Introduction
During the Solubility Product experiment you calculated the Solubility Product, Ksp, for calcium hydroxide, an ionic solid that is sparingly soluble in water. This was achieved by titrating a saturated solution of Ca(OH)2 prepared at a certain temperature. The saturated, aqueous, solution of Ca(OH)2 is represented in equation form as shown below.
The equilibrium expression for calcium hydroxide is shown below.
Ksp = [Ca2+][OH–]2 Eq. 1
Equilibrium constants are temperature-dependent and the value of an equilibrium constant can be related to temperature and the Gibbs Free Energy, Gº, through the equation:
∆G°=-RTlnK Eq. 2
In this case we can substitute our equilibrium solubility product constant, Ksp, for K. R is the Gas Constant, 8.314 J K-1 mol-1, and T is the temperature in Kelvin. This equation assumes that solutions used are 1 M. In this experiment, you will use the Ksp value from the previous lab and collect data that will allow you to determine Ksp at two further temperatures. Using the Ksp data you will determine the thermodynamic parameters of enthalpy and entropy associated with the dissolution of Ca(OH)2.
∆G°=∆H°-T∆S° Eq. 3
where T is the temperature in Kelvin. We assume here that both Hº and Sº do not vary with temperature. This is not always a safe assumption (see your text for an explanation), but is considered so for this reaction. By substituting Eq. 3 into Eq. 2 we obtain:
-RTlnKsp=∆H°-T∆S° Eq. 4
Eq. 4 can be rearranged algebraically to obtain an equation that has the same form as the equation of a straight line (i.e. of the form y = mx + c):
lnKsp=-∆H°R1T+∆S°R Eq. 5
So a plot of ln Ksp versus 1/T should produce a straight line with a negative slope of -Hº/R and a y-intercept value of Sº/R.
Objectives
Two weeks have been allocated for this experiment, so you may apportion your experimental procedures accordingly. In this experiment, you will
Titrate one saturated Ca(OH)2 solution prepared at two different temperatures with a standard HCl solution. This will provide you with a total two Ksp values, one for each temperature. The values at a particular temperature can be averaged.
Determine the [OH–] for the saturated Ca(OH)2 solution.
Calculate the Ksp of Ca(OH)2 at each temperature.
Determine the thermodynamic parameters Gº,Hº, andSº.
Figure 1
Materials
Procedure
- Obtain and wear goggles.
- Connect a Temperature Probe to Channel 1 and a pH Sensor to Channel 2 of the Vernier computer interface. Connect the interface to the computer using the proper interface cable.
- Set up a ring stand, ring, filter funnel, and filter paper.
- Obtain about 50 mL of chilled saturated calcium hydroxide solution. Quickly record the temperature of the solution and filter your sample of Ca(OH)2 solution into a clean beaker. CAUTION: Calcium hydroxide solution is caustic. Avoid spilling it on your skin or clothing.
- Measure out 20.0 mL of the filtered solution into a 250 mL beaker using a volumetric pipet. Record the precise volume of Ca(OH)2 solution that you are using in the titration.
- Obtain about 100 mL of 0.0500 M HCl solution. CAUTION: Handle the hydrochloric acid with care. It can cause painful burns if it comes in contact with the skin.
- Set up the beaker of Ca(OH)2 solution on a magnetic stirrer. If you are not using a magnetic stirrer, use a glass stirring rod to stir the solution throughout the titration.
- Use a utility clamp to suspend the pH Sensor on a ring stand as shown in Figure 1. Position the pH Sensor in the Ca(OH)2 solution, and adjust its position so that the sensor is not struck by the magnetic stirring bar.
- Connect a buret to the ring stand. Rinse and fill the buret with the 0.0500 M HCl solution. It is not necessary for the volume of HCl in the buret to be at exactly 0.00 mL. It is only sufficient that the meniscus level of HCl in the buret be at the 0.00 mL mark or below.
- Start the Logger Pro program on your computer. Open the file “23 Ksp” from the Advanced Chemistry with Vernier folder.
- Conduct the titration carefully. The guidelines below are general suggestions; use your judgment in conducting the titrations to get the best results. Remember that you should be able to record volumes dispensed by a buret to two places after the decimal point and that a buret measures volumes added.
- Before you have added any of the HCl titrant, click and monitor pH for 5-10 seconds. Once the displayed pH reading has stabilized, click . In the edit box, type “0” (for 0 mL added). Press the ENTER key to store the first data pair.
- Add a small amount of the titrant, up to 0.50 mL, although it does not have to be exactly 0.50 mL. When the pH stabilizes click . The volume that you will enter is found by subtracting the initial volume (before you added any HCl) from your new volume reading on the buret. In other words, enter the actual volume that you added (final volume – initial volume) and press ENTER.
