Acid-Base Titrations and Solution Concentrations Notes | Leaving Cert Chemistry

Standard Solutions and Primary Standards

A standard solution is simply a solution of accurately known concentration. You can make one either by weighing out an exact mass of pure solid and dissolving it in a measured volume of water, or by finding its concentration through a titration against another reliable standard.

Not every chemical can be weighed out to make a standard solution directly. Many substances pick up moisture from the air, react with gases, or break down over time. That brings us to primary standards. A primary standard is a substance that can be obtained in a stable, pure, and soluble solid state, so you can weigh it accurately and dissolve it in water to make a solution of precisely known concentration.

To work as a primary standard, a compound needs to satisfy several conditions:

High purity: It should be virtually 100% pure so that the mass on the balance belongs entirely to the target compound.
Stability in air: It must not absorb water vapour or carbon dioxide from the atmosphere, nor should it lose water of crystallisation.
High relative molecular mass ( $M_r$ ): A large molar mass means you weigh out a bigger mass for the same number of moles. That keeps your percentage weighing error very low.
Good water solubility: It needs to dissolve readily and completely at room temperature.
Fast and complete reaction: It must react instantaneously and according to a clean, known stoichiometric ratio without side reactions.

In our laboratory, anhydrous sodium carbonate ( $\text{Na}_2\text{CO}_3$ , $M_r = 106.0$ ) is the main primary standard for acid-base work. We use it to standardise solutions of hydrochloric acid. In redox chemistry, ammonium iron(II) sulfate (Mohr's salt, $(\text{NH}_4)_2\text{Fe}(\text{SO}_4)_2\cdot 6\text{H}_2\text{O}$ ) serves as a primary standard to standardise potassium manganate(VII). Mohr's salt contains water of crystallisation, but unlike many hydrated crystals, it stays stable in air and does not lose that water on standing.

Common lab chemicals often fail these tests:

Sodium hydroxide ( $\text{NaOH}$ ): Solid pellets absorb moisture from the air so quickly that they dissolve in their own puddles. This property is called deliquescence. They also react with atmospheric carbon dioxide to form sodium carbonate. As a result, you can never weigh out pure $\text{NaOH}$ .
Hydrochloric acid ( $\text{HCl}$ ): Concentrated hydrochloric acid is a gas dissolved in water. It gives off hydrogen chloride gas fumes whenever the bottle opens, meaning its concentration drops over time.
Sulfuric acid ( $\text{H}_2\text{SO}_4$ ): It is hygroscopic, meaning it constantly pulls water vapour out of the surrounding air into the liquid.
Hydrated sodium carbonate ( $\text{Na}_2\text{CO}_3\cdot 10\text{H}_2\text{O}$ ): Washing soda crystals are efflorescent. They lose water of crystallisation to the air, turning powdery and changing mass unpredictably.
Potassium manganate(VII) ( $\text{KMnO}_4$ ): It cannot be made completely pure, and in solution it gradually decomposes when exposed to light.

Preparing a Standard Solution in the Laboratory

Making a standard solution is a fundamental laboratory technique. You will carry it out during practical work, and examiners regularly ask for the full step-by-step sequence in written questions. The standard method breaks down into five clear stages:

Weighing the solid: Place a clean, dry weighing boat on an analytical balance reading to two or three decimal places. Tare the balance or record the mass of the empty boat, then add the dry primary standard (such as anhydrous $\text{Na}_2\text{CO}_3$ ) until you reach the required mass. Record the exact final mass.
Dissolving in a beaker: Tip the solid into a clean beaker containing around $100\text{ cm}^3$ of deionised water. Use a wash bottle filled with deionised water to rinse the weighing boat thoroughly into the beaker, catching every lingering crystal. Stir the mixture with a clean glass rod until the solid dissolves completely.
Transferring with washings: Pour the dissolved solution through a clean filter funnel into a volumetric flask, usually a $250\text{ cm}^3$ flask. Do not stop there. Rinse the beaker, the stirring rod, and the funnel several times with deionised water from your wash bottle, letting all these washings run straight into the volumetric flask.
Making to the mark: Add deionised water until the liquid level sits roughly a centimetre below the etched line on the neck. Put down the wash bottle and switch to a dropper or Pasteur pipette. Looking at eye level so you avoid parallax error, add water drop by drop until the bottom of the meniscus rests right on the graduation mark.
Mixing thoroughly: Push the stopper firmly into the neck of the volumetric flask. Invert the flask and shake it back and forth at least fifteen to twenty times. If you skip this step, the solution near the bottom remains more concentrated than the liquid in the narrow neck.

