow.
• Giving pH to three or more significant figures as if it were a concentration; the digits after the decimal point carry the precision.

• Calculate questions in this module are long. Set out each step with a heading (moles of titrant, mole ratio, moles in aliquot, scale to original volume, concentration or mass) and show units. A 5–7 mark titration question gives a mark for almost every line.
• Watch for dilution and aliquots: if 25.00 mL of a 250.0 mL solution is titrated, multiply the moles by 10 to get back to the original sample.
• Keep at least four significant figures until the end, then round to match the data (titration data are usually four significant figures).
• Explain pH differences by writing ionisation equations and referring to the extent of ionisation and $[{\text{H}}^{+}]$.
• When asked to justify an indicator, state the pH at equivalence and why, and show that the indicator's range includes it.
• For practical-method questions, name the equipment, what it is rinsed with, how the end point is detected, and how reliability (concordant titres) and accuracy (primary standard, calibrated glassware) are achieved.

• Module 5: $K_a$ and $K_w$ are equilibrium constants; buffers and indicators are Le Chatelier's principle in action.
• Module 7: carboxylic acids are weak acids and amines are weak bases; esterification is catalysed by acid.
• Module 8: precipitation titrations, colorimetry and the analysis of household and environmental samples use the same mole and dilution calculations.
• Year 11 Module 3–4: mole concept, concentration and $q=mc\Delta T$ calorimetry.