Isothermal Titration Calorimetry in the Student Laboratory - American

In the Laboratory

Isothermal Titration Calorimetry in the Student Laboratory Lars Wadsö* and Yujing Li Division of Building Materials, Lund University, Box 118, 221 00 Lund, Sweden *[email protected] Xi Li Applied Chemistry, Wuhan University of Technology, Wuhan, Hubei, China

Titration is a common procedure in analytical chemistry and several titration experiments have been described in this Journal. Typically, these experiments involve the stepwise or continuous addition of one solution with a known concentration (the titrant) to a solution with an unknown concentration (the analyte) and the task is to determine the concentration of the latter. A typical example is the experiment presented by BelleOudry (1) that describes a method to determine the sulfate content of water. In student experiments, the endpoint of the titration is often determined visually with an indicator, but other techniques, for example, potentiometric and spectrometric techniques, may also be used. The most common titration is probably the strong acid-strong base titration in which the endpoint, when the pH passes 7, is visualized with an indicator. This article is about isothermal titration calorimetry (ITC), which is a titration technique in which the heat produced by the titration is measured. It is usually not used for quantitative analysis, but rather to investigate the thermodynamics of noncovalent interaction (binding). However, from well-designed ITC experiments, it is possible to evaluate stoichiometry, equilibrium constant, Gibbs energy, enthalpy, and entropy of a binding process. In contrast to other titration techniques, ITC is a general technique that can be used for all systems in which it is possible to stepwise add one component to the other. Two recent reviews (2, 3) describe ITC applications in diverse fields such as drug design, polymer chemistry, cellular biology, and nanotechnology. Of special interest is the use in structure-based drug design in which the drug-target interaction can be quantified by the binding thermodynamics (4, 5). ITC is the only experimental technique available that divides the binding energy into its enthalpic and entropic components (6) giving an insight into the molecular interactions. In a previous article in this Journal (7), we described the design of an isothermal (heat conduction) calorimeter for student experiments. The instrument is placed in an insulated box, but not actively thermostatted, as commercial calorimeters are. Here we describe a stirring device and a titration pump for use with this student calorimeter and the use of this instrumentation for titration experiments. These presented student experiments have been used in measurement technology courses for PhD-students in which the participants have different backgrounds (physical chemistry, food science, material science etc.). The Stirring Device For the titration experiments, stirring is necessary to bring the titrant in close contact with the analyte. We have managed

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Figure 1. Schematic of the arrangement of the stirring device in the isothermal calorimeter (described in ref 7). The four calorimeters, each with a sample holder and a reference holder, are placed in a metal box (10 mm aluminum) inside a box of insulation material (50 mm) (only half of which is shown). The magnets moving outside the sample ampule holders are shown fastened to the rod that is moved by the motor placed outside the insulation (see Figure 2).

this by using permanent magnets moving outside the ampoules containing the analyte and a Teflon-coated ball-shaped magnetic stirrer (Figure 1). Four small, but strong, neodymium magnets for the four calorimeters are fastened with short pieces of silicon tubing on a 4 mm cylindrical stainless-steel tube that slides on two brass bearings placed on the outside of the insulated box. An electrical motor with a gearbox (L149 21:1 6 V, Micro Motors SRL, Verderio Inferiore, Italy) is placed outside the insulation and is connected to the tube through a crankshaft (Figure 2). As the rod is made from a thin-walled stainless-steel tube, it has a low heat capacity and its movement through the insulation only slightly increases the noise level. The rocking (not rotating) motion of the magnets is not very efficient, but it gives sufficient mixing in the half-filled ampules used in the present experiments. The effectiveness of a stirrer is best tested by injecting some ink and visually studying the process. Two advantages with this arrangement are that it only uses one motor to stir multiple calorimeters and that it does not interfere with the injection device that normally accesses the reaction ampoules from above. Commercial ITC instruments usually have both the stirrer axis and the injection syringe (often combined into one unit) entering from above into the ampoule. Note that stirring produces heat from friction, but that this is not a problem as long as it is a constant thermal power.

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r 2010 American Chemical Society and Division of Chemical Education, Inc. pubs.acs.org/jchemeduc Vol. 88 No. 1 January 2011 10.1021/ed100649e Published on Web 10/25/2010

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Journal of Chemical Education

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In the Laboratory

Figure 2. Motor arrangement for the stirring. The motor (A) is fastened to a holder (D and E) that is fastened to the outside of the insulated box. A crankshaft (B) transfers the rotations to the stainless-steel tube (C) on which the magnets are fastened (Figure 1).