Apparatus sequence showing weighing, dissolving, transferring all washings, aligning the meniscus and inverting the stoppered flask.

Units of Concentration and Conversions

Concentration tells us how much solute is dissolved in a particular volume or mass of solution. The Leaving Certificate specification expects you to move comfortably between six different units:

Molarity ( $\text{mol L}^{-1}$ or $\text{M}$ ): The number of moles of solute in one litre ( $1000\text{ cm}^3$ ) of solution.

\text{Molarity} = \frac{\text{moles of solute}}{\text{volume in litres}}

Mass concentration ( $\text{g L}^{-1}$ ): The mass in grams of solute in one litre of solution. You switch between molarity and mass concentration using the molar mass ( $M_r$ ):

\text{Mass concentration (g L}^{-1}\text{)} = \text{Molarity (mol L}^{-1}\text{)} \times M_r

Percentage mass per volume (\% w/v): The mass in grams of solute dissolved in $100\text{ cm}^3$ of solution. Because one litre contains ten $100\text{ cm}^3$ units, converting from $\text{g L}^{-1}$ to $\%\text{ (w/v)}$ is as simple as dividing by 10:

\%\text{ (w/v)} = \frac{\text{Concentration in g L}^{-1}}{10}

Percentage mass per mass (\% w/w): The grams of solute in $100\text{ g}$ of the overall solution. This format is standard on commercial bottles of concentrated acids.
Percentage volume per volume (\% v/v): The volume of liquid solute in $\text{cm}^3$ present in $100\text{ cm}^3$ of solution. You see this on bottles of alcoholic drinks, though remember that vinegar acidity is traditionally measured in $\%\text{ (w/v)}$ .
Parts per million (p.p.m.): For dilute aqueous solutions, $1\text{ p.p.m.} = 1\text{ mg L}^{-1}$ ( $0.001\text{ g L}^{-1}$ ). We use p.p.m. for trace quantities, such as calcium and magnesium ions in hard water samples.

Practical Conversion Examples

Converting p.p.m. to $\text{mol L}^{-1}$ A water sample contains $12\text{ p.p.m.}$ of dissolved $\text{Ca}^{2+}$ ions.

$12\text{ p.p.m.} = 12\text{ mg L}^{-1} = 0.012\text{ g L}^{-1}$
$\text{Molarity} = 0.012\text{ g L}^{-1} \div 40.08\text{ g mol}^{-1} = 3.0 \times 10^{-4}\text{ mol L}^{-1}$

Converting \% (v/v) to $\text{mol L}^{-1}$ using density A bottle of cider contains $5.0\%\text{ (v/v)}$ ethanol ( $\text{C}_2\text{H}_5\text{OH}$ , $M_r = 46.07$ ). Pure ethanol has a density of $0.79\text{ g cm}^{-3}$ .

$5.0\%\text{ (v/v)}$ gives $5.0\text{ cm}^3$ of pure ethanol in $100\text{ cm}^3$ , which scales up to $50.0\text{ cm}^3$ of ethanol in one litre.
$\text{Mass of ethanol} = 50.0\text{ cm}^3 \times 0.79\text{ g cm}^{-3} = 39.5\text{ g per litre}$ .
$\text{Molarity} = 39.5\text{ g L}^{-1} \div 46.07\text{ g mol}^{-1} = 0.86\text{ mol L}^{-1}$ .