- Continue adding the HCl solution in increments that lower the pH consistently, and enter the actual volume after each increment. (For example, let’s say our starting measurement on the buret was 0.25 mL and that we added some HCl to the beaker from the buret. Our new measurement on the buret is 0.85 mL. The volume that we added is 0.85 – 0.25; so 0.60 mL of HCl were added. Now we add some more HCl to the beaker and our latest measurement is 1.40 mL. The volume of HCl that we added for this increment is 1.40 – 0.85; so 0.55 mL, etc.)
- When you reach the equivalence point, continue adding the HCl solution until the pH value remains constant.
- When you have finished collecting data, click . Choose Store Latest Run from the Experiment menu to save the results of the first trial.
- Follow the steps below to find the equivalence point, which is the largest increase in pH upon the addition of a very small amount of HCl solution. A good method of determining the precise equivalence point of the titration is to take the second derivative of the pH-volume data, a plot of 2pH/vol2.
- Open Page 3 by clicking on the Page window on the menu bar.
- Analyze the second derivative plot and record the volume of HCl at the equivalence point.
- Dispose of the reaction mixture as directed. Rinse the pH Sensor with distilled water in preparation for the second titration.
- Repeat the necessary steps to titrate a second sample of the filtered Ca(OH)2 solution. Conduct a third trial if directed by your instructor.
- Obtain about 75 mL of distilled water and heat it on a hotplate to around 50 – 60 ºC. Add about 1.5 g of solid calcium oxide and allow the solution to heat for a further minute or two.
- Record the temperature of the solution and quickly, but carefully, filter it into a clean, dry 150 mL beaker. Measure out three 20.0 mL aliquots of the filtered solution into three separate 250 mL beakers using a volumetric pipet. Record the precise volume of Ca(OH)2 solution that you are using in each titration. 20.0,20.0, 15.0
- Allow the solutions to cool to room temperature.
- Repeat steps 6 – 15 to obtain titration data on the heated Ca(OH)2 solution.
Lab Report
Calculate the averages of the Volume (HCl) at equivalence points at different temperatures:
The saturated, aqueous, solution of Ca(OH)2 is represented in equation form as shown below.
Titration of saturated solution of Ca(OH)2 with HCl:
H+ + OH- = H2O
Calculation of Ksp, ∆G° for Trial 1 and 2:
n(OH-) = Volume(HCl) * [HCl] = 21.84 mL * 0.05 mole/L = 0.001092 mole
[OH-](initial) = n(OH-) / Volume(Ca(OH)2) = 0.001092 mole / 20 mL = 0.0546 M
[Ca2+](initial) = [OH-](initial) /2 = 0.0546 M /2 = 0.0273 M
The equilibrium expression for calcium hydroxide is shown below.
Ksp = [Ca2+][OH–]2
Ksp = (0.0546 M)2 * 0.0273 M = 8.14 * 10-5 M3
Equilibrium constants are temperature-dependent and the value of an equilibrium constant can be related to temperature and the Gibbs Free Energy, Gº, through the equation:
∆G°=-RTlnK
∆G° = -8.314 J K-1 mol-1 * (86.7 + 273) K * ln(8.14 * 10-5 M3) = 2.82 * 104 J mol-1
Calculation of Ksp, ∆G° for Trial 3 and 4 (see the attached Excel file):
Ksp = (0.0356 M)2 * 0.0178 M = 2.26 * 10-5 M3
∆G° = -8.314 J K-1 mol-1 * (69 + 273) K * ln(2.26 * 10-5 M3) = 3.04 * 104 J mol-1
∆G°=∆H°-T∆S°
-RTlnKsp=∆H°-T∆S°
lnKsp=-∆H°R1T+∆S°R
Make a table of 1/T and lnKsp in Excel, and plot lnKsp versus 1/T (see the attached file). The equation obtained from the plot is:
y = −8902.8x + 15.334
−8902.8 = −∆H°/R
∆H° = 8902.8 * R = 8902.8 K* 8.314 J K-1 mol-1 = 7.40 * 104 J mol-1
15.334 = ∆S°/R
∆S° = 15.334 * R = 127.49 J K-1
Discuss the implications of those values.
∆G°: Gibbs free energy is the chemical potential that is minimized when a system reaches equilibrium at constant pressure and temperature.
∆H°: Enthalpy is a measure of the total energy of a thermodynamics system.
∆S°: Entropy is a mathematically-defined thermodynamic quantity associated with the amount of order, disorder, and/or chaos in a thermodynamics system.
What controls the feasibility of the ionization of Ca(OH)2: Entropy or enthalpy?
Enthalpy controls the feasibility of the ionization of Ca(OH)2.
Is it more favourable at lower or higher temperatures?
It is more favorable at higher temperatures.
