EXPERIMENT 9
Thermodynamics and Solubility
Introduction
The most common way to experimentally determine the value of the thermodynamic variables, such as ∆G°, ∆H°, or ∆S°,
is to measure the concentrations of reactants and products at equilibrium and calculate the value of the equilibrium
constant. In order to obtain all three thermodynamic variables, the equilibrium constant must be determined for at least
two temperatures. The standard free energy change, ∆G°, is related to the value of the equilibrium constant at a particular
temperature by the following relationship:
∆G° is also related to ∆H° and ∆S° by the following equation:
If you rearrange these two equations and solve for lnK, you obtain the following equation:
Luckily, ∆H° and ∆S° vary little with temperature. Therefore, for small temperature variations, ∆H° and ∆S° are considered
to be constant. If both ∆H° and ∆S° are constants, then equation above is the equation of a straight line with lnK as the y
variable and 1/T as the x variable. The straight line would have a slope equal to ∆H°/R and intercept equal to ∆S°/R.
If you measure the value of K at two temperatures, T1 and T2, K at T1 is equal to the value of K at T1 and K(T2) be equal to
the value of K at T2. Thus you now have 2 new equations that can be
If you subtract equations, and rearrange them back into the equation for a line, you now have
Solving for ∆H°:
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Once you know the value of an equilibrium constant at two temperatures, you can calculate the value of ∆H° for that
reaction. Once, the values for ∆G° and ∆H° have been determined for a reaction, then ∆S° for the reaction can be
determined by solving for ∆S°:
In Your Lab…
In today's experiment, you will determine the solubility product, Ksp, of calcium hydroxide, Ca(OH)2 by measuring the
concentration of Ca(OH)2 in a saturated solution. Calcium hydroxide is a sparingly soluble salt that dissolves according to
the following reaction:
The solubility product expression for this reaction is:
You will determine the concentration of Ca(OH)2 in a saturated solution by titrating the saturated solution against a
standardized hydrochloric acid solution. The neutralization reaction of Ca(OH)2 with HCl is:
From the concentration of Ca(OH)2 in the saturated solution, you will be able to determine both the Ca2+ and OH¯
concentrations in the saturated solution. Plugging the ion concentrations into the solubility product expression will give you
a value for the Ksp for Ca(OH)2. You will measure the Ksp at both room temperature and at the temperature of boiling
water. This will give you two values of Ksp at two temperatures which will allow you to calculate ∆G°, ∆H°, and ∆S°.
Calcium hydroxide is an unusual salt in that it is more soluble in cold water than in hot water. This property allows us to
perform this particular experiment which could not be done with most salts which increase in solubility as the solution is
heated. Do not feel that you have done something wrong when you find that the solubility, and thus the Ksp, is higher for
the cold water than the hot water for this salt.
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Lab Procedures
Your TA must sign your data before leaving lab or you will not receive credit for attending the lab.
You will work in pairs in this lab; 1 partner does Part 2, the other partner does Part 3
Part 1: Preparation of dilute hydrochloric acid (Repeat this prep if you need more HCl for your titrations)
1. Add exactly 2.00 mL of the stock 1.00M HCl solution to a 50 mL volumetric flask using your 10 mL graduated
cylinder. Fill to the line with distilled water and mix well. This diluted solution is to be used in all titrations.
Repeat as needed for the titrations.
2. Take a small portion (~5 mL) of the diluted HCl solution and rinse the insides of the buret with it. Fill the buret with
the diluted HCl solution.
Part 2: Determination of Ksp for Ca(OH)2 at Room Temperature
3. Create a saturated solution of calcium hydroxide by adding 0.10-0.30g of Ca(OH)2 to 30 mL of distilled water in a
50 mL beaker. You should see some undissolved calcium hydroxide at the bottom of the beaker. If not, add a
little more calcium hydroxide.