Converting \% (w/w) to $\text{mol L}^{-1}$ using density Bench hydrochloric acid is sold as $36.0\%\text{ (w/w)}$ with a measured density of $1.18\text{ g cm}^{-3}$ ( $M_r = 36.46$ ).

$1000\text{ cm}^3$ of this acid solution has a mass of $1000 \times 1.18 = 1180\text{ g}$ .
$\text{Mass of pure HCl} = 36.0\% \times 1180\text{ g} = 424.8\text{ g}$ .
$\text{Molarity} = 424.8\text{ g L}^{-1} \div 36.46\text{ g mol}^{-1} = 11.7\text{ mol L}^{-1}$ .

Dilutions and Volumetric Glassware Technique

When you add pure water to a concentrated solution, you change its volume and concentration, but the number of dissolved moles stays unchanged:

V_1 \times M_1 = V_2 \times M_2

The dilution factor tells you how many times more dilute your final solution is compared to the original sample:

\text{Dilution factor} = \frac{V_2}{V_1} = \frac{M_1}{M_2}

If you dilute $10.0\text{ cm}^3$ of commercial vinegar up to $50.0\text{ cm}^3$ in a volumetric flask, your dilution factor is $50.0 \div 10.0 = 5$ . Each $25.0\text{ cm}^3$ portion you pipette into a conical flask holds the equivalent of $25.0 \div 5 = 5.0\text{ cm}^3$ of original vinegar. Always calculate this factor straight from the numbers given in the question; never guess that it is 10.

Ten cubic centimetres of vinegar is diluted to fifty; a twenty-five cubic centimetre aliquot contains the acid originally present in five cubic centimetres.

In a serial dilution, you dilute a sample through several repeated steps using the same ratio. For example, three consecutive $1:10$ dilutions give an overall dilution factor of $10 \times 10 \times 10 = 1000$ .

How to Rinse Volumetric Glassware

Piece of Glassware	Main Job	Correct Rinsing Protocol
Volumetric Flask	Prepares and holds an exact total volume of solution	Rinse with deionised water only. Leaving residual droplets of the solution inside would add extra solute and throw off the final concentration.
Pipette	Measures and delivers a fixed aliquot into the conical flask	Rinse with deionised water first, then with the solution it will contain. This washes out dirt without letting leftover water droplets dilute the measured sample.
Burette	Delivers variable, measured volumes of titrant	Rinse with deionised water first, then with the solution it will contain. Ensure the jet below the tap is filled with liquid.
Conical Flask	Holds the reacting mixture during titration	Rinse with deionised water only. Rinsing with the analyte would leave extra droplets of reactant behind, artificially inflating your titre.

Essential Bench Rules

Open the burette tap quickly to flush the tip before writing down your starting volume. An air bubble trapped in the jet will wash out during titration, which makes the burette reading higher than the volume actually added.
Take the funnel out of the top of the burette straight after filling. A funnel left in place will drip extra drops of titrant down the wall while you are titrating.
Read the bottom of the meniscus at eye level for all clear solutions.
Let the pipette drain under gravity with the tip resting against the inner neck of the flask. Never blow out the last drop stuck in the tip; the glassmaker calibrated the pipette to leave that droplet behind.
Use a wash bottle to rinse splashes on the inside walls of the conical flask down into the mixture as you titrate. Deionised water adds no extra moles of reactant, so it does not affect your result.

Indicators and Le Châtelier's Principle

An acid-base indicator is a weak acid or a weak base where the undissociated molecule has a completely different colour from its ionised conjugate form. An indicator changes colour over a characteristic range of roughly two pH units.

Weak acid and weak base indicator diagrams connect added acid or base to ion removal, equilibrium shifts and the dominant colour form.

