Determination of a Solubility Product Constant
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Abstract: The solubility product constant (Ksp) of potassium hydrogen
tartrate (KHC4H4O6 , “Cream of Tartar” ) will
be evaluated by determining the concentration of hydrogen tartrate ion (HC4H4O6-
) in a saturated solution of potassium hydrogen tartrate by titration
with sodium hydroxide. You may have
seen crystals of this compound on corks from white wine bottles.
Introduction
The solubility
product constant, Ksp: When an ionic solid is added
to pure water, it dissolves at a relatively rapid initial rate. But as the concentration of dissolved ions
increases, so does the rate of reprecipitation. Soon the rate of reprecipitation equals the rate of dissolution,
and there is no more net dissolution
of solid. The state of dynamic
equilibrium has been attained. Of
course, there may be very rapid dissolution and reprecipitation, evidenced by
changes in the shape of particles of solid, even though their masses remain the
same.
For an ionic compound, the equation for dissolution
is
(1) AnBm(s)
Û n Am+(aq)
+ m Bn-(aq)
When equilibrium has been attained, the solution is
said to be saturated. If solid is added
to the mixture of solid and solution at equilibrium, none will dissolve; if
solid is removed, the concentration of ions in solution will remain the
same. Since the presence of solid has
no effect on the equilibrium concentrations of ions in the saturated solution,
the equilibrium constant expression for equation (1) does not include a term
referring to the solid. The
equilibrium constant is called the solubility product constant, and it is
defined as
(2) Ksp = [Am+]n[Bn-]m
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The solubility product constant is extremely useful
for predicting solubilities of salts not only in pure water, but in solutions
which already contain one or the other of the ions in the dissolving substance.
For example, potassium hydrogen pththallate, HC8H4O4,
is a slightly soluble ionic compound whose structure is shown to the
right. We can look up the solubility of
potassium hydrogen phthallate in the CRC Handbook
of Chemistry and Physics, and find it to be 10 g per 100 mL of water at 25oC.
The
Ksp can be calculated from the solubility as follows:
The concentration of a saturated
solution (at equilibrium) is:
(3) 
Since
KHC8H4O4 dissolves and dissociates almost
completely to give K+ ions and HC8H4O4-
ions, the concentration of each ion is also .49 M, and Ksp is:
(4) Ksp = [K+][HC8H4O4-]
= (.49)(.49) = .24
It
might seem that stating the solubility is simpler and more efficient than
stating the value of Ksp. But having
the value of Ksp is really much more useful than having the solubility, because
with it solubilities in solutions containing "common ions" can be
calculated. For example, we can calculate
the solubility of potassium hydrogen phthallate in a solution already containg
4 M KCl:
KHC8H4O4 Û K+ + HC8H4O4-
init. C(M) 4
M 0
change +
x + x
eq. C(M) 4
+ x x
Ksp = .24 = [4 + x][x] @
[4][x]
x = .06 M
.06 mol/L x 204 g/mol = 12 g/L
or only 1.2 g in 100 mL,
compared to the solubility of 10 g in 100 mL of pure water.
Potassium Hydrogen Tartrate: The substance used in this experiment has had a profound impact
on both the technological and
theoretical development of chemistry.
Cooks call it "cream of tartar."
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Oenologists (wine experts) and producers sometimes
use the German name "weins¬ure" (wine acid) or "wine lees" for
this solid, which precipitates during the fermentation of grapes. Grapes, like may fruits, are high in this
natural "fruit acid", with the formula KHC4H4O6,
whose structure is shown to the right.
Traces of calcium tartrate found in a pottary jar from ruins of a
neolithic village in northern Iran have been used as evidence that wine was
being produced 7000 years ago[1],
because the only significant natural source of tartaric acid is grapes.
Cream of tartar is used as a source of acid in
home-made baking powder, which also contains sodium hydrogen carbonate. When moist, they react to give CO2
which causes breads to rise:
(5) HC4H4O6-
+ HCO3- Û C4H4O62- + H2CO3
(6) H2CO3 Û H2O + CO2(g)
Many
cooks find cream of tartar superior to the sodium aluminum sulfate (NaAlSO4)
which is the acid used in modern "double-acting" baking powders.
