Experiment 11: Ksp & THERMODYNAMICS OF
DISSOLUTION OF LEAD(II) CHLORIDE
Purpose:
The solubility product and thermodynamic data for the dissolution of lead(II)
chloride are to be determined.
Introduction:
In several of the previous experiments, the concept of equilibrium was
studied for compounds in solution. This experiment addresses the equilibrium between ions
in solution and solid compounds. It further serves to connect the thermodynamic aspects of
equilibrium by investigating the effects of temperature on the equilibrium. You will
determine the entropy, enthalpy, and free energy change for the process of dissolving
lead(II) chloride in water. This is done by determining the variation of the solubility product
as a function of temperature. When PbCl2 dissolves, the following equilibrium is
established:
Pb2+(aq) + 2 Cl (aq)
PbCl2(s)
Equation 1
As you remember, solids are not included in equilibrium expressions. Thus, at equilibrium
the solubility product is written as follows:
Ksp = [Pb2+][ Cl ]2
Equation 2
Once equilibrium is established, ∆G is zero. However, ∆Gº, the free energy change between
reactants and products in their standard states, is not zero. In other words ∆G at equilibrium
is zero, but the reaction getting to equilibrium is not zero. It is ∆Gº that determines how
much lead(II) chloride will dissolve in water at a specified temperature.
We know that ∆Gº is related to ∆Hº and ∆Sº as shown in Equation 3 below. We also know
∆Gº is related to the solubility product as shown in Equation 4.
∆Gº = ∆Hº
T∆Sº
Equation 3
∆Gº = RT ln Ksp where R = 8.314 J mol 1 K
1
Equation 4
By combining the two equations, we get:
∆Hº
T∆Sº = RT ln Ksp
Equation 5
Rearranging Equation 5 to solve for ln Ksp gives us Equation 6:
H
ln K sp = _
R
y
=
m
1
T
S
R
Equation 6
x + b
Equation 6 is now in the form of a linear plot (y = mx + b). Therefore if a plot of ln Ksp
versus 1/T were prepared, the resulting straight line would have a slope (m) that equals
(∆Hº/R) and a y-intercept (b) that equals (∆Sº/R). These values can then be used to solve
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EXPERIMENT 11: Ksp & THERMODYNAMICS OF DISSOLUTION OF PbCl2
for ∆Hº and ∆Sº. With these values, we can use Equation 3 to solve for ∆Gº at a given
temperature.
To determine the solubility product, we need the molar concentration of lead(II) ions, [Pb2+],
and the molar concentration of chloride ions, [Cl ], of a saturated solution of PbCl2. In this
experiment you will prepare a saturated solution of PbCl2 and titrate the dissolved lead
chloride with silver nitrate in the presence of potassium chromate. You are actually titrating
the chloride in solution. The chromate ion will serve as the indicator for the reaction. Table
11.1 contains solubility products at 25 C as well as physical appearance information for
select compounds that should help you make sense of the titration.
Name
Lead(II) chloride
Lead chromate
Silver chloride
Silver chromate
Nitrate and
potassium ions
Table 11.1
Formula
Color of solid
PbCl2
white
PbCrO4
Orange-yellow
AgCl
white
Ag2CrO4
Light rust brown
NO3 and K+
__
Solubility product
5
1.7 X 10
2.3 X 10 13
1.8 X 10 10
2.6 X 10 12
soluble
Although the Ksp of AgCl is larger than that of Ag2CrO4, the molar solubility of Ag2CrO4 is
actually slightly larger than that of AgCl. In other words, Ag2CrO4 is slightly more soluble
than AgCl. As aqueous AgNO3 is being added to the saturated PbCl2, AgCl will precipitate
out first until all of the Cl is gone before the Ag2CrO4 begins to form.
Ag+ (aq) + Cl (aq)
2Ag+ (aq) + CrO4 (aq)
AgCl (s)
Ag2CrO4(s)
You will begin by adding an excess amount of K2CrO4 to your saturated solution of PbCl2.
Immediately an orange-yellow precipitate of PbCrO4 will form. Note that there is still
excess CrO42 in solution for the titration. As you begin adding Ag+ in the form of aqueous
AgNO3, a white AgCl (s) will form, but this will not be visible as the color is masked by the
bright orange-yellow color of the PbCrO4. At the point when you have added enough Ag+ to
precipitate out all of the Cl in solution, Ag+ will begin to precipitate out the CrO42 that is
still in solution. The end point is therefore the change in color from orange-yellow
(PbCrO4) to light rust brown (Ag2CrO4).
