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Determining the Ksp of Calcium Hydroxide: Three Ways to Ask the Question.
Objective: Determine the Ksp of Calcium Hydroxide, an insoluble salt, by the following means:
 Quantitative determination of [OH-] by titration with standardized HCl;
 Quantitative determination of [OH-] by measurement of pH;
 Quantitative determination of [Ca2+] by AA.
Introduction:
In your career as a scientist, you will often use published tables of physical constants. One such
collection of data is the table of solubility products (Ksp) for water-“insoluble” salts:
This table was NOT devised by a clever philosopher in an ivory
tower from thin air, nor did it come from Mt. Sinai. It is the
distilled result of careful lab work and experiment. Each
number in the table may in fact have been reported by several
different groups of scientists getting the data using a number of
different techniques. In this lab you will have an opportunity to
add a line to this table.
First of all, a reminder of what a solubility product, the
Ksp is. If you dump an ionic compound, say, sodium chloride,
NaCl, into a bucket of water and stir it up with a spoon, it will
dissociate into its constituent ions:
NaCl(s) + nH2O  Na+(aq) + Cl-(aq)
That is to say, if you put solid sodium chloride in a lot of water
(that’s what the ‘n” stands for), the water will pull the sodium
and chloride ions apart and surround them (that’s what the
“(aq)” stands for)
If you keep adding NaCl to your bucket of water, the
solution will become more and more concentrated, until you
reach a point at which no more NaCl will dissolve. In the case
Handbook of Chemistry & Physics, 55th ed.
of sodium chloride, this happens when 1000 grams of NaCl is
dissolved in 2.80 L of water at 25oC. Add more NaCl, and it
won’t dissolve. When you have solid, undissolved salt sitting
on the bottom of your bucket, no matter how much more salt you dump in, no more will go into solution. The
solution is said to be saturated. What is going on at the ionic level is:
NaCl(s) + nH2O  Na+(aq) + Cl-(aq)
Na+(aq) + Cl-(aq)  NaCl(s) + nH2O
As fast as solid NaCl dissolves, making Na+ and Cl- (The forward reaction), sodium and chloride ions come
together and make solid sodium chloride (the reverse reaction).
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This condenses to:
NaCl(s) + nH2O ⇄ Na+(aq) + Cl-(aq)
The ⇄ double-headed arrow indicates that the forward and reverse reactions are going at the same rate. This is
the state of equilibrium. This being the case, of course one can write the equilibrium expression for the
reaction:
Ksp = [Na+][Cl-]
The [NaCl] and the [H2O] are constant, and incorporated into the Ksp. (The equilibrium constant, K, is given
the subscript “sp” to indicate that it is describing the solubility of a salt, just as the equilibrium constant, K, is
given the subscript “a” to indicate that it is describing the dissociation of an acid). The Ksp for NaCl is 37.3 at
25oC.
The Ksp will vary with temperature. For example, the process of dissolving NaCl is endothermic:
Heat + NaCl(s) + nH2O ⇄ Na+(aq) + Cl-(aq)
LeChatelier’s Principle says that if you add heat to the system (put the bucket of water on the stove), the
equilibrium will shift right. More NaCl will dissolve. The Ksp increases from 37.3 at 25oC to 43.3 at 100oC.
NaCl is a soluble salt…that is, quite a bit of it will dissolve in water before the solution becomes
saturated. The large Ksp value tells you the same thing. Other salts, such as silver chloride or copper (I) sulfide
(cuprous sulfide, Cu2S) are relatively insoluble in water. Their Ksp values are correspondingly tiny (Ksp [AgCl] =
[Ag+ ][Cl- ] = 1.56 x 10-10. Ksp[Cu2S] = [Cu+ ]2[S= ] = 2 x 10-47.
In this lab, you will determine the Ksp of calcium hydroxide:
Ca(OH)2(s) + nH2O ⇄ Ca2+(aq) + 2OH-(aq)
Ksp[Ca(OH)2] = [Ca2+][OH-]2
In order to calculate the Ksp, you must determine the concentration of Ca2+ and the concentration of OH-. To
make life slightly less complicated, you know that the two concentrations are related, so you only have to find
one and you have the other.(If you measure the [Ca2+] you know that the [OH-] is twice as much. If you
measure [OH-] then you know that the [Ca2+] is half as much). In this lab, you will determine the Ksp of
calcium hydroxide in the following ways:
1. Measure the [OH-]: You will titrate a known volume of a saturated solution of calcium
hydroxide with HCl of a known concentration.
