9.3.E - Acid/Base Analysis

In chemistry a titration is a common laboratory method of quantitative chemical analysis that is often used to determine the unknown concentration of an acid or a base using a neutralisation reaction. Because volume measurements play a key role in titration, it is also known as volumetric analysis. A reagent, called the titrant, is prepared as a standard solution. A known concentration and volume of titrant (acid) reacts with another solution (base) to determine its concentration.

Analysing acids and bases in chemistry using pH is also an important diagnostic tool. The pH of a solution is a logarithmic measure of the concentration of hydrogen ions present.

The pH of a solution can be calculated using the formula

pH = -log10[H+]


In this unit you will learn to

  • Calculate the concentration of an unknown solution from titration data
  • Prepare a standard solution
  • Perform titrations using suitable procedures
  • Interpret titration graphs
  • Select a suitable indicator for a titration
  • Calculate pH

Standard Solutions

Before you start a titration you need one solution, either acid or base, that has a known concentration. This solution is known as standard solution.

Volumetric flasks come in different sizes but
each is designed to accurately hold a
specified volume.

A primary standard is made by accurately weighing a solid and dissolving it in an accurately known volume in a volumetric flask. A secondary standard is one determined by titration against a primary standard.

Not all acids and bases are suitable for use as primary standards as their properties can affect the validity of the procedure. Primary standards are almost always solids and should:

  • Have a high purity,
  • Be chemically and physically stable so that they do not decompose or react on heating,
  • Not absorb moisture from the air so that an accurate mass can be weighed, and
  • Be highly soluble in water.

Good examples of standards that fit these qualities are the base, sodium carbonate (Na2CO3) and the acid oxalic acid (COOH-COOH).

This video shows how to make a solution of known concentration
from a solid solute. The procedure is basically the same for
preparing a primary standard of acid or base.

To prepare a primary standard, the following steps should be followed:

  1. Heat the standard in an oven to remove any moisture from between the crystals and then store the standard in a dessicator to prevent further aborption of moisture from the air.

  2. Weigh (accurately) a small amount into a small, dry beaker.

  3. Dissolve the solid in a small amount of distilled water.

  4. Clean a volumetric flask with water and use a funnel to add the standard to the flask. Rinse the beaker to ensure all of the standard in transferred to the volumetric flask.

  5. Add distilled water to the flask until it is just below the graduated mark and then add distilled water dropwise until the meniscus lies on the graduated mark. Place the stopper on the volumetric flask and invert it several times to mix thoroughly.

The actual concentration of the primary standard can be determined by calculating the number of moles of standard that was weighed out (n=m/Mr) and then calculating its concentraiton using c = n/V.


Titration Technique

Once a primary standard has been prepared, it can be used in a titration to determine the concentration of an unknown soluiton. To conduct a titration accurately, each piece of equipment should be cleaned specifically.

A pipette and pump is used to deliver a
precise know volume to the conical flask.

The pipette is rinsed twice with distilled water and then once with the solution going into it. The burette is also rinsed twice with water and then with the solution it will deliver. The sides of the conical flask can be rinsed with distilled water because once the solution has been put into it, only the number of moles present is important. Adding more water will not change the number of moles in the conical flask.

The standard can be placed in the flask or the burette depending on which colour change is easiest to detect at the end point. The end point is the volume at which the indicator undergoes a permanent colour change. The equivalence point in a titration is the volume at which complete neutralisation has occurred. The end point is observed visually while the equivalence point represents a microscopic occurence in the conical flask. The purpose of the indicator's colour change is the make the end point and equivalence point occur at the same time so we know when to stop adding titrant and record the volume.

Good titration procedure is essential to getting an accurate result for the unknown concentration. This requires precise volume measurements and attention to detail in technique. Use the following procedure as a guide to good technique.

The main aspects of a sound titration procedure to determine the
concentration of an unknown solution.

  1. The pipette is used to draw up a precise volume of solution, either the substance being analysed or the standard. A suction device should be used with the pipette. The volume is released into the clean conical flask. This volume is known as an aliquot. The small volume remaining in the pipette should be left there and not tapped out.

  2. The burette is filled to the 0.0 mL mark.

  3. A few drops of indicator are added to the solution in the flask. As little as possible should be used so that a colour change can be determined accurately. Too much indicator may affect the accuracy of the titration as the indicator itself is acidic or basic.

  4. The burette tap is released allowing the titrant to flow into the conical flask until the end point is reached. Remember the end point is indicated by a permanent colour change of the indicator.

  5. The volume at the bottom of the meniscus is recorded.

  6. This process is repeated until a volume is repeated. If time is an issue, three titrations may be conducted and an average taken. The first titration (a rough titration) may be discounted from this process as it may be used to identify the approximate position and slow down the delivery of the titrant.

  7. This video shows you the proper technique for performing a titration.

    The reliable titre volumes are calculated and averaged. Reliable titre volumes should be within 0.1 mL of each other. The concentration of the solution is determined through a consideration of the stoiciometric ratios of the reacting acid and base.

  8. A titration can also be conducted using computer based technology. An alternative to using an indicator may be to use a pH probe attached to a data logger. The probe can be placed into a conical flask and as the titrant is added, you look for a sudden rise in pH. This will identify the equivalence point.



The basic equipment used to perform a titration.

In a nutshell, a titration involves adding a solution of an acid to another solution of a base until the neutralisation reaction is complete, at which point you stop adding acid (or vice versa). From the known concentration and volume of the standard solution and the volume of the unknown, you can calculate the concentration of the unkown.

Let's say that 25.00 mL of an unknown concentration of hydrochloric acid was placed in a conical flask. It required 12.50 mL a 0.150 mol L-1 solution of sodium hydroxide (which came from the burette) to neutralise it completely. This means that after 12.50 mL of sodium hydroxide was added, there was no more hydrochloric acid left and only a salt (sodium chloride) and water were present in the solution in the conical flask.

The equation for this reaction would be

HCl (aq) + NaOH (aq) → NaCl (aq) + H2O (l)

To work out the concentration of the acid we would

  1. Calculate the number of moles of sodium hydroxide that was delivered by the burette.

  2. Compare the molar ratios of sodium hydroxide and hydrochloric acid.

  3. Calculate the concentration of hydrochloric acid.

We would do this as follows:

  NaOH HCl
Volume 0.01250 L 0.0250 L
Number moles Step 2 - NNaOH : NHCl

1.88 x 10-3 mol
Concentration 0.150 mol L-1

In this example, the molar ratio of HCl to NaOH used in Step 2 of the calculations was 1:1. This ratio can change depending on the number of hydrogen ions the acid has available or the number of hydroxide ions the base provides. The following table shows a comparison of molar ratios for different combinations of acids and bases.

Acid Base Equation Nacid : Nbase
sodium hydroxide H2SO4 (aq) + 2NaOH (aq) → Na2SO4 (aq) + 2H2O (l) 1 : 2
phosphoric acid sodium hydroxide H3PO4 (aq) + 3NaOH (aq) → Na3PO4 (aq) + 3H2O (l) 1 : 3
hydrochloric acid calcium hydroxide 2HCl (aq) + Ca(OH)2 (aq) → CaCl2 (aq) + 2H2O (l) 2 : 1
calcium hydroxide H2SO4 (aq) + Ca(OH)2 (aq) → CaSO4 (aq) + 2H2O (l) 1 : 1

A video showing how to perform titration calculations.

All titrations based on neutralisation reactions require both an acid and a base. The solution of known concentration is called a standard solution. The solution whose concetration we are trying to determine is generally called the unknown. In doing calculations for titrations you should always follow these steps:

  1. Calculate the number of moles of the standard solution used using the fomular n = cV.

  2. Compare the molar ratios of the standard with the unknown to work out the number of moles of unknown solution required for neutralisation.

  3. Calculate the concentration of the unknown by using the formula c = n/V.

It should now clear to you how we use the data collected from a titration to determine the concentration of an unknown solution. Next we turn our attention to aspects of the titration procedure such as how we know when complete neutralisation has occurred and when to stop the titration and how to ensure that our data is valid and reliable.


Interpreting Titration Data

The titration curve (above) obtained from a
strong acid in the conical flask and a strong
base in the burette.

The titration curve (above) obtained from a
weak acid in the conical flask and a strong base
in the burette.

A titration curve is constructed by plotting data obtained during a titration with the volume of solution from the burette (titrant volume) on the x-axis and the pH of the mixture in the conical flask on the y-axis. The shape of the curve tells us a great deal about the chemistry of the process and provides an interesting summary of what we have learned so far about acids and bases.

Strong Acid and Strong Base

The titration of a strong acid with a strong base produces the titration curve shown on the right. Note the sharp transition region near the equivalence point (when the amount of hydroxide ions is in the equivalent stoichiometric ratio with hydrogen ions). Also remember that the equivalence point for a strong acid-strong base titration curve is exactly 7 because the salt produced does not undergo any hydrolysis reactions (more on this in the next section on the pH of salt solutions). From this graph, the pH of the equivalence point can be determined as being mid-way between the start and finish of the vertical section.

A suitable indicator for the titration would be one that has its pH range somewhere in the steepest part of the titration curve. This would be anything between pH = 3 and pH = 11.

