Exp 7: The Gibbs Free Energy of the Autoionization of Water -2-
The Gibbs Free Energy of the Autoionization of Water
Purpose
In this experiment, you will measure the pH for water at a series of temperatures and calculate the ion product constant, Kw,. With this information, you will calculate the Gibbs free energy for the autoionization of water at each temperature.
Introduction
The pH of water is determined by the autoionization constant at a given temperature. At 298K, the autoionization constant of water, Kw, is 1.0x10-14.
H2O « H+ + OH- Kw = 1.0x10-14 at 298K
Since Kw = [H+][OH-] = 1.0x10-14, [H+] = [OH-] = 1.0x10-7and pH = -log(1.0x10-7)=7.0. However, the value of Kw changes with temperature and so does the pH of the water.
The enthalpy and entropy changes of the reaction H+ + OH- « H2O are (nearly) independent of temperature. Hence, we can use the change in the pH of pure water as a function of temperature to determine the thermodynamics of this reaction. Let us start with the fact that the equilibrium constant for this reaction is Keq.
H+ + OH- « H2O
For this equilibrium at a given temperature T,
At temperature T, neutrality is achieved when [H+] = [OH-]
Therefore, or and
Calculating ∆G
1) Experimental Method: ∆Gº = -RT lnKeq
2) Theoretical Method: ∆Gº = ∆Hfº - T∆Sº
∆Hf kj/mol / Sº kj/KmolH2O / -286 / 0.070
H+ / 0 / 0
OH- / -230 / -0.011
Suggested Background Reading
Background material for the topics covered in this experiment can be found in the following sections of your textbook:
1) Chemical equilibrium 2) Acid-base chemistry 3) Autoionization
Chemicals and Equipment
Chemicals / EquipmentSodium chloride
Pure distilled water / LabPro unit with pH probe and temperature probe
Ice bath
Hot plate
250 ml beakers
Thermometer
Experimental Procedure
1. Prepare about 200ml of a 0.1M NaCl solution.
2. Set up the LabPro unit to simultaneously measure the pH and temperature of the dilute NaCl solution. From the “Experiment” menu, choose “Data Collection” and change the time interval to 300 seconds. Plug your pH probe into channel 1 and the temperature probe into channel 2 of your LabPro unit. (You may have to tell the Logger Pro device which temperature probe you are using).
3. Prepare an ice-water bath and allow the temperature to stabilize near 0°C.
4. Cool down a sample of the dilute NaCl solution to approximately 5°C using the ice bath.
5. Place the pH and Temperature probes into the cooled NaCl solution.
6. Begin collecting temperature/pH versus time data. The length of your experiment and the data collection parameters will depend on how quickly you heat your solution in the next step. You may have to repeat the experiment several times to choose a correct set of parameters.
7. Gently heat the solution using a heating plate while recording the pH. Stop your experiment when the temperature of the solution reaches 80°C. Do not leave the pH probe in the solution as the temperature increases above 80°C! Remove it from the solution if you heat to a higher temperature.
8. Save your data! (Your instructor will assist you with manipulating the data as described below if you have problems.) Save your data!
Data Analysis
To have Logger Pro do these calculations for you, you need to make a new calculated column for each calculation. Follow the sequence of menus & steps shown here:
Data Menu à New Calculated Column à Name, Short Name, Units, Equation
1) Using the solution pH, calculate the [H+] of the solution.
[H+] ∆H ____ 10^–“pH”
2) Using the [H+] of the solution, calculate the equilibrium constant (Keq).
Keq Keq _____ 1/(“[H+]”•“[H+]”)
3) Using the equilibrium constant (Keq), calculate the DGo for the reaction.
∆G ∆G kj –8.3•(“Temp”+273)•ln(“Keq)”/1000
4) Verify your data by calculating the DGo for the reaction using standard enthalpies (from the appendix in your textbook) of formation and the thermodynamic equation: DGo = DHo - TDSo.
5) Determine the percent error between your measured and calculated values for DGo.