Titration FAQ – Molarity Equation, Curve, Calculation, & more

Titration is an analytical technique which allows the quantitative determination of a specific substance (analyte) dissolved in a sample. It is based on a complete chemical reaction between the analyte and a reagent (titrant) of known concentration which is added to the sample:

Analyte + Reagent (Titrant) = Reaction Products

A well-known example is the titration of acetic acid (CH₃COOH) in vinegar with sodium hydroxide, NaOH:

CH₃COOH + NaOH → CH₃COO^- + Na⁺ + H₂O

The titrant is added until the reaction is complete. In order to be suitable for a determination, the end of the titration reaction has to be easily observable. This means that the reaction has to be monitored (indicated) by appropriate techniques, e.g. potentiometry (potential measurement with a sensor) or with colour indicators. The measurement of the dispensed titrant volume allows the calculation of the analyte content based on the stoichiometry of the chemical reaction. The reaction involved in a titration must be fast, complete, unambiguous and observable.

• To learn more download the Handbook Basics of Titration

Titration curves illustrate the qualitative progress of a titration. They allow a rapid assessment of the titration method. A distinction is made between logarithmic and linear titration curves.

The titration curve has basically two variables:

The volume of the titrant as the independent variable. The signal of the solution, e.g. the pH for acid/base titrations as the dependent variable, that depends on the composition of the two solutions.

The titration curves can take 4 different forms, and should be analysed with the appropriate evaluation algorithms. These four forms are: the symmetric curve, asymmetric curve, the minimum/maximum curve, and the segmented curve

• Download - Handbook Basics of titration to see all curves explained in detail
   

Acid-base titration is a quantitative analysis used to determine the concentration of an unknown acid or base solution by adding measured volumes of a known base or acid titrant that neutralizes the analyte.

In the titration of an acid HA with a strong base (e.g. NaOH) the following two chemical equilibria occur:

Acid-base reactions are very fast, and the chemical equilibrium is established extremely rapidly. Acid-base reactions in aqueous solutions are thus ideal for titrations. If the solutions used are not too dilute, the shape of the titration curves depends only on the acidity constant K_a.

• To learn more download the Handbook Basics of Titration

The amount-of-substance concentration of a solution of an entity X (symbol c(X)) is the amount of substance n divided by the volume V of the solution.

N is the number of molecules present in the volume V (in litres), the ratio N/V is the number concentration C, and N_A is the Avogadro constant, approximately 6.022×10²³ mol⁻¹.

The usual units employed in analysis are mol/L and mmol/L.

Endpoint titration mode (EP):

The endpoint mode represents the classical titration procedure: the titrant is added until the end of the reaction is observed, e.g., by a colour change of an indicator. With an automatic titrator, the sample is titrated until a predefined value is reached, e.g. pH = 8.2.

Equivalence point titration mode (EQP):

The equivalence point is the point at which the analyte and the reagent are present in exactly the same quantities. In most cases it is virtually identical to the inflection point of the titration curve, e.g. titration curves obtained from acid/base titrations. The inflection point of the curve is defined by the corresponding pH or potential (mV) value and titrant consumption (mL). The equivalence point is calculated from the consumption of titrant of known concentration. The product of concentration of titrant and the titrant consumption gives the amount of substance which has reacted with the sample. In an autotitrator the measured points are evaluated according to specific mathematical procedures which lead to an evaluated titration curve. The equivalence point is then calculated from this evaluated curve.

In a back titration we use two reagents – one that reacts with the original sample (A) and a second, that reacts with the first reagents (B).

First, a precisely measured excess of reagent A is added to the sample. After the reaction ends, the remaining excess of reagent A is then back titrated with a second reagent B. The difference between the added amount of the first and second reagent then gives the equivalent amount of the analyte. The back titration is used mainly in cases where the titration reaction of the direct titration is too slow or direct indication of the equivalence point is unsatisfactory. For example, for calcium content determination using reagents EDTA (A) and ZnSO₄ (B)

• Classical, well-known analytical technique
• Fast
• Very accurate and precise technique
• High degree of automation possible
  
• Good price/performance ratio compared to more sophisticated techniques
• It can be used by low-skilled and trained operators
• No need for highly specialised chemical knowledge

There are several assay reactions which are used in titration:

Acid/Base reactions:

Examples: Acid content in wine, milk. Acid content in ketchup. Content of inorganic acids like sulfuric acid.