Weak Acid and Strong Base

If a strong base is used to titrate a weak acid (below right), the pH at the equivalence point will not be 7. There is a lag in reaching the equivalence point, as some of the weak acid is converted to its conjugate base. A solution of a weak acid and its conjugate base acts as a buffer. Buffers act to resist changes in pH due to the addition of other acids or bases. In the graph, we see the resultant lag that precedes the equivalence point, called the buffering region. In the buffering region, it takes a large amount of base to produce a small change in the pH of the acid solution in the conical flask.

Because the salt produced in this neutralisation reaction is basic, the pH will be greater than 7 at the equivalence point. In this case the pH at the equivalence point is closer to 9. A suitable indicator for this titration would be one that is changing colour at pH = 9 such as phenolpthalein.

Similarly, titrations involving strong acids and weak bases will have equivalence points at a pH less than seven as shown in the curve below.

For a titration between a strong acid and a weak base the curve will look similar to that between a strong acid and a strong base. The only difference is that the equivalence point will occur at a pH of less than 7 because the salt produced is acidic. In such a titration an indicator such as methyl orange can be used as it changes colour in the acidic pH range.


Calculating pH

Paul Andersen explains pH as the power of hydrogen. He explains how
increases in the hydronium ion (or hydrogen ion) concentration can
lower the pH and create acids. He also explains how the reverse is
true. An analysis of a strong acid and strong base is also included.

Acids are characterised by the presence of hydrogen ions (H+) or more precisely hydronium (H3O+) ions in aqueous solutions. Bases are typically those compounds containing hydroxide (OH-) ions. The H+ ions of acids and the OH- ions of bases react with each other to form water, so acids and bases are said to neutralise each other. For this reason they are considered to be opposites. Here you will learn to measure and to express in concise terms the degree of acidity or basicity of solutions. The famed pH scale was devised precisely for this purpose.

Ionisation of Water

An understanding of acidity and basicity in water solutions is based on the concept of the ionisation of water. Pure water ionises in itself by a mere 0.000001 %. The self-ionisation is shown in the following equation.

H2O (l) + H2O (l) → H3O+ (aq) + OH- (aq)

For convenience, the hydronium ion iis often written as H+ and then the ionisation of water can be simplified to

H2O (l) → H+ (aq) + OH- (aq)

You can see from the equation that in pure water there are as many H+ ions as there are OH- ions. That is, the H+ ion concentration, [H+], and the OH- concentration, [OH-], are equal. The actual concentration of each is extremely small. In pure water these are both known experimentally to be only 1 x 10-7 (0.0000001) mol L-1.

[H+] = [OH-] = 1 x 10-7 mol L-1

In acid solution the H+ ion concentration is greater than 10-7 mol L-1 and the OH- ion concentration is less than that such that [H+] > [OH-].  In basic solution the opposite is true and OH- ions predominate such that [OH-] > [H+].

Thinking about the above relationship another way we could write

[H+] x [OH-] = 1 x 10-14 mol L-1

We will use this expression later to find out what the concentration of hydrogen ions is in a base such as calcium hydroxide.

pH Scale

Equations for calculating
pH or H+ concentration.

Based on our understanding of H+ and OH- ion concentrations in aqueous solutions, we are now ready to examine the meaning of the pH scale. This scale constitutes a highly convenient method for specifying the acidity (or basicity) of a solution. The pH is actually the power of the H+ ion concentration with its sign changed. A solution with an H+ ion concentration of 10-3 mol L-1 has a pH of 3. A pH of 6 means an H+ ion concentration of 10-6 mol L-1.

All pH values less than 7 indicate acidic solutions and all values greater than 7 indicate basic solutions. A neutral solution has a pH of 7 since the H+ and OH- ion concentrations are equal.  It should also be emphasised that each pH unit on the scale means a tenfold increase or decrease in H+ ion concentration from the previous number. Thus, a pH range of 0 to 14, for example, represents a range of concentration of H+ (or OH-) ions from 1 mol L-1 to 10-14 mol L-1 (from 1 to 0.00000000000001), a tremendous range.

The pH scale showing the concentration of hydronium (hydrogen) ions corresponding to pH values as well as the pH
of come common substances.

Let us consider an acid and a base in terms of calculations involving hydrogen and hydroxide concentrations and pH.

Substance [H+] mol L-1 [OH-] mol L-1 pH
0.15 mol L-1 HCl 0.15
0.15 mol L-1 Ca(OH)2 2 x 0.15 = 0.30

In this example you should note that to calculate the pH of a base where you do not know its hydorgen ion concentration, we must first calculate it using the expression for the self-ionisation of water.