4. Record the temperature of the solution in your laboratory notebook.
5. Filter the saturated Ca(OH)2 solution through a piece of filter paper in a funnel into a 100 mL beaker.
6. Using a 10 mL graduated cylinder, measure out 5.00 mL of the filtered solution with a plastic pipet. Pour the 5.0
mL of solution into a clean 125 mL Erlenmeyer. Add 10 mL of distilled water to the solution and about 5 drops of
bromothymol blue.
7. Record the initial volume of HCl in the buret to the nearest 0.01mL in your laboratory notebook.
8. Titrate with the diluted HCl until the color of the solution changes from blue to greenish yellow.
9. Record the final volume of HCl solution added to the nearest 0.01 mL in your laboratory notebook.
10. Repeat for a total of 3 titrations.
11. Rinse out the Erlenmeyer flasks after use.
Part 3: Determination of Ksp for Ca(OH)2 in Boiling Water
1. Using a 50 mL beaker, heat approximately 30mL of distilled water to boiling on your hot plate. Add about 0.100.30g of Ca(OH)2 gently to the boiling water and stir for 2 minutes. You should still see some undissolved calcium
hydroxide. If not, add a little more calcium hydroxide.
2. Record the temperature of the solution to the nearest degree.
3. Set up your filtration apparatus while the solution is heating.
4. Quickly filter this solution. While the filtrate is still very hot, quickly measure out three 5.00 mL portions of the
filtered solution (using a plastic pipet and a 10 mL graduated cylinder) into three 125 mL Erlenmeyer flasks. (You
may need to borrow one of your partners flasks)
5. Add 10 mL of distilled water to the solution and about 5 drops of bromothymol blue to each Erlenmeyer flask.
6. Record the initial volume of HCl in the buret to the nearest 0.01mL in your laboratory notebook.
7. Titrate with the diluted HCl until the color of the solution changes from blue to greenish yellow.
8. Record the final volume of HCl solution added to the nearest 0.01 mL in your laboratory notebook.
9. Repeat the titration using the remaining two samples of Ca(OH)2.
10. Rinse out the Erlenmeyer flasks well with distilled water after use.
Laboratory Data
Include the correct number of significant figures and units for each value
Concentration of Stock HCl Solution
Temperature of saturated Ca(OH)2 Solution
_________
_________
Tables 1 and 2: Titration of Ca(OH)2 Solution at Room Temperature and at the boiling point
You need initial and final buret readings for each trial at each temperature.
Be sure to record your partner’s data.
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Data Sheet; Chemistry 114: Experiment 9
Name: ____________________________________________ Date:________ Section:________
TA Signature:
3/29/2011
___________________________________________________________________
4
Calculations
Remember to show 1 example of each calculation either handwritten or typed on a separate sheet.
Include correct significant figures and units
Concentration of Diluted HCl
The following formula can be used to determine the concentration of the dilute HCl used in the titrations. Set up
the equation to solve for M2, the concentration of the diluted HCl.
M1V1=M2V2
M1 = concentration of stock solution
V1= volume of stock solution used
M2 = concentration of diluted solution
V2 = total volume of diluted solution
Moles HCl Used in the Titration
Multiply the volume of diluted HCl solution added (in liters) during the titration by the concentration of diluted HCl
solution. Repeat for all 6 titrations.
Moles Ca(OH)2 in the Saturated Solutions
For every mole of Ca(OH)2 used, you needed 2 moles of HCl, so divide the moles of HCl used in the titration by 2
to find the moles of Ca(OH)2 in the titrated solutions.
2 HCl(aq) + Ca(OH)2   → 2 H2O(l) + CaCl2(aq)
Concentration of Ca(OH)2 in the Saturated Solutions
Calculate the concentration of Ca(OH)2 in the saturated solution by dividing the number of moles of Ca(OH)2 by
the volume of saturated solution used in liters.
Concentration of Ca2+ and OH- in the Saturated Solutions
2+
Calculate the concentrations of Ca and OH¯ in the saturated solution by using the following relationships:
[Ca2+] = [Ca(OH)2]
[OH-] = 2 x [Ca(OH)2]
Values of Ksp for Ca(OH)2
Enter the concentrations for Ca2+ and OH- into the Ksp expression for Ca(OH)2 and calculate a value for Ksp at
room temperature. Average your three values. Repeat the calculations for the three titrations using the saturated
Ca(OH)2 solution in boiling water. Find the average Ksp for this solution as well.