Precipitation reactions:

Examples: Salt content in crisps, ketchup and food; Silver content in coins, Sulfate content in mineral water; Sulfate content in electroplating bath

Redox reactions:

Examples: Content of copper, chromium and nickel in electroplating baths

Complexometric reactions:

Examples: Total hardness of water (Mg and Ca); Calcium content in milk and cheese; Cement analysis

Colloidalprecipitation reaction:

Examples: Anionic surfactant content in detergents; Anionic surfactant content in washing powders; Anionic surfactant content in liquid cleanser.

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Titrations can be classified according to the indication principles and the chemical reaction occurring:

Potentiometry:

The direct measurement of the galvanic potential developed by an electrode assembly is called potentiometry, while the performance of a titration by use of this method is referred to as a potentiometric titration.

The potential U that develops should be measured, if at all possible, at zero current with a high impedance signal amplifier for the following reasons:

• The basis of potentiometry is the Nernst equation, derived for sensors in chemical and electrical equilibrium. An excessive current flow across the phase boundary surfaces concerned would disturb this equilibrium.
  
• A further reason for use of a high impedance measuring input results from the special construction of pH and ion-selective electrodes. The measuring circuit includes the ion-selective membrane, whose electrical resistance can easily be 100–1000 MΩ. If the experimental error due to the voltage divider effect is to be kept below 0.1%, the input impedance of the measuring instrument should be at least 1000 times higher. This can be seen from the following equation:
  

For very high resistance sensors, signal amplifiers with an input impedance of 10¹² Ω are thus necessary.

Voltametry:

This indication technique involves the measurement of the potential difference between two metal electrodes that are polarized by a small current. As in the case of potentiometry, the voltametric titration curve is a potential-volume curve.

The following measuring equipment is needed:

The stabilized power supply source provides the current. The resistance R connected in the circuit must be selected such that a current Ipol can be generated in the range 0.1 – 20 μA. The potential U that develops between the electrodes is measured exactly as in potentiometry. One of the main applications of voltametric indication is the determination of water by the Karl Fischer method.

Photometry:

The basis of photometric indication is the decrease in intensity at a particular wavelength of a light beam passing through a solution. The transmission is the primary measured variable in photometry and is given by

T: Transmission

I₀: Incident light intensity

I: Transmitted light intensity

If all light is absorbed, then I = 0 and hence T = 0. If no light is absorbed,

I = I₀ and T = 1 (or %T = 100%).

In photometry, work is frequently performed using absorption as the measured variable. The relation between transmission and absorption is described by the Bouguer- Beer-Lambert Law:

A = − log T = A = ε · b · c

A: Absorption

ε: Extinction coefficient

c: Concentration of the absorbing substance

d: Path length of the light through the solution

From the above relation it can be seen that there is a linear relation between absorption A and concentration c.

In comparison with potentiometric sensors, photoelectric sensors have a number of advantages in titration:

• they are easier to use (no refilling of electrolyte solutions, no clogging of the junction)
  
• longer lifetime (they are virtually unbreakable)
  
• they can be used to perform all classical titrations to a color change (no change in traditional procedures and standards).
  

Photometric indication is possible for many analytical reactions:

• Acid-base titrations (aqueous and nonaqueous)
  
• Complexometry
  
• Redox titrations
  
• Precipitation titrations
  
• Turbimetric titrations
  

In phototitration a wavelength should be selected which gives the greatest difference in transmission before and after the equivalence point. In the visible region such wavelengths are usually in the range 500 to 700 nm.

Examples of use: Complexometric and turbidimetric reactions.