H3O+ + OH-  2H2O
If you know the volume and the concentration of HCl required to titrate the OH_ completely,
then you know the moles of HCl you used, and thus the moles of OH-. You know the volume of
saturated Ca(OH)2 you used, so you can calculate the concentration (moles/L) of OH-. You know that
the [Ca2+] is ½ the [OH-], so you can plug everything into the equilibrium expression and calculate Ksp.
2. Measure the pH:
You can measure the pH of a solution which an ordinary pH meter. Given the pH, you can then
easily calculate the pOH. (pH + pOH = 14 at 25oC). The pOH is of course –log[OH-]. You can thus get
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the [OH-], and then the [Ca2+] will be ½ that. Plug everything into the equilibrium constant and
calculate Ksp.
3. Measure [Ca2+]:
There are several methods for determining [Ca2+]. The method we will use is atomic absorption
spectroscopy. (review last semester’s Iron Lab). Using a calcium lamp and several standards of known
calcium concentration, you will make a standard curve of absorption vs. [Ca2+], and use that to
determine the [Ca2+] in the saturated calcium hydroxide solution. That in hand, you know that the [OH-]
= 2[Ca2+]. Plug everything into the equilibrium constant and calculate Ksp.
☛WEEK 1:
Make 500 mL of a saturated calcium hydroxide solution. This is the
simplest solution you will ever make. Put a spatula-load or two of solid Ca(OH)2 into a clean 500 mL
bottle. Fill with distilled water. Cap and shake. If all the calcium hydroxide dissolves, add more
until you can still see some white flakes of Ca(OH)2 floating around. Cap. Shake. Leave until next
week.
☛WEEK 2:
This is when the actual experiments begin.
You will need:
EQUIPMENT LIST
1
1
5
1
4
2
1
5
1 set
1
funnel
Ringstand/ring
Qual filter papers
buret
Erlenmeyer flasks
Erlenmeyer flasks
Pastuer pipettes and bulbs
Stirring motor + magnet
volumetric flasks + caps
Volumetric pipettes and
blue bulb
pH meter
standards (pH 10)
wash bottle
wash beaker
Indelible marker
125 or 250 mL
<=50 mL
If available.
25 mL
1, 2, 5, 10, and 25 mL
pH meters set up on
back bench
Have a couple handy
You will also need:
 The saturated calcium hydroxide solution you made last week
DON’T SHAKE IT UP!
 Standardized 0.0500 M HCl >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>In carboy at end of bench
RECORD THE EXACT CONCENTRATION LISTED ON THE CARBOY!
 A dropper bottle of 0.1% Methyl Orange >>>>>>>>>>>>>>>>>On the riser
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To avoid traffic jams:
DRAWER Numbers 101-170: Start SCHEME I FIRST (Titration), Then SCHEME II (AA), Then
scheme III (pH).
DRAWER NUMBERS 171-239: Start SCHEME II (AA) FIRST, Then SCHEME I (Titration),
Then scheme III (pH).
DRAWER NUMBERS 240-308: Start SCHEME III (pH) FIRST, Then SCHEME I (TITRATION),
Then scheme II (AA).
SCHEME I. DETERMINATION OF [OH-] by titration with standard HCl.
A. GET out your SATURATED CALCIUM HYDROXIDE AND FILTER IT: The first
thing you need to do is get out your saturated calcium hydroxide solution that you made last
week. Don’t shake it up! Make sure that there is solid calcium hydroxide settled on the bottom
of the bottle. If not, add more solid calcium hydroxide. Set up a funnel and filter paper and filter
about 125 mL of the calcium hydroxide into a clean, DRY, beaker or Erlenmeyer flask.