Weak Acid Indicators ( $\text{HIn}$ )

A weak acid indicator sets up a dynamic equilibrium in water:

\text{HIn}_{(aq)} \rightleftharpoons \text{H}^+_{(aq)} + \text{In}^-_{(aq)}

\text{Colour A} \quad \rightleftharpoons \quad \text{Colour B}

When you place this indicator in an acidic solution, the high concentration of $\text{H}^+$ ions shifts the equilibrium position to the left according to Le Châtelier's principle. You see Colour A. If you add base, hydroxide ions react with $\text{H}^+$ to make water, removing $\text{H}^+$ from solution. The system responds by shifting to the right to replace the lost hydrogen ions, producing more $\text{In}^-$ and showing Colour B.

Weak Base Indicators ( $\text{InOH}$ )

A weak base indicator sets up this equilibrium:

\text{InOH}_{(aq)} \rightleftharpoons \text{In}^+_{(aq)} + \text{OH}^-_{(aq)}

\text{Colour X} \quad \rightleftharpoons \quad \text{Colour Y}

In a basic solution, the abundance of $\text{OH}^-$ drives the position of equilibrium to the left, showing Colour X. In an acid, added $\text{H}^+$ combines with $\text{OH}^-$ to produce neutral water molecules. The equilibrium shifts right to replenish the hydroxide ions, giving Colour Y.

Concept Example

Question: A student adds phenolphthalein to ethanoic acid in a conical flask, then runs sodium hydroxide in from a burette. Why does the solution start colourless and suddenly switch to pink? Explanation: Phenolphthalein is a weak acid indicator: $\text{HIn} \rightleftharpoons \text{H}^+ + \text{In}^-$ , where $\text{HIn}$ is colourless and $\text{In}^-$ is pink. While acid is in excess, the plentiful $\text{H}^+$ ions keep the equilibrium shifted to the left, so the mixture stays colourless. Once all the acid reacts, the first excess drop of sodium hydroxide supplies $\text{OH}^-$ ions that remove $\text{H}^+$ . The equilibrium shifts right to make $\text{In}^-$ , turning the solution permanently pink.

Investigating pH Titration Curves

A pH titration curve is a graph showing how the pH of the mixture changes as you add titrant from a burette. In class investigations, you generate this curve by gathering primary data with a calibrated digital pH probe.

A clamped burette adds base to acid in a stirred beaker while an immersed probe connects to a pH meter.

Generating a Primary pH Curve

Calibrate your pH probe with two buffer solutions, usually pH 4 and pH 7.
Pipette $25.0\text{ cm}^3$ of acid into a clean beaker, lower the probe into the liquid, and mix gently with a magnetic stirrer.
Run base in from the burette in $1.0\text{ cm}^3$ portions, recording the pH reading each time.
When you notice the pH climbing rapidly, slow down and add the base in small increments of $0.1\text{ to } 0.2\text{ cm}^3$ .
Keep adding base past the neutralisation point until the pH readings flatten out near the top.
Plot pH on the vertical axis against the volume of base added in $\text{cm}^3$ on the horizontal axis.

The equivalence point is the exact midpoint of the steep, near-vertical section of the curve. Reading straight down from this midpoint to the horizontal axis gives you the equivalence volume of titrant.

Four schematic rising pH curves compare strong and weak acids and bases, with indicator bands and equivalence points relative to pH seven.

Four Curve Shapes You Need to Know

Strong acid against strong base (e.g. $\text{HCl}$ titrated with $\text{NaOH}$ ): The curve starts low around $\text{pH } 1$ . It rises gradually, then jumps vertically between roughly $\text{pH } 3$ and $11$ . The equivalence point sits right at $\text{pH } 7$ . Both methyl orange (range $3.1 - 4.4$ ) and phenolphthalein (range $8.2 - 10.0$ ) fall inside this vertical jump, so either indicator works well.
Weak acid against strong base (e.g. $\text{CH}_3\text{COOH}$ titrated with $\text{NaOH}$ ): Starts higher, around $\text{pH } 3$ . The vertical jump is shorter, extending from about $\text{pH } 7$ to $11$ . The equivalence point lies on the alkaline side, typically between $\text{pH } 8.5$ and $9.0$ , because the ethanoate salt formed hydrolyses in water:

\text{CH}_3\text{COO}^- + \text{H}_2\text{O} \rightleftharpoons \text{CH}_3\text{COOH} + \text{OH}^-

Phenolphthalein is the right choice here because its colour-change band ( $8.2 - 10.0$ ) fits on this vertical jump. Methyl orange would change colour much too early, before the reaction finishes.

Strong acid against weak base (e.g. $\text{HCl}$ titrated with $\text{NH}_3$ ): The steep section falls lower on the scale, between roughly $\text{pH } 3$ and $7$ . The equivalence point sits in the acidic region, around $\text{pH } 5$ . Methyl orange works reliably here because its colour-change range ( $3.1 - 4.4$ ) lies along this steep section; phenolphthalein would not be suitable as its range lies entirely outside this vertical region.
Weak acid against weak base (e.g. $\text{CH}_3\text{COOH}$ titrated with $\text{NH}_3$ ): This curve has no sharp vertical step. It shows only a gentle inflection point. No chemical indicator can give a distinct colour change over such a sluggish rise, so indicators cannot be used. A digital pH meter can trace the curve, though identifying the exact equivalence volume remains difficult because the slope changes so gradually.

Investigation: Determining Ethanoic Acid in Vinegar (EI 4.1.5)

Commercial vinegar is an aqueous solution of ethanoic acid ( $\text{CH}_3\text{COOH}$ ). Finding its concentration using standardised sodium hydroxide is a required experimental investigation (marked with the superscript EI in the specification).

Because solid sodium hydroxide absorbs water and reacts with air, you cannot weigh it out as a primary standard. You must standardise it through a reliable experimental chain:

Standardise a hydrochloric acid solution against primary standard anhydrous sodium carbonate using methyl orange.
Titrate your sodium hydroxide against that freshly standardised hydrochloric acid.
Use the newly standardised sodium hydroxide to titrate your vinegar.

Standardised sodium hydroxide runs from a burette into diluted vinegar with phenolphthalein on a white tile; the end point is permanent pale pink.

Practical Investigation Steps

Objective: Find the concentration of ethanoic acid in commercial vinegar in both $\text{mol L}^{-1}$ and $\%\text{ (w/v)}$ .
Key apparatus: $25.0\text{ cm}^3$ pipette with safety filler, $250\text{ cm}^3$ volumetric flask, $50\text{ cm}^3$ burette, conical flask, white tile, wash bottle with deionised water.
Why we dilute the vinegar: Neat commercial vinegar contains between 4% and 8% (w/v) ethanoic acid, roughly $0.7\text{ to } 1.3\text{ mol L}^{-1}$ . If you titrated neat vinegar directly with $0.10\text{ mol L}^{-1} \text{ NaOH}$ , you would need only about $2\text{ to } 4\text{ cm}^3$ of neat vinegar in the flask, which gives large percentage reading errors, or else well over $100\text{ cm}^3$ of base from the burette. Diluting the vinegar tenfold lets you pipette a sensible $25.0\text{ cm}^3$ sample and gives titres of roughly $17\text{ to } 33\text{ cm}^3$ , which fit comfortably in a $50\text{ cm}^3$ burette.
Procedure:

Pipette $25.0\text{ cm}^3$ of commercial vinegar into a $250\text{ cm}^3$ volumetric flask. Add deionised water to near the neck, then use a dropper to bring the bottom of the meniscus level with the line. Stopper the flask and invert it twenty times.
Pipette $25.0\text{ cm}^3$ of this diluted vinegar into a conical flask rinsed only with deionised water. Add two to three drops of phenolphthalein indicator.
Fill the burette with your standardised $\text{NaOH}$ (having rinsed it with deionised water and then $\text{NaOH}$ ). Check that the tap jet has no trapped air bubble and take away the funnel.
Place the conical flask on a white tile. Titrate while swirling continuously until one single drop turns the liquid from colourless to a permanent pale pink.
Repeat until you get two concordant titres that agree within $0.10\text{ cm}^3$ , then average them.