In the manner described above, you will be able to determine the [Cl ] present in the
saturated solution. From the stoichiometry in Equation 1, that will also allow you to
calculate the [Pb2+]. Once you have the molar concentrations of these two species you can
calculate the Ksp of PbCl2 of the saturated solution.
You will actually prepare saturated solutions at four different temperatures. Equation 6 then
allows us to graphically determine the standard enthalpy and standard entropy change.
Application of Equation 3 gives us the standard free energy change.
EXPERIMENT 11: Ksp & THERMODYNAMICS OF DISSOLUTION OF PbCl2
105
Safety Precautions:
Keep your goggles on at all times.
Use of disposable gloves is highly recommended.
AgNO3 and chromate solutions will discolor your skin and stain your clothing.
Lead(II) solutions are toxic, may be fatal if swallowed or inhaled.
Procedure: Work with one partner, but prepare your own graphs.
Preparation of saturated solutions of lead(II) chloride:
4.5 g
125 mL
1. Place about 9 g of lead(II) chloride in a 400-mL beaker, and add 250 mL of deionized
water. Add a magnetic stir bar.
2. Using a hotplate bring the solution to a boil while stirring. This will ensure that the
solution is saturated. Place a 20-mL volumetric pipet in a separate beaker of boiling
deionized water.
two
3. While waiting for the solution to boil, obtain four 250-mL Erlenmeyer flasks. To each
of these flasks add about 30 mL of 0.10 M K2CrO4. Label them as #1, 2, 3 and 4.
One team does 70°C-25°C
4. Once the solution comes to a boil, remove the beaker from the hotplate and place it on a
ceramic heat pad. Insert a temperature probe into the solution so that you can monitor
the temperature of the solution as it cools. When the temperature falls to about 90ºC,
record the exact temperature, and then using the hot 20-mL pipet, transfer 20.0 mL of
the solution into your 250-mL Erlenmeyer flask #1. During the transfer it is important
that you do not transfer any of the solid whatsoever. This transfer must be done quickly
before the solution cools significantly. Also, it needs to be done quickly before any
solids crystallize out and clog up the pipet. Record the temperature in the beaker
AGAIN when the transfer is complete. You will be using the average of the two
temperatures (before and after) for the temperature for this sample.
5. Return the pipet to the hot water to keep it hot. Wash off any solid that may have
crystallized on the inside or outside of the pipet. Keep an eye on the hot water.
(One team does 90°C and 50°C, the other team does 70°C and 25°C)
6. Continue to cool the original solution in the beaker and repeat the sample collection
process at about 70ºC, 50ºC, and 25ºC, each time recording the temperature before and
after the transfer. These are to be placed in flasks 2, 3, and 4 respectively. When cooling
the solution from 50ºC to 25ºC you will need to use a cold water bath to save time, but
don’t let it overcool. Before you record the temperature, make sure it has had time to
equilibrate.
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EXPERIMENT 11: Ksp & THERMODYNAMICS OF DISSOLUTION OF PbCl2
Titration of the PbCl2 samples:
Instructor’s Demonstration:
To be sure you don’t miss the end point, your instructor will demonstrate the change in
color expected at the end point. Pay attention as your instructor adds an aqueous solution
of AgNO3 dropwise to a saturated solution of PbCl2 containing K2CrO4. You can see that
the change in color is quite subtle, but not difficult to recognize once you know what to
expect.
7. It should not come as a surprise that AgNO3 is expensive. PLEASE DO NOT WASTE
OUR AgNO3 solution! Obtain 100 mL of AgNO3 in a beaker. You can get more later as
needed.
two
50 mL
8. You should now have four Erlenmeyer flasks, each flask containing about 50 mL; 20 mL
lead(II) chloride sample and 30 mL potassium chromate. Set up a buret containing 0.100
M AgNO3. Remember to rinse the buret 3 times with 10 mL portions of the silver
nitrate solution prior to filling the buret and get rid of the air bubbles at the buret tip.