Conductivity:

Conductivity is the ability of a solution let a current pass through. The measuring unit of conductivity are µS/cm (microsiemens/centimeter) or mS/cm (millisiemens/centimeter). A high value indicates a high number of ions. The amount of current flowing in the solution is proportional to the amount of ions. If we know the conductivity of a solution, we can get an idea of the total content of ions. Moreover if the ions are known, even a statement about their concentration can be made.

To measure conductivity a voltage is applied across two plates immersed in the solution. The plates are metallic, or graphite poles can be used as well. While the solved ions will start to move towards the plates the electric current will flow in between the plates.

The principle of conductometric titration.

During the titration, one of the ions is replaced by the other and invariably these two ions differ in the ionic conductivity with the result that conductivity of the solution varies during the course of titration. Therefore, if you add a solution of one electrode to another, the final conductance will rely on the occurrence of reaction. But if there is no chemical reaction in the electrolyte solutions, there will be an increase in the level of conductance. The equivalence point may be located graphically by plotting the change in conductance as a function of the volume of titrant added.

Thermometric Titration:

The elementary statement, that every chemical reaction is accompanied by a change in energy, is precisely what constitutes the basis of thermometric titration. During endothermic reactions, energy is absorbed and a temperature drop is observed. The opposite is true for exothermic reactions where energy is released. The equivalence point (EQP) of a titration can be detected by monitoring the change in temperature (Figure 1). In the course of an exothermic titration, the temperature increases until the EQP is reached. After that, the temperature initially stabilizes, followed by a subsequent temperature drop. The opposite happens for endothermic titration

As described above, a temperature decrease is observed during the course of the endothermic titration reaction. Once the equivalence point has been reached, the temperature stabilizes. The endpoint is determined by calculating the second derivative of the curve (segmented evaluation).

The only requirements of a thermometric titration are: a chemical reaction with a large energy change, a precise and fast thermometer and a titrator capable of performing a segmented evaluation of the titration curve.

• Learn more about Thermometric Titration

Coulometric titration

The technique of coulometric titration was originally developed by Szebelledy and Somogy [1] in 1938. The method differs from volumetric titration in that the titrant is generated in situ by electrolysis and then reacts stoichiometrically with the substance being determined. The amount of substance reacted is calculated from the total electrical charge passed, Q, in coulombs, and not, as in volumetric titration, from the volume of the titrant consumed.

• Learn more about coulometric titration, read our article on UserCom 7

A non-comprehensive listing of industries using titration:

• Car Manufacturing, Ceramics, Chemical industry, Coal products, Coating, Cosmetics
  
• Detergents
  
• Electronic, Electroplating, Energy, Explosives
  
• Food & Beverage
  
• Glass, Government
  
• Health
  
• Leather
  
• Machinery
  
• Packing materials, Paints, Pigments, Paper&Pulp, Petroleum, Pharmaceuticals, Photo, Plastic products, Printing & Publishing
  
• Rail, Rubber
  
• Stone (Clay, Cement)
  
• Textile, Tobacco
  
• Water
  
• Zeolite

Incremental titrant addition (INC)

The titrant is added in constant volume increments dV. Incremental titrant addition is used in non-aqueous titrations, which sometimes have an unstable signal, and also in redox and in photometric titrations, where the potential jump at the equivalence point occurs suddenly. Notice that in the steepest region of the curve there are relatively few measured points.

Dynamic titrant addition (DYN)

A constant pH- or potential change per increment allows the variation of the volume increment between minimum and maximum volume increment.
Thus, the analysis can be speeded up by using big increments in the flat regions of the titration curve. In addition, more measured points are obtained in the steepest region of the curve leading to a more accurate evaluation.

This discrepancy in results is primarily noticeable when performing acid/base titrations using one of the pH indicators. The first reason for this is that these pH indicators change color over a pH range rather than at a fixed value. The actual point at which the color change occurs is very much sample dependant and may not coincide with the chemical equivalence point. This can result in a small discrepancy in result which is easily nullified by standardizing the titrant using a similar method as is used for samples.