Figure 4. Result of a series of acid-base titrations. Each arrow shows the time of an injection. The heats evaluated by integrating the four peaks were 3.74, 3.64, 3.65, and 2.93 J. Table 1. Calculated Enthalpies for Acid-Base Titration Results from Student Groups Group A

Figure 3. The titration pump. A plastic ampule (A) is connected to a stainless-steel guide tube (B). The injections are made through a long needle (C) that is connected to a plastic syringe (D) containing the solution to inject. This syringe is fastened to an aluminum holder (E). The injections are made by rotating the screw (F) that pushes the syringe plunger.

Baselines for experiments with stirring should always be taken with the stirring on. If the viscosity (or the stirring rate) changes during an experiment, the baseline will also change. This is not a problem in the present types of titration measurements, but could be a problem in other applications, for example, if the viscosity of a polymer solution changes during the experiment. The Titration Pump For the titration measurements, a precise and accurate titration pump is needed. We built pumps using a long headless screw (10 mm diameter, 1 mm pitch). The arrangement is shown in Figure 3. Injections are made by rotating the screw whole turns or half turns. The screw presses on the syringe plunger and the liquid is injected through a long needle attached to a 1 mL disposable plastic syringe by a Luer-slip fitting. A 50 cm length of 0.4 or 0.5 mm stainless-steel tube serves as a guide to the ampoule. We have used 1 mL disposable plastic syringes with Luer-slip fittings. The syringes are calibrated (in μL/turn) by injecting water on a balance (our pumps have 16.4 μL/turn). Acid-Base Titration The neutralization reaction between a strong base and a strong acid is an example of a reaction with a large equilibrium constant. This reaction has a well-known enthalpy and is therefore often used as a test or calibration reaction in calorimetry (8). 102


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Vol. 88 No. 1 January 2011

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Enthalpy/(kJ/mol)a

Enthalpy/(kJ/mol)b

-55.8

-55.8

B

-52.4

-52.5

C

-59.1

-58.1

D

-55.2

Literature (25 °C)c

-54.9 -56.1

a Mean value from the first three peaks calculated from the amount of OHin each injection. b Calculated from the total amount of heat produced and the amount of H3Oþ in ampule. c Literature value taken from ref 8. Measurements were made at 20-25 °C.

In our experiment, about 10 mL of HCl (aq, 0.025 M) is placed in a plastic ampoule and neutralized by injections of 65.6 μL of NaOH (aq, 1 M) (four turns on our manual syringe pump, each turn giving 16.4 μL) every 40 min. Stirring is necessary and was accomplished as described above. As long as there is acid left in the ampoule, heat from the neutralization reaction will be released when base is injected, but when all acid is consumed at the neutralization point, no more heat will be measured. This will take place after about four injections as there is 250 μmol H3Oþ in the ampoule and every injection contains 65.6 μmol OH-. The results of the measurements made at about 21 °C (the calorimeter is unthermostated and will therefore have the temperature of the room where it is placed) are shown in Figure 4. The heats are determined by integrating each peak separately. As the neutralization is a 1:1 reaction, the enthalpy can be calculated either from the heat produced after each injection of a known amount of base or from the sum of the heats from all peaks as a known amount of acid is neutralized. Results generated from student groups in lab are listed in Table 1. Note also that one can determine both the reaction enthalpy and the concentration of one of the components if the concentration of the other is known. In this case, it is not possible to determine the equilibrium constant as it is very large (1014 at 25 °C). One complication with titration experiment is that the heat produced in an injection is the sum of two heats: the heat of dilution of the concentrated solution in the syringe and the heat from the reaction of interest. Therefore, a second titration

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r 2010 American Chemical Society and Division of Chemical Education, Inc.

In the Laboratory

experiment should be done to measure only the dilution heat. This is accomplished by performing an identical experiment, except that there is only water in the ampoule. Then, the heat of dilution can be subtracted from the acid-base reaction heat. However, for the concentrations and volumes used in the present acid-base experiment, the dilution enthalpy does not need to be taken into account, as it is small compared to the neutralization enthalpy. Binding Titration The second experiment described here is a typical binding experiment for which ITC is commonly used, for example, in pharmaceutical research. The macrocyclic crown ether 18-crown-6 (1,4,7,10,13,16-hexaoxacyclooctadecane) is a “cage molecule” (Figure 5) into which a Ba2þ ion (and other ions such as Kþ) can be noncovalently bound. The primary use of 18-crown-6 is as a catalyst, but it is also frequently used as a model compound in binding studies. Substances with cage structures can be used to catch small molecules that are attracted to the interior of the molecule. The most common example are zeolites that can be used, for example, to remove divalent ions (9) or organic vapors from air (10, 11). To calculate the binding enthalpy and the equilibrium constant, the resulting series of peaks should have a sigmoid shape. The first peaks should be high and then there should be a gradual decrease to lower values. The experiments were done at room temperature (about 22 °C) by stepwise injecting 65.6 μL of BaCl2 (aq, 1 M) solution into a polyethylene ampoule containing 10 mL of 18-crown-6 (aq, 0.020 M). Six injections were made with 15 min between the injections. With this time period between the injections, the peaks were not separated from each

