Chem(Bio) Week 11– Ksp and the solubility of Calcium Hydroxide
Lab Overview:
Determine Go, Ho, and So for the solvation of calcium hydroxide
Water and possibly harvest plants (details provided in lab)
Ksp and the solubility of Calcium Hydroxide
Keywords: Ksp, Go, Ho, and So
Objectives:
Determine Ksp (solubility constant) for calcium hydroxide in aqueous solution
Use this to determine Go, Ho, and So for the solvation of calcium hydroxide
From the 128L lecture, you should be familiar with the relationship between the Gibbs
Free Energy of the system, the enthalpy and entropy and this experiment sets out to
determine these quantities experimentally for the solvation of calcium hydroxide in
water. Before starting to discuss the experiment, it is worth quickly reviewing the theory
a wee bit that defines an equilibrium and how this is related to the free energy Go.
Consider the system where we have A and B in an equilibrium as shown below:
A↔B
Remember this interconversion is a dynamic process with the forward and back reactions
occurring simultaneously such that there is always reactions occurring in both directions.
This does not necessarily mean that the concentrations of A and B are equal, we can have
a huge amount of A, a small amount of B and as long as the rate of forward and back
reactions stays equal, these concentrations are maintained. Hence, the equilibrium can
also lie towards favoring either A or B and the position of the equilibrium can also be
changed by modifying the experimental conditions. It is important to remember this is not
a static system and there is always reaction occurring, just at equilibrium, there is no net
reaction since the forward and back reaction are exactly balanced in magnitude..
We can therefore measure the equilibrium constant for a reaction (K) from the
concentrations of the reactants on both sides
For the reaction A ↔ B,
K = [products]/[reactants] = [B]/[A]
Chem(bio) Spring 2012 – Week 11-1
Chem(Bio) Week 11– Ksp and the solubility of Calcium Hydroxide
Hence by measuring the concentrations of the various species, it is possible to determine
the equilibrium constant K. This is important as the equilibrium constant is related to the
Gibb’s Free Energy ( Go) by the following equation:
Go = -RTlnK
Following on from this, it is then possible to determine values for Ho and So for the
system which is the ultimate goal for this experiment.
Go = Ho -T So
Solubility of Calcium Hydroxide
We have already encountered solubility in the lab and lecture. To some degree, all salts
are soluble in water. The degree of solubility is governed by equilibrium and related in
the solubility product constant, Ksp.
The solubility of an ionic compound in water may be thought of as a reaction where the
solid dissociates into its ions in solution. (this is an equilibrium reaction as shown below)
Most salts have a greater solubility at increased temperature. Calcium hydroxide is
unusual in that it is more soluble at low temperatures than at high temperatures. In
this experiment, the solubility of calcium hydroxide, Ca(OH)2, will be determined at
room temperature and 100oC as suggested in the following reaction.
Ca(OH)2 (s) ↔ Ca2+ (aq) + 2OH- (aq)
(1)
Once equilibrium has been established and the excess solid removed by filtration, the
concentration of hydroxide ion may be determined via an acid/base titration with HCl.
H3O+ (aq) + OH- (aq) → 2 H2O (l)
(2)
In this titration, bromothymol blue will be used as an indicator. While HCl is added, the
initial blue color will begin to turn green. When it is “stop-light green,” the pH is about
7. The end point is reached when the entire solution turns from green to yellow with
the addition of one drop. Past the endpoint, the solution remains yellow so we are
looking for that addition which just initiates the color change from green to yellow.
Reaching the green color is the indicator that you are very close to the endpoint From the
volume of HCl required to reach the end point, the [OH-] in the Ca(OH)2 solution may be
determined. (Note that the molar solubility of Ca(OH)2 is half of the [OH-] found by the
titration.) From the molar solubility, the Ksp, Go, Ho, and So for the dissociation of
calcium hydroxide will be determined.
Chem(bio) Spring 2012 – Week 11-2
Chem(Bio) Week 11– Ksp and the solubility of Calcium Hydroxide
Determination of Ksp, Go, Ho, and So
The concentration of OH- that is formed by the dissociation of Ca(OH)2 is found by
titration with standardized HCl. Since HCl is a strong acid and H3O+ and OH- react in a
1:1 stoichiometry, the hydroxide concentration may be found from the following
equation.
MHClVHCl = MOH-VOH-
(3)
The molar solubility of Ca(OH)2 (s) is simply half of this [OH-] as evidenced by equation
(1). According to the law of mass action, the equilibrium constant for equation (1), Ksp,
may be determined from this molar solubility.
Ksp = [Ca2+][OH-]2
2+
(4)
-
Please note that the [Ca ] is half of the [OH ] determined by the titration.
The equilibrium constant for this reaction is not only important for its own sake, but also
because it allows for the determination of the Gibb’s Free Energy ( Go) for the
dissociation of Ca(OH)2 according to the following equation.