The second reason for this difference is primarily one of the sensitivity of the human eye to color change. While a color change may have already started to occur, the human eye has still not detected any change. This can be demonstrated by using a photometric sensor such as the METTLER TOLEDO DP5 phototrodes. Using one of these sensors there is a clear change in light transmittance long before the human eye detects any color change. In the typical acid/base titration using potentiometric indication with a pH sensor, the sharp change in signal occurs at the first trace of excess acid (or base) and is therefore a more true indication of the end point.

Generally there are three main electrode problems when performing a non-aqueous titration. The first is the problem of having an aqueous electrolyte with a non-aqueous solvent. Replacing the electrolyte in the electrode easily solves this. The second problem relates to the fact that the sample is non-conductive, resulting in a poor electrical circuit between measuring and reference half-cells or parts of the electrode if combined. This results in a noisy signal, particularly when using a sensor with a standard ceramic junction in the reference. A partial solution to this problem is to use a sensor with a sleeved junction, such as the DG113 electrode. This sensor has LiCl in ethanol as the standard electrolyte and, rather than a ceramic junction, has a polymer sleeve resulting in a larger contact area between working and reference parts and therefore lower noise.

The third problem is not a problem of the electrode itself, but rather the handling of the sensor. In order for a glass (pH) sensor to function correctly, it is necessary that the glass membrane (bulb of electrode) is hydrated. This is achieved by conditioning the electrode in deionized water. During the non-aqueous titration this membrane is gradually dehydrated reducing the response of the electrode. To prevent this or rectify this problem the electrode should be regularly reconditioned by soaking in water.

Naturally, this depends on the stability of the titrant and on what measures have been taken to protect the titrant from the typical contaminants that could cause a reduction in concentration. The most common examples of this titrant protection are the storage of light sensitive titrants in dark bottles e.g. iodine solutions, the protection of Karl Fischer titrants from moisture using e.g. molecular sieve or silica gel, and the protection of certain strong bases e.g. sodium hydroxide, from absorption of carbon dioxide.

• Download - Handbook Basics of titration to see all curves explained in detail

Automated titrators are microprocessor-controlled instruments which allow the automation of all operations involved in titration:

1. Titrant addition
2. Monitoring of the reaction (Signal acquisition)
3. Recognition of the endpoint
4. Data storage
5. Calculation
6. Results storage
7. Transfer of data to printer or computer/external system

Automated titrators follow a defined sequence of operations. This sequence is basically the same for all different models and brands. It is performed and repeated several times until the endpoint or the equivalence point of the titration reaction is reached (titration cycle). The titration cycle consists mainly of 4 steps:

1. Titrant addition
2. Titration reaction
3. Signal acquisition
4. Evaluation

Each step has different specific parameters (e.g. increment size) which have to be defined according to the specific titration application. More complex applications require more steps, e.g. dispensing of an additional reagent for back titrations, dilution, adjusting of the pH value. These steps and the corresponding parameters are resumed in a titration method.

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The classical way:

Titration is a classical analytical technique widely used. Originally, it was performed by adding the titrant using a graduated glass cylinder (burette). With a tap the titrant addition was regulated manually. A change in colour indicated the end of the titration reaction (endpoint). At first, only those titrations showing a significant colour change upon reaching the endpoint were performed. Later titrations were coloured artificially with an indicator dye. The precision achieved depended mainly on the chemist's skills and, in particular, on his different colour perception.

The modern way:

Titration has experienced a strong development: manual and -later- motorized piston burettes allow reproducible and accurate titrant addition. Electrodes for potential measurement replace the colour indicators, achieving higher precision and accuracy of the results. Graphical plot of potential versus titrant volume allows a more exact statement about the reaction than the colour change at the endpoint. With microprocessors the titration can be controlled and evaluated automatically. This represents a relevant step towards complete automation.

Today and tomorrow:

Development is not yet complete. Modern autotitrators allow the definition of complete analysis sequences achieving maximum flexibility in method development. For each application the specific method can be defined by combining simple operation functions like "Dose", "Stir", "Titrate", "Calculate" in a defined sequence. Auxiliary instruments (sample changers, pumps) help in reducing and simplifying the work load in laboratories. A further trend is the connection to computers and Laboratory Information Management Systems (LIMS).