other (Figure 6, left). However, the peaks can be separated from each other after the experiment by a mathematical procedure known as Tian correction (see eq 4 in ref 7 and the supporting information; the time constant is about 400 s for 10 mL aqueous solution in the present calorimeter) (Figure 6, right). Stirring is necessary and was accomplished as described above. The equilibrium constant K and the binding enthalpy ΔH are determined by finding the best fit to the measured data. In this experiment, it is important to correct for the heat of dilution of the concentrated BaCl2 solution. Although the binding has larger enthalpies than the dilution, a correction for the dilution will give results in closer agreement with literature values. The correction is made by doing a separate experiment with identical injections of BaCl2 (aq, 1 M) into water. The results of this heat of dilution experiment are then subtracted from the heats of the binding experiment (Table 2). The students simultaneously run the titration experiment and the dilution experiment in the four-channel student instrument. The evaluation is made by assuming a binding model, and then finding the K and ΔH that give the best fits to measured results. In the present case, the process is assumed to be a 1:1 binding (with 18-crown-6 called A, Ba2þ called B, and the complex of A and B called C): AþBhC ð1Þ The equilibrium constant K is K ¼

½C ½A½B

ð2Þ

and the heat produced, Q, in an experiment in which nC moles of C are formed is Q ¼ nC ΔH

ð3Þ

In the evaluation, we find the K and ΔH that best fit the results of the measurement. This can either be made by trial-and-error or by numerical optimization to minimize the sum of the squared errors for each injection X ð4Þ ðQi calc - Qi mea Þ2 where Qi are the heats, calculated and measured, produced at each injection, i.

Figure 5. The chemical structure of 18-crown-6.

Figure 6. The primary result of one Ba2þ to 18-crown-6 binding experiment (left) and the same data after the Tian correction (right). Note the different thermal power scales and that the peaks to the right have been separated from each other so that they can be integrated one by one. The result of a dilution experiment is also given in the lower curves (that have been shifted slightly downward).


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In the Laboratory Table 2. Measured Heats in a Ba2þ to 18-Crown-6 Titration Experiment and the Corresponding Dilution Experiment Measured Heats/J Injection number

Titration

Dilution

1

2.135

0.087

2

2.073

0.061

3

1.661

0.056

4

0.434

0.052

5

0.118

0.054

6

0.080

0.054

For the evaluation, by trial-and-error or by a numerical procedure such as the Nelder-Mead simplex method (12), Qicalc must be calculated for each titration step i by solving the following equation system written in terms of amounts (n) of substances nA þ nC ¼ nA 0

ð5Þ

nB þ nC ¼ i 3 nB inj

ð6Þ

K 3 nA 3 nB ¼ nC 3 V i

ð7Þ

where nA0 is the initial amount of A, i is the injection number, nBinj is the amount of B injected in each injection, and Vi is the volume after injection i. The equations are solved by inserting nA and nB from eqs 5 and 6 into eq 7, which gives the following second-order equation for nC: Vi ðnC Þ2 þ nA 0 - i 3 nB inj nC þ nA 0 3 i 3 nB inj ¼ 0 ð8Þ K This is solved for each titration step by the standard method for solving a second-order equation, (nc)2 þ k1nc þ k0 = 0; qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi - k1 ( ðk1 Þ2 - 4k0 ð9Þ nC ¼ 2 The heats generated by each titration can be calculated (using eq 3) as Qi calc ¼ ðnC i - nC i - 1 ÞΔH

ð10Þ

This is done for different values of K and ΔH until one finds values that give a good fit to the results. An example of the measured and calculated heats is given in Figure 7. Student results for the equilibrium constant and enthalpy found by least-squares optimization (eq 4) are given in Table 3 and are compared with literature values. It should be noted that it might seem more difficult to get a good value of the equilibrium constant than of the enthalpy. However, from the equilibrium constant, one can calculate the standard Gibbs energy ΔG° ΔG ° ¼ - RT ln K

ð11Þ

and Gibbs energy and enthalpy are comparable quantities, as is seen in the following fundamental relation: ΔG ° ¼ ΔH ° - T ΔS °

ð12Þ

Here we have assumed that the concentrations are low enough so that activity equals the concentration. Values of K, ΔG°, and ΔH are given in Table 3, and it is seen that the results we get with our simple arrangement compares well with the literature values