Ksp = [Ca2+][OH-]2
Value of ∆G°
Using the room temperature average value for Ksp, calculate the value of ∆G° for the solubility of Ca(OH)2 using
the following equation:
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Remember to convert your temperatures to Kelvin and include the sign (+/-) with your value.
Value of ∆H°
Using the room temperature and the boiling temperature values for Ksp and the two temperatures calculate the
value of ∆H° for the following reaction using the following equation:
Remember to convert your temperatures to Kelvin and include the sign (+/-) with your value.
Value of ∆S°
Calculate ∆S° at room temperature for the reaction by using the following reaction:
Remember to convert your temperatures to Kelvin and include the sign (+/-) with your value.
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Results
Include the following results in your lab report.
Include the correct number of significant figures for each measurement.
Table 3: Ksp Calculations for Ca(OH)2 Solution at Room Temperature
Trial 1
Room T
Well Number
Trial 2
Room T
Trial 3
Room T
Concentration of
Diluted HCl (M)
Moles HCl
Moles of CaOH2
Concentration of
CaOH2 (M)
Concentration of
2+
Ca (M)
Concentration of
OH (M)
Ksp
Average Ksp
_________
Table 4: Ksp Calculations for Ca(OH)2 Solution at Room Temperature
Trial 1
Room T
Well Number
Trial 2
Room T
Trial 3
Room T
Concentration of
Diluted HCl (M)
Moles HCl
Moles of CaOH2
Concentration of
CaOH2 (M)
Concentration of
2+
Ca (M)
Concentration of
OH (M)
Ksp
Average Ksp
_________
Table 5: Thermodynamic Calculations for Ca(OH)2 Solutions
Well Number
Room T
Hot
∆G°
∆H°
∆S°
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Discussion Questions
You must use your data to answer these questions. If the answer you give does not reflect YOUR data and
results, you will receive no credit for the question.
1. Calculate pKsp values from both of your experimental Ksp values and the actual Ksp. Then, using your average
pKsp at room temperature as your experimental value, calculate your percent error based on the actual pKsp of
-6
Ca(OH)2. The tabulated Ksp for Ca(OH)2 is 6.5 x10 at 25°C.
pKsp= -log Ksp
% Error =
Experimental pK sp - Actual pK sp
Actual pK sp
x100
2. In general, the solubility of most salts increases as the temperature increases. Based on your results and the
comparison to the pKsp values given above, how does temperature affect solubility of Ca(OH)2? Is this the result
you expected to see?
3. Calcium carbonate, CaCO3, is 100 times less soluble in cold water than Ca(OH)2. Carbon dioxide is a component
of air that readily dissolves in water. Write the chemical reaction that describes the reaction of aqueous Ca(OH)2
with aqueous CO2. How does this equation help explain why you should boil the water for several minutes before
adding the solid Ca(OH)2.
4. Explain how the negative and positive signs of ∆G°, ∆H°, and ∆S° on the values tell you about the process of
Ca(OH)2 dissolving in water.
5. Compare the tabulated Ksp values (found in your textbook or online) for Ca(OH)2 with Mg(OH)2 and Sr(OH)2.
What trend do you see in the Ksp values when related to the location of these cations in the periodic chart? Briefly
explain why this trend exists.
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Prelab 9 Chem 114
Name: _____________________________________
Section#: _______________
Show work to support answers. Attach additional sheets if necessary, but report your answers on this sheet. Please circle
your final answers.
∆G = ∆H -T∆S = 0 for phase change
o
o
o
∆H =∆H (products) - ∆H (reactants)
o
ln Keq = ln (K2/K1) = (∆H /R)[(1/T1) - (1/T2)]
o
∆G = –RT ln Keq
∆S = qrxn / T
o
o
lnK= ∆H /RT + ∆S /R
R = 8.314J/molK=0.0821Latm/molK
A saturated solution of Mg(OH)2 is prepared and allowed to equilibrate at 25˚C. A 25.00 mL sample of the solution is
titrated with 0.0051M HCL solution. 1.40mL of the HCl solution are required to fully react with the sample.
