A thermometric titration is one of a number of instrumental titration techniques where endpoints can be located accurately and precisely without a subjective interpretation on the part of the analyst as to their location. Enthalpy change is arguably the most fundamental and universal property of chemical reactions, so the observation of temperature change is a natural choice in monitoring their progress. It is not a new technique, with possibly the first recognizable thermometric titration method reported early in the 20th century (Bell and Cowell, 1913). In spite of its attractive features, and in spite of the considerable research that has been conducted in the field and a large body of applications that have been developed; it has been until now an under-utilized technique in the critical area of industrial process and quality control. Automated potentiometric titration systems have pre-dominated in this area since the 1970s. With the advent of cheap computers able to handle the powerful thermometric titration software, development has now reached the stage where easy to use automated thermometric titration systems can in many cases offer a superior alternative to potentiometric titrimetry.
Comparison between potentiometric and thermometric titrations Potentiometric titrimetry has been the predominant automated titrimetric technique since the 1970s, so it is worthwhile considering the basic differences between it and thermometric titrimetry.
Potentiometrically sensed titrations rely on a free energy change in the reaction system. Measurement of a free energy dependent term is necessary.
ΔG0 = -RT lnK (1)
Where: ΔG0 = change on free energy R = universal gas constant T = temperature in kelvins (K) or degrees Rankine (°R) K = equilibrium constant at temperature T ln is the natural logarithm function
In order for a reaction to be amenable to potentiometric titrimetry, the free energy change must be sufficient for an appropriate sensor to respond with a significant inflection (or "kink") in the titration curve where sensor response is plotted against the amount of titrant delivered.
However, free energy is just one of three related parameters in describing any chemical reaction:
ΔH0 = ΔG0 + TΔS0 (2)
where:
ΔH0 = change in enthalpy ΔG0 = change in free energy
ΔS0 = change in entropy
T = temperature in K
For any reaction where the free energy is not opposed by the entropy change, the enthalpy change will be significantly greater than the free energy. Thus a titration based on a change in temperature (which permits observation of the enthalpy change) will show a greater inflection than will curves obtained from sensors reacting to free energy changes alone.
Thermometric titrations
In the thermometric titration, titrant is added at a known constant rate to a titrand until the completion of the reaction is indicated by a change in temperature. The endpoint is determined by an inflection in the curve generated by the output of a temperature measuring device.
Consider the titration reaction:
aA + bB = pP (3)
Where:
A = the titrant, and a = the corresponding number of moles reacting B = the analyte, and b = the corresponding number of moles reacting P = the product, and p = the corresponding number of moles produced
At completion, the reaction produces a molar heat of reaction ΔHr which is shown as a measurable temperature change ΔT. In an ideal system, where no losses or gains of heat due to environmental influences are involved, the progress of the reaction is observed as a constant increase or decrease of temperature depending respectively on whether ΔHr is negative (indicating an exothermic reaction) or positive (indicating an endothermic reaction). In this context, environmental influences may include (in order of importance):
Heat losses or gains from outside the system via the vessel walls and cover; Differences in the temperature between the titrant and the titrand; Evaporative losses from the surface of the rapidly mixed fluid; Heats of solution when the titrant solvent is mixed with the analyte solvent; Heat introduced by the mechanical action of stirring (minor influence); and Heat produced by the thermistor itself (very minor influence).
If the equilibrium for the reaction lies far to the right (i.e. a stoichiometric equilibrium has been achieved), then when all analyte has been reacted by the titrant continuing addition of titrant will be revealed by a sharp break in the temperature/volume curve. Figures 1a and 1b illustrate idealized examples.
The shape of experimentally obtained thermometric titration plots will vary from such idealized examples, and some of the environmental influences listed above may have impacts. Curvature at the endpoint might be observed. This can be due to insensitivity of the sensor or where thermal equilibrium at the endpoint is slow to occur. It can also occur where the reaction between titrant and titrand does not proceed to stoichiometric completion. The determinant of the degree to which a reaction will proceed to completion is the free energy change. If this is favourable, then the reaction will proceed to be completion and be essentially stoichiometric. In this case, the sharpness of the endpoint is dependent on the magnitude of the enthalpy change. If it is unfavourable, the endpoint will be rounded regardless of the magnitude of the enthalpy change. Reactions where non-stoichiometric equilibria are evident can be used to obtain satisfactory results using a thermometric titration approach. If the portions of the titration curve both prior to and after the endpoint are reasonably linear, then the intersection of tangents to these lines will accurately locate the endpoint. This is illustrated in Figure 2.