Go = -RTlnKsp
(5)
Note that in equation (5) R is the ideal gas constant (R = 8.314 J/mol.K) and T is the
absolute temperature in Kelvin.
At this point, it appears as though the final aspect of the experiment is to use this value of
Go to determine Ho and So from the following equation.
Go = Ho -T So
(6)
However, we realize that at after one titration, we only have Go and T. In other words,
we have one equation and two unknowns and this cannot be solved using only this data.
This is the reason that the solubility of calcium hydroxide, Ca(OH)2, is determined at
both room temperature and 100oC. Using the free energies, Go, found at two
temperatures, Ho and So are calculated by solving for two unknowns in two equations.
The two equations are equation (6) with the experimentally determined values of Go and
T in Kelvin.
Chem(bio) Spring 2012 – Week 11-3
Chem(Bio) Week 11– Ksp and the solubility of Calcium Hydroxide
Example of Calculations
Consider the following example which determines the molar solubility, Ksp, Go, Ho,
and So for the dissociation of strontium hydroxide,
Sr(OH)2 (s) ↔ Sr2+ (aq) + 2OH-
(7)
Two solutions of Sr(OH)2 are allowed to equilibrate: one at 0oC and the other at 25oC. A
10.00 mL aliquot of each solution is titrated with 0.2000 M HCl. 3.37 mL of the acid are
required for the 0oC solution and 62.90 mL for the 25oC solution.
At 0oC, the [OH-] is found using equation (3):
MHClVHCl = MOH-VOH- ; (0.2000 M)(3.37 mL) = MOH-(10.00 mL)
MOH- = 0.0674 M
2+
-
Since [Sr ] = ½[OH ], the molar solubility of Sr(OH)2 at 0oC is 0.0674 M / 2 = 0.0337
M. From this value, Ksp at 0oC is found using equation (4):
Ksp = [Sr2+][OH-]2 = [0.0337][0.0647]2 = 1.53 x 10-4
Go is then found using equation (5), remembering that 0oC is 273 K.
Go = -RTlnKsp = -(8.314 J/mole.K)(273K)ln(1.53 x 10-4) = 19,900 J/mol = 19.9 kJ/mole
Using this same methodology for the 25oC data, the molar solubility was determined to
be 0.6290 M, the Ksp was found to be 0.995; and Go was calculated to be 0.012 kJ/mole.
Now equation (6) is applied at both temperatures:
At 0oC; Go = Ho - T So; 19.9 kJ/mole = Ho – (273 K) So
At 25oC; Go = Ho - T So; 0.012 kJ/mole = Ho – (298 K) So
(8)
(9)
Subtracting equation (9) from equation (8) gives
19.9 kJ/mole = (25 K) So
Therefore, So = 0.80 kJ/mole.K. Using this value of So in either equation (8) or
equation (9) gives Ho = 240 kJ/mole.
Chem(bio) Spring 2012 – Week 11-4
Chem(Bio) Week 11– Ksp and the solubility of Calcium Hydroxide
Experiment Overview
As always, the experiment can be split into a variety of parts, the first entails preparing a
standardized solution of hydrochloric acid for all subsequent titrations, the latter parts
involve carry out determinations of Ksp at two separate temperatures.
(1) Prepare and standardize a 0.025 M HCl solution using a standard sodium hydroxide
solution.
(2) Determine Ksp at room temperature
(3) Determine Ksp at 100 °C
(4) Determine Go and use this to determine Ho and S° for the solvation of calcium
hydroxide.
Part One – Preparation of 0.025 M HCl Solution
Solutions of approximately 1 M hydrochloric acid are available in the lab. Determine
how much you will need to dilute to prepare 1 liter of 0.025 M hydrochloric acid and
prepare this solution using the 1 L plastic bottle. Be sure to mix this well before filling
the burette with the acid.
To standardize the acid solution, collect ~ 50 mL of the standard NaOH (molarity will be
on the board) and titrate 10.00 mL portions of the standardized sodium hydroxide diluted
with ~30 mL of DI water using bromothymol blue as the indicator. Repeat this titration as
necessary to obtain an accurate and precise molarity for the standardized acid
Note the color change we are looking for on the bromothymol blue indicator. We are
titrating a basic solution (indicator is blue) with an acid from our burette and ending at an
acidic pH (indicator is yellow). The endpoint of the reaction occurs when the last traces
of the blue color disappear but because the endpoint is not colorless, we actually see a
color change from blue at start, through green and finally ending at yellow. The green
color in the middle arises from a mixture of indicator molecules displaying blue and
yellow. We are interested in the point where one drop causes the last disappearance
of any traces of the blue color which means the drop which causes a change from a
green color to a pure yellow is the endpoint of the reaction.
