Adapted from an Exercise used at the University of Kansas by J. M. McCormick
Last Update: November 18, 2008
Introduction
The autoionization of water 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. Because ions are formed in the reaction, 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 for the reaction H+ (aq) + OH+ (aq) → H2O (l) and evaluate its dependence on ionic strength (and therefore, the enthalpy change for the autoionization of water and its dependence on ionic strength). See the Calorimetry Background page, and Atkins and de Paula1 for more information on enthalpy and the theory of calorimetry in solution.
Procedure
The Parr model 1451 solution calorimeter will be used in this experiment along with a Parr model 6772 calorimetry thermometer.
The dissolution of NH4Cl at 25 °C (ΔsolutionH = +15.21 ± 0.02 kJ/mole) will be used to determine the heat capacity of the calorimeter. A standard should be run between each sample and at least two, and preferably three, standards should be run each 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, dry NH4Cl weighed to the nearest 0.1 mg. This endothermic reaction should produce a temperature decrease of ~0.5 °C.
To evaluate the molar enthalpy change, ΔrH, for the reaction H2O (l) → H+ (aq) + OH- (aq), you will study the reaction of HCl with NaOH. 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 the limiting reagent. The loading of the cell can also be done by weight using the density values from Table 1. It is also possible to determine the actual volumes delivered by the pipets by measuring the mass of the solutions delivered volumetrically. Perform at least three calorimetry runs for this reaction during the first week. Helpful hint: you can start data acquisition before the solutions are standardized.
| Substance | Cp (J·K-1·g-1) | Density (g·ml-1) |
| H2O (l) | 4.184 | 0.998 (20 °C) |
| 0.997 (25 °C) | ||
| 0.996 (30 °C) | ||
| NH4Cl (s) | 1.573 | |
| 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.
The ionic strength of the solution may be calculated from the concentrations and volumes of the reactants,2 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. Therefore, the ionic strength at which the reaction takes place can be changed by changing the concentrations of the HCl and NaOH in the initial solutions. Note that one of the solutions (the limiting reagent) must be precisely known and that there is a limit to the concentrations that you can use and still observe a meaningful ΔT.
Results and Analysis
From the NH4Cl standardization runs, the heat capacity of the calorimeter, Cp(K) can be obtained using the weights of H2O and NH4Cl. Once Cp(K) is known, ΔrH(T2) for any other reaction can be determined by the same method. 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 for the reaction studied along with the uncertainty at the 95% confidence level. Graphically report the dependence of ΔrH on ionic strength showing the uncertainties with error bars, if that is the best way to present the data.
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. If necessary, convert your experimental values to the temperature for which the literature values are quoted (assume the heat capacity is independent of temperature). 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.
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