Potassium hydrogen tartrate is the "salt"
obtained when tartaric acid (H2C4H4O6)
is half neutralized with potassium hydroxide:
(7) H2C4H4O6
+ KOH Û H2O + KHC4H4O6
Louis
Pasteur revolutionized our understanding of molecular structure when he found
two kinds of tartaric acid crystals forming in fermenting grapes, both having
the same formula. The two forms are
identical except that their molecules are mirror images of one another, like
your right and left hand. The forms
differ in the direction which they rotate polarized light, and only the
dextrotartaric acid (right-rotating) is found in most living things. Tartaric acid is used in soft drinks,
candies, bakery products, tanning, photography, and in gelatin desserts. Tartaric acid or potassium hydrogen tartrate
was called faecula ("little yeast") by the Romans, and the derivation
of the word from "Tartarus" (in Greek mythology, the abysmal regions
of hell, below Hades) is of alchemical origin.
Our interest in potassium hydrogen tartrate is an ancient one.
Most
commercial potassium hydrogen tartrate is obtained from the sediments in the
manufacture of wine. Knowing the value
of Ksp and how to apply it is important
to our understanding of the fermentation technology.
Method
A saturated solution of potassium
hydrogen tartrate is prepared by stirring KHT in water for 20 minutes so that
the following equilibrium is attained:
(8) KHT(s) Û K+ + HT-
Where
HT- represents the hydrogen tartrate ion, HC4H4O6-. The concentrations of K+ and HT-
are needed to evaluate Ksp.
(9) Ksp = [K+][HT-]
The
hydrogen tartrate or bitartrate ion concentration is determined by titration
with NaOH:
(10) C4O6H5-
+ OH- Û C4O6H42-
+ H2O
The
solid KHT must be removed by filtration before the solution is titrated,
otherwise reaction (8) will provide HT- as the OH-
consumes it, and all the KHT will dissolve.
The amount (in mol) of bitartrate is
equal to the amount of hydroxide, which is calculated from the volume of sodium
hydroxide standard solution used in the titration:
(11) n(mol) = C(M) x V(L)
If
the potassium bitartrate is dissolved in pure water, the concentration of
potassium ion must be equal to the concentration of bitartrate ion, and Ksp can
be calculated:
(12) Ksp = [K+][HT-] =
[HT-]2
If
the potassium bitartrate is dissolved in 0.l0 M potassium chloride solution,
the "common ion" K+ should (by LeChatelier's Principle)
lower the solubility of the potassium bitartrate. Because the value of Ksp is constant, increasing the
concentration of one ion must decrease the concentration of the other. In this case, the concentration of
bitartrate is determined as above, but the concentration of potassium ion is
0.1 M + [HT-], so the value of Ksp is
(13) Ksp = [K+][HT-] =
(0.10 + [HT-])[HT-]
Prelaboratory Assignment
Procedural:
1. Suppose 1.5 g (rather than 1.0 g) of potassium hydrogen tartrate
is mixed with 75 mL of water or KCl solution in steps 1 and 2 of the
procedure. Would this increase,
decrease, or have no effect on the value of Ksp?
2. In step 3 of the procedure, the filter paper and holder used to
filter the KHT solution must be clean and dry, but the beaker used to collect
the KHT from the burette in step 4 need not be dry. Why will water cause an error in the first case and not in the
second?
Theoretical:
3. If water at the boiling point is saturated with potassium
hydrogen tartrate, 30 mL of the solution requires 49.5 mL of 0.2 M NaOH in a
titration. What is the Ksp of potassium
hydrogen tartrate at this temperature, and what is the solubility in g/L?
4. At a certain temperature, 16.7 mL of 0.45 M NaOH solution is
required to titrate 30.0 mL of a 0.1 M KCl solution saturated with potassium
bitartrate. What is the Ksp
of KHT at this temperature?
5. A student realized that the after KHT dissolves, bitartrate ion
might be involved in the equilibrium
(14) HT- + H2O Û H2T + OH-
The HT- would
then not be available for titration with NaOH, and misleading results would be
obtained. Why has the student reached
an incorrect conclusion (all the HT- will be titrated even though
reaction (14) may, in fact, proceed)?
Procedure:
1. Tare a 150 or 250 mL beaker on the balance, add about 1 g of
finely ground potassium hydrogen tartrate ("KHT"), and record the
mass. Repeat for a second sample.