1. Write the balanced chemical equation for the reaction of the salt with the HCl.
2. Write the equilibrium reaction for the solubility of the Mg(OH)2 in water.
3. Calculate the molarity of the salt solution from the titration data.
4. What are the concentrations of the cation and the anion in the salt solution?
5. Calculate the Ksp of the salt from the concentrations of the cation and anion in the salt solution.
6. Calculate ∆G for the salt using the Ksp you calculated for the question above.
7.
Is the reaction spontaneous or nonspontaneous? Why did you answer that way?
8. If you calculate a positive ∆Hº for this reaction, what does that tell you about your reaction?
9. What is an unusual thermodynamic property of calcium hydroxide?
10. How does this property make it possible to perform this particular experiment?
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Experiment Checklist: This sheet must be attached to your lab report
Points:
_____
Format (in order)
(0 / 5)
5pts
Each numbered section should be on separate page(s), unless otherwise noted.
Typed in size 10 font, single spaced, headings: size 12 font
(1) Title page: Title, Name, TA name, Course, section and date
(2) Purpose and procedure: Both should be on 1 single page
(3) Original Data: Must have TA signature, handwritten in lab
(4) Sample Calculations: May be handwritten
(5) Results Table: Typed table
(6) Discussion Questions
(7) Conclusions
(8) Experiment checklist: Last page in each experimental write-up
_____
Purpose
(0 / 5)
5pts
Paragraph of complete sentences summarizing purpose of experiment
Must include a clear explanation of what was learned in experiment
_____
Procedure
(0 / 5)
5pts
Full procedure not needed, just any changes to experimental procedures
(1) Give experiment title and page (s) of instructions:
ex: Buffers: Pg. 4-5
(2) Heading of each portion of experiment:
ex: Part 1: Making a dilution
(3) Under each heading note changes and line of experiment where changed
(4) Note why each change was made, if no changes, state “no changes made”
_____
Data
(0 / 5)
(0 / 5)
(0 / 5)
(0 / 5)
20pts
Original data sheet must have TA signature or 50 point deduction
_____ All data required in the lab is recorded
_____ Observations are recorded during the experiment
_____ Data is neat and legible
_____ Data is in tables as described in the lab manual
_____
Calculations
(0 -15 sliding)
15pts
Calculations can be hand written. Only 1 sample calculation is required.
_____ All calculations listed in experiment are present and correct
_____ Calculations must be labeled with the headings given in the calculation section
_____
Results
(0 / 5 / 10)
10pts
Typed tables with all results. Must match calculations from original data
_____ All results are present
_____ Results match calculations
_____ Results must be labeled with the headings given in the calculation section
_____
Discussion
Questions
(0 / 3 / 6) X 5
30pts
Answers must be correct, typed and in complete sentences for full credit.
Conclusions
(0 / 5 / 10)
10pts
_____
Q1 _________Q2 _________ Q3 _________ Q4 _________ Q5 _________
_____
_____
_____
_____
_____
_____
_____
_____
Deductions:
______ Total Score
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5 - 10 complete sentences typed in paragraph form IN YOUR OWN WORDS
_____ Error sources are specific to experiment
_____ Discrepancies between data collected and expected results are explained
_____ Clear final sentence about success in relation to purpose of experiment
Checklist missing: -10 pts
Original data sheet missing -50pts
Significant figures are incorrect in data and/or results -10pts
Units are missing from data and/or results -10pts
Calculations not performed with data from data sheet: -50 pts
Lab report is not typed (original data& calculations can be handwritten) -20pts
Plagiarism (copying from another source): -100 pts
Lab technique points: up to 20pt deduction at your TAs discretion
_____ Late or unprepared
_____ Lab area not clean
_____ Improper waste disposal
_____ Disruptive behavior
100pts
10