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Have you ever wondered why your titration results are not reproducible? This blog post discusses the most common random and systematic errors that can happen during a titration. It should serve as a guide to help identify and minimize the sources of these errors in titration experiments.

## Introduction

Titration, a common technique to analyze the content of a substance, was invented back in the 18th century. In brief, it is performed manually by using a glass buret (filled with a titrant) and either a beaker or Erlenmeyer flask which contains the sample.

The main sources of error during manual titration are parallax errors, visual perception, and the choice of the buret size. In modern times, these errors are often overcome by switching from manual titration to using autotitration. However, there are still some norms and standards which require the use of manual titration.

## Sources of errors in titration

What is needed to perform a titration? For manual titration only a buret, a beaker or Erlenmeyer flask, and an indicator are required. Error sources mainly come from the precision of the buret, the indicator, and from the titrant. These individual errors can add up to approximately ±0.2 mL which could be quite large depending on the volume of the endpoint.

We will take a closer look at the most common errors in the next sections.

## Systematic errors in titration

Systematic errors are errors which can be avoided by meeting certain requirements. These kinds of errors are identifiable and can be fixed.

Common systematic errors include a change in temperature, standardization, choice of the indicator, parallax errors, and the choice of the buret volume. These errors are discussed in more detail below.

Temperature plays an important role, especially during an analysis series. Each solution has a specific coefficient of thermal expansion. The coefficient is defined as such:

#### V = V0 ∙ (1 + γ ∙ ∆T)

Where V corresponds to the volume at a certain temperature, V0 to the nominal volume, γ to the coefficient of thermal expansion (in 10-3K-1), and ∆T corresponds to the temperature difference between the temperature of the nominal volume (V0) and the measured temperature (in K).

Depending on the thermal expansion coefficient (γ), keeping the temperature of the solution constant could be a critical point. For example, n-hexane has a coefficient of 1.35. Assuming the solution is 1.000 L at 20 °C and the ambient surroundings are 25 °C, the volume of the solution is 1.007 L at this temperature. This corresponds to an error of 0.7%.

Therefore, the coefficient of thermal expansion for a solution may be an important enough factor to regulate the temperature in the laboratory to obtain reproducible results.

Titer determination is often neglected and the nominal value which is written on the bottle is then used for titration. This might be an option for certain titrant solutions. However, many titrants still require this step to avoid large errors in the results.

In general, the titer determination is a part of the analysis and should be performed regularly. When using stable acids and bases, the titer determination can be performed on a weekly basis. For other titrants like iodine or DPIP (dichlorophenolindophenol), the titer determination should be done daily, as the titer concentration reduces significantly with exposure to UV radiation or reaction with oxygen.

What to consider when standardizing titrant

Figure 1. Titration curve of TRIS with HCl. The pink line shows the pH value where the phenolphthalein indicator changes color while the green line shows the pH value where the indicator should ideally change its color.

Choosing the proper indicator is essential for an accurate and reliable analysis. Figure 1 shows an example titration curve of TRIS (tris(hydroxymethyl)aminomethane) with hydrochloric acid.

TRIS is used for the titer determination of HCl. If phenolphthalein is used as the indicator in this situation, the endpoint would be observed at pH 8.2. This would correspond to an endpoint volume of approximately 2 mL instead of 8 mL.

For correct results, this analysis requires an indicator which changes its color at approximately pH 5. In this case the more proper choice of indicator would be either methyl red or methyl orange.

Recognition of endpoints (EP)

Figure 2. Parallax error occurs if the user reads the buret values from different angles.

The parallax error occurs if the laboratory analyst does not look at the meniscus horizontally, but from an angle. In this case, readings are different depending on the reading angle (Figure 2).

Many people do not really consider the buret size when preparing for a titration. They just take the largest buret in stock and carry out the analysis.

However, the error introduced by using too large of a buret can contribute to poor result quality.

For example, 10 mL burets normally have a tolerance of ±0.02 mL and for 50 mL burets there is a tolerance of ±0.05 mL. To carry out a precise analysis, you must take care to use the appropriate buret size.

Systematic errors are not the only ones which can occur during a titration. There are always random errors as well which are more difficult to handle. The most common random errors in titration are discussed in the next section.

## Random errors in titration

Random errors are errors which occur by chance and not always with the same specificity. They are harder to identify than the systematic errors.

In the following sections, some examples of random errors are shown including contamination, air bubbles in the buret, absorption of gases, and visual perception

Contamination is always a problem waiting to occur. It might happen e.g., when cleaning the beaker after titration, or if the cleaning solution was not properly eliminated after washing. Additionally, there is always the possibility that some sample adhered to the glass and could not be removed properly. These issues can lead to a significant titration error.

Figure 3. Left: a buret with air bubbles inside. Air bubbles such as these can lead to errors in the results if they are released during a titration. Therefore, ensure that no air bubbles are contained in the buret. Right: a properly filled buret without air bubbles.

This is a random error which is very easily circumvented.

When filling the glass buret, observe if any air bubbles are present at the outlet. If so, open the valve several times to ensure that no more air bubbles are present in the glass tube.

Depending on the size of the air bubble, this can lead to significant errors.

There are many titrants which have an affinity for the absorption of gases. For example, sodium hydroxide absorbs carbon dioxide from ambient air. A small amount of the sodium hydroxide forms sodium carbonate, thereby reducing the concentration of the titrant.

If the titer determination is not performed regularly, this leads to additional errors. Nevertheless, there are some materials which can be packed in an absorption tube to prevent such reactions and errors from happening. Some of these materials are listed in Table 1.

Table 1. Commonly used absorption tube packing materials and their uses.
Filling material Protective use against
Molecular sieve Water
Soda lime Carbon dioxide
Cotton Dust
Figure 4. Titration of HCl with NaOH and phenolphthalein as indicator. Each picture differs only in the addition of one drop of NaOH.

Everyone experiences colors and color intensity differently. This can lead to slight deviations depending on the person carrying out the titration. An example is shown in Figure 4. The colors obtained in these images (1–5) differ only by the addition of one drop of sodium hydroxide.

The question arises where the «correct» endpoint should be chosen out of the five images. If this is not handled the same way by different users, then the precision of the results will suffer.

Automated liquid handling – The key to accurate and reproducible results

## How autotitration can reduce errors

Most of the errors discussed in this article can be circumvented by switching to automated titration.

There is generally a much higher resolution for dosing steps when using autotitrators which makes volume measurement and results more accurate and reproducible. A sensor is used to objectively detect the equivalence point so there is no need to depend on individual perception of an indicator’s color change.

Out of all of the types of errors discussed in this article, only two need to be considered when applying autotitration: those related to temperature and air bubbles. Most automatic titrators offer an option to automatically prepare the tubing, eliminating any remaining bubbles before analysis. Temperature sensors can be connected to most autotitrators so that the temperature compensation can be done automatically.

There are so many benefits when switching from manual titration to autotitration. Find out more below!

How to Transfer Manual Titration to Autotitration

Manual vs. Automated Titration: Benefits and Advantages to Switching

## Conclusion

Titration is a very reliable, accurate, and easy-to-use analysis method. However, care must still be taken to avoid or eliminate different error sources. Systematic errors can easily be eliminated by meeting certain requirements, while random errors are more difficult to identify and to avoid.

By using autotitration in the lab, most of the errors discussed in this article are of no more concern. Additionally, automated titration saves time and gives users more accurate and reproducible results.

## Manual vs. Automated Titration: Benefits and Advantages to Switching

Titration is one of the most commonly used analytical methods. Manual, semiautomated, and fully automated titrations are well-known options and are examined in detail in several academic studies. This White Paper summarizes the advantages and benefits of automated titration in comparison to manual titration. The increase in accuracy and precision of measurements as well as significant time and cost savings are discussed.