2. Add 75 mL of distilled water and a magnetic stirrer to one of the
flasks containing KHT, and add 75 mL of 0.10 M KCl to the other. Stir the first flask for a sufficient time
to saturate the water with KHT. At room
temperature this may require 10 minutes.
If a magnetic stirrer is not available, swirl the flasks every minute or
two. If a magnetic stirrer is used,
transfer it to the second flask after the first one has been stirred for about
10 minutes.
3. Assemble a Luer-lok filter assembly with a dry 2.1 cm filter
disk. Draw as much of the KHT
suspension as possible into a 20 or 60 mL syringe, attach the syringe to the
filter apparatus, and eject 10-15 mL of the solution into a burette. Rinse the burette with the solution and
discard it. Fill the burette with the
remaining solution from the syringe/filter apparatus. Remove the syringe from the filter to refill it when necessary,
to provide enough solution to fill the burette. Open the stopcock briefly to eliminate bubbles from the burette.
4. Use the burette to deliver at least 35 mL of the KHT solution to
a clean (but not necesarily dry) 250 mL beaker or Erlenmeyer flask. Record the precisely measured volume.
5. Repeat steps 3 and 4 for the solution of KHT in 0.1 M KCl.
6. Rinse and fill a clean burette with 0.05 to .1 M standard NaOH
solution. Make sure that no air bubbles
are trapped in the stopcock. Add a
few drops of phenolphthalein indicator to the KHT solutions, titrate them with
NaOH, and record the volumes.
Equipment and Supplies
(2) 50 mL burettes (2)
250 mL Erlenmeyer flasks
(2) 150 mL beakers 60 mL
plastic syringe
magnetic stirrer burette
stand and clamp
phenolphthalein indicator Luer-lok
Syringe filter holder and filter paper
0.4 g potassium hydrogen
tartrate 150 mL 0.10
M KI or KCl
50 mL 0.050 M standard NaOH
solution
Projects:
I. Free Energy (DG), Entropy change (DS) and Enthalpy of solution
for KHTar: Repeat the experiment, but
dissolve the KHTar in water at different temperatures[2]. Determine the equilibrium constant at 0oC.
Repeat at a higher temperature as well
to see if the same trend is observed.
If the reaction is exothermic, decreasing the temperature should
increase the value of Ksp, but the value as well as the sign of DH can be determined from the equation which
predicts how K changes with T:
OR 
Where
K1 and K2 are the equilibrium constants at temperatures T1
and T2 (Kelvins), and R is the ideal gas constant, 8.31 J/mol
K. If measurements are made at several
temperatures, the second equation shows that a plot of ln K vs. 1/T should be a
straight line with slope -DH/R.
Does the sign of DH agree with predictions from LeChatelier’s
Principle? Does its value reflect
involvement of a large amount of bond energy (DH reflects formation and
destruction of bonds as long as DV for the reaction is small,
when DH» DE).
II. Calculation of DG and DS for the reaction: The value of the free energy change, DG, can be calculated from the equilibrium
constant:
and
DS can be calculated from DH (calculated in Project I) and DG, by using the Gibbs Equation :
Interpret
the value of DS: In terms of increases or decreases in disorder, explain the
relationship between DS and the chemical equation
for what is actually happening.
III. Radiochemical Determination of the Ksp of
Ba(OH)2: In an earlier experiment, we
eluted Ba-137 from a minigenerator and determined it’s halflife. That same Ba-137 could be used as a
radiochemical tracer to determine the Ksp for barium hydroxide. The total count for 10-20 drops of eluent in
a planchette should be determined and the time recorded. The tracer solution might be washed into a
30 mL beaker with 2 mL of 2.0 M Ba(NO3)2
“carrier,” then 2 mL of 2-4 M NaOH added to precipitate the Ba(OH)2. Stirring for a few minutes with a stirring
rod coated with previously-precipitated Ba(OH)2 is sometimes
necessary to accelerate this slow process.
The suspension is then drawn into a syringe, a LuerLok filter attached,
and after a few drops are discarded, 20 drops of filtrate are added to a
planchette and counted, and the time recorded.
The precipitate could also be counted.
Repeat counts (and times) of the filtrate could be used to confirm the
halflife.
The carrier is added because radiotracers are present at
chemically insignificant concentrations (only a few thousand atoms in many
cases). