Ionic Strength Dependence of ΔrH for the Reaction
H2O (l) → H+ (aq) + OH– (aq)
Adapted from an Exercise used at the University of Kansas by J. M. McCormick
Last Update: December 19, 2012
The autoionization of water, H2O (l) → H+ (aq) + OH+ (aq), is arguably one of the most important chemical reactions known. It is key to understanding many of water’s properties and is fundamental in the understanding of biological processes that depend on these properties. However, because ions are involved, the ionic strength of the solution in which the reaction occurs can play an important role. In this exercise you will use solution calorimetry to determine the enthalpy change, ΔrH, for the autoionization of water, and evaluate its dependence on ionic strength, by determiningΔrH for the neutralization reaction of a strong acid with a strong base (i. e., the reverse of the reaction of interest). See the Calorimetry Background page, and Atkins and de Paula1 for more information on enthalpy and the theory of calorimetry in solution.
A Parr solution calorimeter will be used in this experiment along with a Parr model 6772 calorimetry thermometer. Although the available calorimeters look different (the model 1451 calorimeter has a model 1661 calorimetry thermometer incorporated into the calorimeter), their basic construction and method of operation are the same. IMPORTANT! Read the operating instructions for both the calorimeter and the thermometer very carefully, beforecoming to the laboratory. These documents contain information that will not be duplicated here. Given the time constraints and the extreme fragility of parts (and cost) of the solution calorimeter your utmost attention to the instrument’s operational details is essential to successfully completing this exercise.
The dissolution of NH4Cl at 25 °C (ΔsolutionH = +14.77 ± 0.02 kJ/mole)2 will be used to determine the heat capacity of the calorimeter. A standard should be run between each sample and three standards should be run each period. If you work efficiently, you should be able perform six runs (three samples, three standards) during a three-hour laboratory period.
To run the standard, load the Dewar with ~100 g of distilled water (if done by weight, weigh to the nearest one hundredth of a gram, if done by volume use a 100-mL pipet). The rotating cell is to be loaded with ~1 g of finely-powdered (use a mortar and pestle), dry NH4Cl weighed to the nearest 0.1 mg. This endothermic reaction should produce a temperature decrease of ~0.5 °C.
To determine ΔrH for the reaction H2O (l) → H+ (aq) + OH– (aq), you will instead study the reverse reaction. Load the solution calorimeter Dewar with 100 ml of a 0.1 M HCl solution and load the rotating cell with 20 ml of a 0.5 M NaOH solution. Note that one of these solutions must be standardized, but that it is not critical that both solutions be standardized, as long as the standard solution is, without any doubt, the limiting reagent. The loading of the cell can be done by weight using the density values from Table 1. You will need to look up the nominal volume that the various volumetric pipets deliver, although you are certainly free to determine the actual volumes delivered by the pipets. Helpful hint: you can start data acquisition before the solutions are standardized.
|H2O (l)||4.1819||0.998 (20 °C)|
|4.1796||0.997 (25 °C)|
|0.996 (30 °C)|
|HCl (0.1 M)||4.150||1.001|
|HOAc (0.1 M)||4.171||0.999|
|NaOH (0.5 M)||4.075||1.020|
Table 1. Heat capacity and density data for the materials studied in this exercise. For solutions, the Cp values refer to a gram of solution. Assume uncertainties of ±1 in the last significant figure.
For either the standard or the neutralization reaction, record the temperature readings every 30 sec, or so, for about 5 min once the apparatus is completely assembled to establish the pre-mixing behavior. During this time you may observe a slight, but steady, temperature change (a slight increase, if the reactants are below room temperature, or a slight decrease, if the reactants are above room temperature). Once you feel that you have obtained a sufficient number of points to define the pre-mixing behavior, start the run by quickly pressing down on the push rod to release the reagent from the rotating cell. IMPORTANT! This operation should be done swiftly, but not violently. Use two hands for this operation (one to depress the rod and the other to steady the calorimeter’s cover). Note that the belt will slip during sample injection. Continue recording data throughout this process and for about 5 min after mixing has occurred to define the system’s behavior after mixing.
After each run, disassemble, clean and dry the calorimeter, as described in the operating instructions. Be extremely careful handling the sample bell, the push rod, and the Dewar; all are extremely fragile and expensive. It is advised that you examine your data after it is obtained (i. e., perform the analysis described below). Based on this analysis, adjust your data acquisition interval and the total acquisition time in maximize your precision while minimizing the total time spent on each run. By examining your data as you take it not only will you be able to more efficiently use your time, you will be able to spot any gross error and correct it immediately. When you are done for the day, clean and dry the calorimeter and return it and the its parts to the proper storage locations.
The ionic strength of the solution may be calculated from the concentrations and volumes of the reactants,3 even though the ionic strength is different for each reactant. Using logic similar to that for a change in temperature (see Calorimetry Background page), we can show that we only need to calculate the ionic strength in the final solution and consider the reaction to have taken place at that ionic strength (for the amount of reactants given above, the ionic strength is approximately 0.08). The ionic strength at which the reaction takes place can be changed in one of several ways. One way is simply by changing the concentrations of the HCl and NaOH in the initial solutions and using the same volumes as called for above. Note, however, that you may need to restandardize the new solutions in this approach and that there is a limit to the concentrations that you can use and still observe a meaningful ΔT. Another way is to change the volume of one, or both, of the solutions and compensating for the missing volume by adding the appropriate amount of distilled water to the calorimeter’s Dewar. Care must be taken in this approach that the limiting reagent remains the same at different ionic strengths (this is less of a problem when both solutions are standardized). The final way in which the ionic strength may controlled is to initially add a salt (e. g., NaCl) to the acid and base solutions so that the solution formed in the calorimeter will have the desired ionic strength. Alternatively, one could pipet a precisely known solution of the salt into the calorimeter’s Dewar before the reaction occurs. However, how best to study the effect of ionic strength on this reaction is left for you to determine.
Results and Analysis
Perform a linear regression on the pre- and post-mixing regions of the temperature as a function of time data and determine the change in temperature caused by the chemical reaction, ΔT, at the time of mixing for each run. From the NH4Cl standardization runs determine the heat capacity of the calorimeter, Cp(K), using the weights of H2O and NH4Cl. From the known value of Cp(K), determine ΔrH for the reaction of interest. At least one graph of a standardization run and one graph of a sample run are to be presented in your report. Report your value of ΔrH at 25 °C for the reaction studied along with the uncertainty at the 95% confidence level. Report the dependence of ΔrH on ionic strength, including the uncertainties at each ionic strength.
Your error analysis should include the propagation of the uncertainty in ΔT, the uncertainties for the values given in Table 1 and the enthalpy of solution of NH4Cl through to the final enthalpy values. Which parameter contributes the most to the uncertainty in the measured enthalpies?
Compare your results to literature values. Perform a significance test between your experimentally determined values and the literature values. Do your results agree with the literature? Suggest reasons for any possible systematic errors. In particular, consider the effects of solution concentrations.
1. Atkins, P. and de Paula, J. Physical Chemistry, 8th Ed.; W. H. Freeman: New York, 2006, p. 37-56.
2. Wagman, D. D.; Evans, W. H.; Parker, V. B.; Schumm, R. H.; Halow, I.; Bailey, S. M.; Churney, K. L. and Nuttall, R. L. J. Phys. Chem. Ref. Data 1982, 11.
3. Atkins, P. and de Paula, J. Physical Chemistry, 8th Ed.; W. H. Freeman: New York, 2006, p. 163-166.