9. Titrate the flask that requires the smallest amount of silver nitrate first (the solution at
25 C). Add a magnetic stir bar to the flask. You will need to perform the entire titration
slowly, since you do not know how much silver nitrate you will need to add. Record the
initial and final buret readings. (Be careful you do not record your data under the wrong
temperature!) The titration has reached its endpoint when a light rust brown color
appears permanently. If you are not sure, ask yourself whether the solution is a bright
yellow. If it is still bright yellow, you have not reached the endpoint. If you are still
unsure, you may ask your instructor to demonstrate the endpoint again.
10. Repeat this titration for the flask that requires the second least amount of silver nitrate.
You can quickly add the amount of silver nitrate that you used for the previous titration
to save time. The last part of the titration must be done slowly. Continue this procedure
until you have titrated all four samples. WATCH OUT THAT YOU DON’T LET
THE AgNO3 LEVEL IN THE BURET GO PAST THE 50.00 mL MARK!
11. Return the magnetic stir bar to your instructor.
CALCULATIONS:
1. Do the necessary calculations to complete the table on the Calculations & Results Page.
2. Plot ln Ksp versus 1/T using Excel. Include a trendline, and display this trendline and the
R2 value on the graph. This must be done individually. Include your name in your graph
title and SAVE the file labeled “CH 124 Ksp -YOUR NAME” in the folder (in the flash
drive) designated by your instructor or lab manager.
3. From the slope and y-intercept of the trendline, determine H and S . Using H and
S calculate G for all four temperatures. Record these values into the Calculations &
Results Page. Show all calculations carefully, with units, on a separate sheet of paper.
Pre-Lab Assignment:
1. Explain in your own words what “molar solubility” means. If a substance has a molar
solubility of 1.2 x 10 6 M at 25 C and we place 1.0 x 10 moles of this substance in a
liter of water at 25 C, will it all dissolve? Explain.
EXPERIMENT 11: Ksp & THERMODYNAMICS OF DISSOLUTION OF PbCl2
107
2. Calculate the molar solubility of AgCl and that of Ag2CrO4 from the solubility products
given in Table 11.1. Show your calculation setups.
3. Based on your answers to Questions 2, which is more soluble? AgCl or Ag2CrO4?
4. Write the molecular, ionic, and net ionic equation for the reaction that leads to the
formation of the color at the endpoint.
5. Prepare your lab notebook as usual. Copy the following data table on a new page in
your lab notebook:
Volume of PbCl2 solution in titration = 20.0 mL
Target Temp
90 C
70 C
50 C
25 C
T (before) in C
T (after) in C
Average T in C
Final Buret Reading for AgNO3 (mL)
Initial Buret Reading for AgNO3 (mL)
Vol AgNO3 added (mL)
Post-Lab Questions:
1. You calculated the solubility product for all four samples of lead(II) chloride, but did not
average them together. Why is it inappropriate to average these solubility products?
Answer in a complete sentence.
2. While transferring 20 mL of the saturated solution of PbCl2 from the beaker to the
Erlenmeyer flask, it is likely that a small amount of the solid got transferred into the
flask as well. How would this error affect your calculated Ksp? (too high? too low?
unaffected?) Explain your answer carefully.
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EXPERIMENT 11: Ksp & THERMODYNAMICS OF DISSOLUTION OF PbCl2
EXPERIMENT 11: Ksp & THERMODYNAMICS OF DISSOLUTION OF PbCl2
Calculations & Results:
CHEM 124 Sec: ______
109
Name: ____________________
Partner’s Name: ____________________
Complete the table below. Include at least one set of sample calculations on a separate
sheet of paper.
Flask 1
Flask 2
Flask 3
Flask 4
Average Temperature
Volume AgNO3 used
Moles of AgNO3 used
Moles of Cl present in
the lead chloride solution
Molarity of the Cl in the
lead chloride solution
Molarity of the Pb2+ in the
lead chloride solution
Ksp of PbCl2
ln Ksp
1/T (Kelvin)
Remember to include units at all steps of your calculations.
Trendline equation:
Slope =
y-intercept =
H =
S =
Temperature
G
~ 90 C
~ 70 C
~ 50 C
~ 25 C
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EXPERIMENT 11: Ksp & THERMODYNAMICS OF DISSOLUTION OF PbCl2