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Figure 7. The measured and calculated heats from one Ba2þ to 18-crown-6 experiment using the Tian correction, subtraction of dilution heats, and the calculation procedure described in the text. Table 3. Three Evaluations of the Equilibrium Constant K and the Binding Enthalpy ΔH from Student Groups Groupa

K/(L mol-1) ΔG°/(kJ mol-1)b ΔH°/(kJ mol-1)

A

7070

-22.0

-30.9

B

8740

-22.3

-33.8

C

10800

-22.8

-29.2

D

7300

-21.9

-29.6

Literature (25 °C)c

5900

-21.3

-31.4

a

Each result is the mean from two titrations experiments and one dilution experiment. b Gibbs energy ΔG° has been calculated from the equilibrium constants. c Literature values taken from ref 8.

measured with much more elaborate microcalorimetry (relative error is only 3 and 1.5% for ΔG° and ΔH°, respectively). Note also that from ΔH° and ΔG° we can calculate the binding entropy ΔS°. Hazards The calorimeter and the data logger are safe to use because they are only powered with low voltages through the USB computer connection. The motor used for the stirring arrangement is safe to use as it is so weak that you can easily stop it with your fingers. Concentrated sodium hydroxide solution is caustic; high temperatures result upon mixing sodium hydroxide with water. The strong hydroxide solution should be handled (filling, closing, and shaking of the vials) using protective coats, gloves, and safety glasses. The same applies to the hydrochloric acid solution. Both barium chloride and the crown ether should be handled with care as they are moderately toxic. Final Comment Isothermal titration calorimetry (ITC) is an advanced method used in, for example, pharmaceutical research, and it is fascinating that three important thermodynamic parameters (ΔH, ΔG°, and ΔS) can be calculated from one experiment. However, it should be noted that the described experiments are not trivial and are therefore best suited for university-level students. It is essential that the procedures given in the student's guide are followed so that the resulting data can be successfully evaluated (some common problems are discussed in the supporting information).


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In the Laboratory

Conclusions It is possible to perform isothermal calorimetric titration (ITC) experiments using a simple unthermostated heat conduction calorimeter and manual injection pumps. The results correlate well with literature values both for neutralization experiments (only enthalpy) and the tested binding experiment (equilibrium constant and enthalpy). Acknowledgment X.L. acknowledges the support of the Chinese Scholarship Council. Literature Cited 1. Belle-Oudry, D. Quantitative analysis of sulfate in water by indirect EDTA titration. J. Chem. Educ. 2008, 85 (9), 1269–1270. 2. Ababou, A.; Ladbury, J. E. A survey of the year 2004: literature on applications of isothermal titration calorimetry. J. Mol. Recognit. 2006, 19, 79–89. 3. Cliff, M. J.; Ladbury, J. E. A survey of the year 2002 literature on applications of isothermal titration calorimetry. J. Mol. Recognit. 2003, 16, 383–391. 4. Holdgate, G. A.; Ward, W. H. J. Measurements of binding thermodynamics in drug discovery. Drug Discovery Today 2005, 10 (22), 1543–1550.


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5. Ladbury, J. E. Isothermal titration calorimetry: application to structure-based drug design. Thermochim. Acta 2001, 380, 209–215. 6. Freire, E. Isothermal titration calorimetry: controlling binding forces in lead optimization. Drug Discovery Today: Technol. 2004, 1 (3), 295–299. 7. Wadsö, L.; Li, X. A simple rate law experiment using a custombuilt isothermal heat conduction calorimeter. J. Chem. Educ. 2008, 85 (1), 112–116. 8. Wadsö, I.; Goldberg, R. N. Standards in isothermal microcalorimetry (IUPAC technical report). Pure Appl. Chem. 2001, 73 (10), 1625–1639. 9. Coker, E. N.; et al. Experiments with zeolites at the secondary-school level: experience from The Netherlands. J. Chem. Educ. 1999, 76 (10), 1417–1419. 10. Chao, P.-Y.; et al. Study of molecular-shape selectivity of zeolites by gas chromatography. J. Chem. Educ. 2008, 85 (11), 1558–1561. 11. Cooke, J.; Henderson, E. J. Experiments for the undergraduate laboratory that illustrate the size-exclusion properties of zeolite molecular sieves. J. Chem. Educ. 2009, 85 (5), 606–609. 12. Nelder, J. A.; Mead, R. A simplex method for function minimization. Computer J. 1965, 7, 308–313.

Supporting Information Available Teachers and student guide to isothermal titration calorimetry; MATLAB files. This material is available via the Internet at http:// pubs.acs.org.


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Isothermal Titration Calorimetry in the Student Laboratory - American

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