Principles of Volumetric Analysis (VCE SSCE Chemistry): Revision Notes

Principles of Volumetric Analysis

What is volumetric analysis?

Volumetric analysis is a laboratory technique used to determine the concentration of a dissolved substance in a solution. The method involves carefully measuring the volumes of solutions that react together. One solution has a known concentration (called a standard solution) and the other has an unknown concentration that you want to find.

Preparing standard solutions

Primary standards

To perform volumetric analysis, you need a solution with an accurately known concentration. This is called a standard solution. Standard solutions are often prepared from substances called primary standards.

For a substance to be used as a primary standard, it should have these characteristics:

• Be readily available in a very pure form
• Have a known chemical formula
• Be easy to store without deteriorating or reacting with substances in the atmosphere
• Have a high molar mass to minimise the effect of weighing errors
• Be inexpensive

Examples of primary standards:

Acids:

• Hydrated oxalic acid ($\text{H}_2\text{C}_2\text{O}_4 \cdot 2\text{H}_2\text{O}$)
• Potassium hydrogen phthalate ($\text{KH}(\text{C}_8\text{H}_4\text{O}_4)$)

Bases:

• Sodium borate ($\text{Na}_2\text{B}_4\text{O}_7 \cdot 10\text{H}_2\text{O}$)
• Anhydrous sodium carbonate ($\text{Na}_2\text{CO}_3$)

Making a standard solution

Standard solutions are prepared by dissolving an accurately measured mass of a primary standard in deionised water to make an accurately measured volume of solution.

Deionised water is water that has had all ions removed. Its high purity makes it ideal for cleaning glassware and preparing solutions.

Equipment for preparing standard solutions:

Digital balances are used to accurately weigh primary standards:

• Top-loading balances can weigh to an accuracy of $0.1$ g to $0.001$ g
• Analytical balances can weigh to an accuracy of $0.0001$ g to $0.00001$ g

Volumetric flasks (also called standard flasks) are used to prepare solutions with accurately known volumes. Common sizes include $100.00$ mL, $250.0$ mL, and $1000.0$ mL.

Procedure for preparing a standard solution:

The following diagram shows the steps involved in preparing a standard solution from a primary standard:

1. Weigh the pure solid primary standard on a balance
2. Transfer the solid into the volumetric flask using a clean, dry funnel
3. Rinse any remaining solid particles into the flask using deionised water
4. Half-fill the flask with deionised water, stopper and swirl vigorously to dissolve the solid
5. Add deionised water up to the calibration line on the neck of the flask. The bottom of the meniscus should be level with the mark when viewed at eye level
6. Stopper and shake the solution to ensure an even concentration throughout

Calculating the concentration of a standard solution

The concentration of a standard solution is calculated using these formulas:

Amount in moles:

$n = \frac{m}{M}$

where $m$ is the mass of solute in grams and $M$ is the molar mass in $\text{g mol}^{-1}$

Concentration:

$c = \frac{n}{V} = \frac{m}{M \times V}$

where $n$ is the amount in moles, $V$ is the volume in litres, and $c$ is the concentration in $\text{mol L}^{-1}$ or M.

Stock solutions are large volumes of commonly used reagents with known concentrations. These are often diluted to obtain convenient concentrations for volumetric analysis.

Conducting volumetric analyses

The titration process

Titration is the process of reacting a measured volume of a standard solution with a measured volume of a solution of unknown concentration.

The solutions are mixed until they have just reacted completely in the mole ratio shown in the balanced chemical equation. This point is called the equivalence point.

From the concentration and volume of the standard solution, you can calculate the number of moles of that substance. Using the mole ratio from the balanced equation, you can then determine the number of moles of the unknown substance. Finally, from the number of moles and the measured volume, you can calculate the unknown concentration.

Key terms:

• Aliquot: A specific, accurately measured volume of solution, usually measured with a pipette
• Titre: The accurately known volume of solution delivered from the burette during a titration
• Equivalence point: The point where the reactants have reacted in the exact mole ratio shown in the balanced chemical equation
• End point: The point during the titration when the indicator changes colour

Equipment used in titrations

The following table describes the main pieces of glassware used in acid-base titrations:

A typical titration setup showing all the equipment together:

Titration procedure

The steps involved in an acid-base titration are:

1. Measure an aliquot using a pipette

A known volume of one solution is measured using a pipette and transferred into a conical flask.

2. Add indicator

A few drops of an appropriate acid-base indicator are added to the conical flask. The indicator will signal when to stop the titration by changing colour.

3. Titrate from the burette

The other solution is slowly dispensed from a burette into the conical flask until the indicator changes colour permanently.

Reading a burette scale

Burettes are calibrated in intervals of $0.10$ mL. The volume is measured at the bottom of the meniscus and estimated to the nearest $0.01$ mL.

The titre delivered from the burette is calculated by:

$\text{Titre} = \text{Final burette reading} - \text{Initial burette reading}$

Concordant titres and averaging

To minimise errors, the titration is repeated several times. The average titre is calculated from three concordant titres.

Example:

Consider this titration data:

• Titration 1 ($20.20$ mL) is a rough titration to find the approximate end point
• Titrations 2, 4, and 5 are concordant: $19.86 - 19.78 = 0.08$ mL (within $0.10$ mL range)
• Average titre = $\frac{19.82 + 19.78 + 19.86}{3} = 19.82$ mL

Selecting an indicator

Understanding pH curves

During a titration, the pH of the solution in the conical flask changes as solution is added from the burette. A graph showing this change is called a pH curve or titration curve.

In this example, sodium hydroxide (a strong base, pH 14) is in the conical flask. As hydrochloric acid is added from the burette:

• The pH decreases slowly at first
• Near the equivalence point, a very small volume of acid causes a large pH change
• The pH drops from 10 to 4 with just one drop of acid
• This is called a sharp end point

Common indicators

Different indicators change colour at different pH ranges:

Matching indicators to titrations

Graph (a) shows a strong acid-strong base titration with a sharp pH drop from pH 10 to pH 4. Phenolphthalein (pH range 8.3-10.0) gives a sharp end point.

Graph (b) shows a strong acid-weak base titration with a less steep pH change. Phenolphthalein would give a broad, inaccurate end point. Methyl orange (pH range 3.1-4.4) is more suitable.

Guidelines for indicator selection:

Accuracy and precision in volumetric analysis

Types of errors

Understanding errors helps improve the quality of analytical results. It's important to distinguish between mistakes and experimental errors.

Mistakes

Mistakes are avoidable errors that should be eliminated by careful technique. Examples include:

• Misreading the numbers on a scale
• Using a pipette of incorrect volume
• Spilling part of a sample
• Incorrect rinsing of glassware

Systematic errors

A systematic error produces a constant bias that cannot be eliminated by repeating the measurement. The error is always in the same direction, making the average either consistently higher or lower than the true value.

Random errors

Random errors follow no regular pattern. Sometimes the measurement is too large, sometimes too small.

Rinsing glassware correctly

Proper rinsing removes trace chemicals from glassware, making results more accurate and precise. However, rinsing with the wrong liquid can introduce errors.

Remember!