B. SET UP THE BURET:
Get a 50-mL buret and rinse it several times with distilled water. Make sure you open the
stopcock and run plenty of distilled water through the tip! Go get about 100 mL of 0.0500 M HCl
from the carboy and write down the actual molar concentration in your notebook! Rinse (with
twirling!) the buret with 3 5-mL aliquots of the HCl, and be sure to run some HCl through the tip
each time. Dump the rinsings in the waste jug. Fill the buret with the 0.0500 M HCl and read it.
DON’T try to fill to an exact number (Like 0.00 mL). This introduces an unconscious bias in your
reading. (You WANT your eye to read 0.00 mL., and your eye, which is to say your brain, will
tend to see what your mind wants, rather than what is there.)
C. MEASURE OUT THE SATURATED Calcium hydroxide solution: Rinse a
25.00 mL volumetric pipette with 3 1-mL aliquots of your filtered saturated Ca(OH)2, and dump
the rinsings (they can go in the sink, and combat acid rain). Carefully pipet 25.00 mL of the
filtered saturated Ca(OH)2 into a 125 mL flask and add 2 drops of methyl orange indicator. Note
the color. If available, put in a clean (need not be dry) magnetic stir bar; otherwise, swirl the
flask the old-fashioned way.
D. Titrate: Titrate the saturated calcium hydroxide to the methyl orange end-point. A
sample of what the color should look like is available on the riser. REMEMBER TO READ THE
BURET ACCURATELY, to 2 significant figures after the decimal point. Try to match that color.
Repeat the titration AT LEAST 2 more times, and preferably more. (Your score will be based in
part upon the precision of your results…the more trials you do, the better your precision!) Other
human beings in the past have gotten >99% precision (<1% error). You can too.
E. CALCULATe Ksp:
Remember – when in doubt, convert to moles.
 You know the volume (in mL) of HCl it took to titrate the calcium hydroxide. You know the
mmoles HCl/mL (it’s the same as moles/L). Calculate mmoles HCl used.
 Write the balanced equation for the reaction between H+ and OH-.. How many mmoles of
OH+ reacted with the mmoles of H+ you added?
 Those mmoles of OH- were in 25.00 mL. Calculate the concentration of OH- in mmoles/mL (=
moles/L)
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 Write the formula of calcium hydroxide. For every mmole of OH- how many mmoles Ca2+?
Calculate the concentration of Ca2+ in mmoles/mL (= moles/L)
 Write the balanced equation for the equilibrium of solid calcium hydroxide with its ions in
water. Write the equilibrium constant expression. Calculate Ksp. Do statistics. See next page.
Sample Format for Data and Results, SCHEME I.
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SCEHEME II. DETERMINATION OF [Ca2+] by aA.
A. GET out your SATURATED CALCIUM HYDROXIDE AND FILTER IT: The first
thing you need to do is get out your saturated calcium hydroxide solution that you made last
week. Don’t shake it up! Make sure that there is solid calcium hydroxide settled on the
bottom of the bottle. If not, add more solid calcium hydroxide. Set up a funnel and filter
paper and filter about 15 mL of the calcium hydroxide into a clean, DRY, beaker or
Erlenmeyer flask.
B. MAKE A SET OF CALCIUM STANDARDS: There is a linear relationship between the
concentration of calcium ion in a sample and the amount of light absorbed at 422.67 nm (the calcium
line). Mathematically, this linear relationship (called the Beer-Lambert Law) is:
A422.67nm = Єbc, where Є is the “extinction coefficient”, a proportionality constant,
b is the path length (How far the light travel through the sample.
The longer the path length, the more Ca2+ ions the light bumps into,
the higher the absorption.).
c is the concentration of Ca2+ The higher the concentration, the more
Ca2+ ions the light bumps into, the higher the absorption.)
A422.67nm is the absorption of light at 422.67 nm. This is the value the
instrument measures.
Thus, the A422.67nm that you read off the instrument is directly proportional to the [Ca2+].