Part Two – Determining Ksp at Room Temperature
Collect 40 mL of the saturated Ca(OH)2 solution (stirring in the lab in a large 4 L
Erlenmeyer) in a 50 or 100-mL beaker and record its temperature to 0.1 oC. Using a
funnel, strain this solution through qualitative filter paper into a clean, dry 125 mL
Erlenmeyer flask. Pipet 10.00 mL of this clear solution into another clean, dry 125 mL
Erlenmeyer flask. Add approximately 25 mL of distilled water and 10-12 drops of the
bromothymol blue indicator. Record the beginning volume level of HCl in the buret.
Chem(bio) Spring 2012 – Week 11-5
Chem(Bio) Week 11– Ksp and the solubility of Calcium Hydroxide
Begin the titration, allowing the titrant to fall from the buret at a rapid drop-by-drop pace.
During this addition, the initial blue color will begin to turn green. When it is “stop-light
green,” the pH is about 7. The end point is reached when the entire solution turns yellow
from green with the addition of just one drop of the acid. Your goal is to deliver the
exact number of drops needed to reach this point. When you have reached the end point,
record the final volume in the buret (again to two decimal places) and calculate the
volume of titrant delivered. As always carry out sufficient titrations to obtain precise
data.
Part Three – Determining Ksp at 100 °C
Add about 100 mL of distilled water to a 250 mL Erlenmeyer flask. Place it on a hot
plate and gently boil. After the water has been boiling for several minutes, add about 2 g
of solid Ca(OH)2 to the water and keep it near boiling with constant stirring/ swirling for
at least 5 minutes.
Lift off the heat using tongs and measure the temperature of the hot solution. Quickly
strain about 40-50 mL of the hot solution through clean, qualitative filter paper into a
clean, dry 125 mL Erlenmeyer flask and stopper with a cork. Allow the solution to cool
to room temperature.
Note as the solution cools, the solubility of calcium hydroxide increases. The point of
lowest solubility was at ~100 °C and we had saturated the solution at this temperature as
it cools. When the solution cools, the amount of calcium hydroxide does not change (if
like most other materials solubility of calcium hydroxide were directly proportional to
temperature, we would see precipitation but this does not happen). Hence when the
solution cools, we can determine the concentration of calcium hydroxide and this can be
used to determine the solubility product at 100 °C.
Pipet 10.00 mL of this clear solution into a clean, dry 125 mL Erlenmeyer flask. Add
approximately 25 mL of distilled water and 3-5 drops of the bromothymol blue indicator.
Gently drop a magnetic stir bar into the flask. As you did in Part Two, titrate the solution
with the standardized HCl until the yellow endpoint is reached. Repeat the titrations as
necessary.
Experiment End
All solutions after titrations are complete can be disposed of down the drain. . At the end
of the lab, all glassware should be thoroughly cleaned with DI water. You will find a
great deal of glassware contains white precipitates around the sides, obviously this is
calcium hydroxide. These can be cleaned initially using the remainder of your acid
solution, if this does not work, additional acid is provided in the corner of the lab. All
such waste can be disposed of down the sink using plenty of water.
Chem(bio) Spring 2012 – Week 11-6
Chem(Bio) Week 11– Ksp and the solubility of Calcium Hydroxide
Data Analysis
Using the previously described calculations, determine Go and use this to determine
Ho and S° for this system.
Grading of Week 11
Quiz time again I’m afraid. Pre-lab Quiz will open Monday noon-ish and you have until
lab start to do it – question is below and it will have simple questions – what is value of
XXX basically, based on the problem below. As many attempts as you need, this is to get
you comfortable with the calculations. Post lab quiz, details in lab.
Pre-Lab Quiz Question
Note: This question, while using a slightly different metal ion, is an exact model of the
calculations you will have to do in the Ksp lab. So to try and help you prepare, this is
given as a pre-lab quiz. The Moodle itself will just ask for the values since the question is
given here. The Moodle will grade automatically and is designed to accept ONLY THE
NUMERICAL ANSWER (the required units will be listed in the question). You have
unlimited attempts at it but it must be done prior to the lab. You may work with your
group on the calculations but each person should submit the answers in their own
Moodle
Saturated solutions of Barium Hydroxide [Ba(OH)2] are prepared at two different
temperatures, equilibrated, filtered and then 15.00 mL portions of this solution are titrated
with 0.180 M Hydrochloric Acid.
Solution Temp (⁰C)
25
65
Titration Volume of HCl (mL)
17
55
What are the values of Ksp and G° at each temperature and what are the values of H°,
and S° for the dissociation of barium hydroxide?
(you will enter all of these values into the moodle pre-lab quiz but do not include units in
your answer – pay attention to the units the question asks you for!)
References
Euler, W. B.; Kirschenbaum, L. J., and Ruekberg, B. J. Chem. Ed. 2000, 77, 10391040.
Chem(bio) Spring 2012 – Week 11-7