Consider the reaction for the equation aA + bB = pP which is non-stoichiometric at equilibrium. Let A represent the titrant, and B the titrand. At the beginning of the titration, the titrand B is strongly in excess, and the reaction is pushed towards completion. Under these conditions, for a constant rate of titrant addition the temperature increase is constant and the curve is essentially linear until the endpoint is approached. In a similar manner, when the titrant is in excess past the endpoint, a linear temperature response can also be anticipated. Thus intersection of tangents will reveal the true endpoint.
An actual thermometric titration plot for the determination of a strong base with a strong acid is illustrated in Figure 3.
The most practical sensor for measuring temperature change in titrating solutions has been found to be the thermistor. Thermistors are small solid state devices which exhibit relatively large changes in electrical resistance for small changes in temperature. They are manufactured from sintered mixed metal oxides, with lead wires enabling connection to electrical circuitry. The thermistor is encapsulated in a suitable electrically insulating medium with satisfactory heat transfer characteristics and acceptable chemical resistance. Typically for thermistors used for chemical analysis the encapsulating medium is glass, although thermistors encapsulated in epoxy resin may be used in circumstances where either chemical attack (e.g., by acidic fluoride-containing solutions) or severe mechanical stress is anticipated. The thermistor is supported by suitable electronic circuitry to maximize sensitivity to minute changes in solution temperature. The circuitry and the design of Metrohm's digital Thermoprobe, when used in combination with the OMNIS titrator, enables the detection of temperature changes as small as 10−5 K.
A critical element in modern automated thermometric titrimetry is the ability to locate the endpoint with a high degree of reproducibility. It is clearly impractical and insufficient for modern demands of accuracy and precision to estimate the inflection by intersection of tangents. This is done conveniently by derivatization of the temperature curve. The second derivative essentially locates the intersection of tangents to the temperature curve immediately pre- and post- the breakpoint.
Thermistors respond quickly to small changes in temperature such as temperature gradients in the mixed titration solution, and thus the signal can exhibit a small amount of noise. Prior to derivatization it is therefore necessary to digitally smooth (or "filter") the temperature curve in order to obtain sharp, symmetrical second derivative "peaks" which will accurately locate the correct inflection point. This is illustrated in Figure 5. The degree of digital smoothing is optimized for each determination, and is stored as a method parameter for application every time a titration for that particular analysis is run.
Because enthalpy change is a universal characteristic of chemical reactions, thermometric endpoint sensing can be applied to a wide range of titration types, e.g.
Acid/base Redox Complexometric (EDTA) and Precipitation
Further, since the sensor is not required to interact with the titration solution electrochemically, titrations in non-conducting media can be performed, as can titrations using reactions for which no convenient or cost-effective potentiometric sensor is available.
Thermometric titrations generally demand rapid reaction kinetics in order to obtain sharp reproducible endpoints. Where reaction kinetics are slow, and direct titrations between titrant and titrand are not possible, indirect or back-titrations often can be devised to solve the problem.
Catalytically enhanced endpoints can be used in some instances where the temperature change at the endpoint is very small and endpoints would not be detected satisfactorily by the titration software.
The suitability of a particular chemical reaction as a candidate for a thermometric titration procedure can generally be predicted on the basis of the estimated amount of analyte present in the sample and the enthalpy of the reaction. However, other parameters such as the kinetics of the reaction, the sample matrix itself, heats of dilution and losses of heat to the environment can affect the outcome. A properly designed experimental program is the most reliable way of determining the viability of a thermometric titration approach. Successful applications for thermometric titrations are generally where titrant-titrand reaction kinetics are fast, and chemical equilibria are stoichiometric or nearly so.
Where thermometric titration determinations may be recommended The analyst wishes to simplify the conduct of a variety of titrations by using one sensor for all. For example, a laboratory might conduct routinely acid/base, redox, complexometric, sulfate and chloride titrations. A single thermometric sensor in conjunction with an autosampler will enable all titrations to be performed in the same carousel load without having to change titration sensors. After preparation of the samples and placing in the carousel, the analyst assigns the appropriate thermometric method to the beaker position in the carousel.