To get the [Ca2+] form the absorbance, you need to construct a standard curve of known [Ca2+] vs. A422.67nm. To
do that, you need a set of solutions of known Calcium ion concentration:
1. Obtain about 15 mL of the stock 0.0100 M CaCl2 from the carboy in a CLEAN, DRY
flask. Label it, and note the EXACT Concentration of CaCl2 in your notebook. Also
get a set of 5 25.00 mL volumetric flasks. Wash them thoroughly. They don’t need to
be dry. Label them “1”,”2”, “5”, “10” and “Sat. Ca(OH)2”. Also obtain a set of 1,2,5
and 10 mL pipettes, and a blue bulb. Wash the pipettes thoroughly, rinse them with
3 1-mL aliquots of the stock 0.01 M CaCl2, and dump the rinsings (they can go
in the sink, and combat acid rain). Carefully pipette 1.00 mL of the standard
CaCl2 to the “1” 25 mL volumetric flask, fill it to the mark with distilled water,
cap it and shake it. 30 inversions in the quantitative norm. Repeat, adding 2, 5
and 10 mL of CaCl2 standard to the other volumetric flasks, and dilute them.
Make a table of stock Ca2+ concentration, volume stock added, volume diluted
and final concentration. Leave a space for A422.67nm:
2. Carefully pipette 5.00 mL of your saturated Ca(OH)2 solution into the last volumetric
flask, dilute to the mark with distilled water, cap and shake.
C. RUN THE AA: In consultation with your lab instructor, take your samples to the
instrument room and run the samples through the AA. Typically, you will start with the
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lowest [Ca2+] (deionized water) and work up to the highest [Ca2+]. Then run your diluted
Ca(OH)2 solution. Record all data in your notebook, and wash and return glassware.
D. Construct a standard curve: Graph A442.69nm (Y axis) vs [Ca2+] (x axis) for
your 4 standards and water. Get the equation of the best-fit straight line (Run it through 0) and
use that to calculate the [Ca2+] in your calcium hydroxide solution. The equation will be in the
form Y = mx where m is the slope of your standard curve. If you know the slope, and the
A442.69nm of your calcium hydroxide, you can solve for x, the [Ca2+]
E. CALCULATE [Ca2+], [OH-], and Ksp:
Standard Curve of Calcium Absorbance at 441.67 nm
0.3
0.25
y = 131.83x
R2 = 0.8646
Abs
0.2
Std curve Ca2+
0.15
Linear (Std curve Ca2+)
0.1
0.05
0
0.00E+ 5.00E- 1.00E- 1.50E- 2.00E- 2.50E00
04
03
03
03
03
[Ca2+] M
Once again, write the formula of calcium hydroxide. For every mole/L of Ca2+ how many moles/L
OH-? Calculate the concentration of OH- in moles/L.
Write the balanced equation for the equilibrium of solid calcium hydroxide with its ions in water.
Write the equilibrium constant expression. Calculate Ksp. Do statistics. See next page.
write the balanced equation for the equilibrium of solid calcium hydroxide with its ions in water.
Write the equilibrium constant expression. Calculate Ksp.
SCHEME III. DETERMINATION OF [OH-] by pH.
A. GET out your SATURATED CALCIUM HYDROXIDE AND FILTER IT: The first
thing you need to do is get out your saturated calcium hydroxide solution that you made last
week. Don’t shake it up! Make sure that there is solid calcium hydroxide settled on the
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bottom of the bottle. If not, add more solid calcium hydroxide. Set up a funnel and filter
paper and filter about 15 mL of the calcium hydroxide into a clean, DRY, beaker or
Erlenmeyer flask.
pH
B. Calibrate the
meter and get the pH of your saturated ca(OH)2
solution: Go do it. Record the pH in your notebook.
C. CALCULATE [OH-], [Ca2+], and Ksp: Keep in mind that if you know the pH, you can
calculate the pOH, and thus the [OH-]. That in hand, once again, write the formula of calcium
hydroxide. For every mole/L of OH- how many moles/L Ca2+? Calculate the concentration of Ca-2+
in moles/L.
Write the balanced equation for the equilibrium of solid calcium hydroxide with its ions in water. Write the
equilibrium constant expression. Calculate Ksp.
In your final write up, be sure to include a summary table of Ksp[Ca(OH)2]’s that you obtained. Suggest ways in
which each method may be subject to error. Writing “human error” will result in the deduction of 10 points
from your final score!
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