Reaction equation:

\text{CH}_3\text{COOH} + \text{NaOH} \rightarrow \text{CH}_3\text{COONa} + \text{H}_2\text{O}

Precautions and Common Experimental Errors

White tile: Sits beneath the conical flask so you spot the very first faint, permanent pink colour against a bright background.
Swirling: Keeps the solutions blending evenly so you do not mistake a brief pink splash for the real end point.
Adding drop by drop near the end: Stops you overshooting the true neutralisation point.
Pipette filler: Essential for safety; never pipette corrosive liquids by mouth.
Overshooting the end point (deep magenta colour): You recorded too high a burette volume, which makes your calculated acid concentration artificially high.
Rinsing the burette with deionised water only: Water droplets left on the walls dilute the $\text{NaOH}$ . You will need a bigger volume of base to neutralise the acid, making your calculated vinegar concentration too high.
Rinsing the pipette with deionised water only: Water droplets left inside dilute the vinegar sample. You deliver fewer moles of acid, the titre is too low, and your calculated concentration comes out too low.

Key terms

Standard solution: A solution whose concentration is accurately known.
Primary standard: A substance that can be obtained in a stable, pure, and soluble solid state so that it can be weighed out accurately and dissolved in water to give a solution of accurately known concentration.
Equivalence point: The point in a titration where the quantity of added titrant is chemically equivalent to the amount of analyte according to the reaction stoichiometry.
End point: The point in a titration at which the indicator changes colour. A suitable indicator makes the end point coincide with the equivalence point.
Deliquescent: The property of a substance that absorbs water vapour from the atmosphere until it completely dissolves to form an aqueous solution.
Concordant titres: Two or more titration volume readings that agree with each other within 0.10 cm³.
Percentage mass per volume (% w/v): The mass of solute in grams dissolved per 100 cm³ of solution.
Parts per million (p.p.m.): For dilute aqueous solutions, the concentration expressed as milligrams of solute per litre of solution (1 mg L⁻¹).

Check yourself

Why is solid sodium hydroxide completely unsuitable for use as a primary standard?
Sodium hydroxide is deliquescent: it absorbs water vapour from the air until it dissolves, and it reacts with atmospheric carbon dioxide to form sodium carbonate. A weighed sample is therefore never pure NaOH.
The burette is rinsed only with deionised water before being filled with sodium hydroxide. What effect does this error have on the calculated concentration of ethanoic acid in vinegar?
The water droplets left inside the burette dilute the sodium hydroxide solution. A larger volume of this dilute base is needed to neutralise the acid, giving a larger titre, so the calculated ethanoic acid concentration is too high.
What is the sharp end point colour change when standardised sodium hydroxide is run from a burette into diluted vinegar containing phenolphthalein?
The colour changes sharply from colourless to a permanent pale pink.
How many grams of anhydrous sodium carbonate (Na₂CO₃, Mr = 106.0 g mol⁻¹) are required to prepare 500.0 cm³ of a 0.0500 mol L⁻¹ standard solution?
Moles required = 0.5000 L × 0.0500 mol L⁻¹ = 0.0250 mol. Mass required = 0.0250 mol × 106.0 g mol⁻¹ = 2.65 g.
Why can chemical indicators not be used to find the equivalence point of a weak acid-weak base titration?
The pH changes only gradually near the equivalence point, so the pH curve has only a small, gradual inflection rather than a steep vertical section. No indicator changes colour over a narrow enough volume to give a sharp end point.

Acid-Base Titrations and Solution Concentrations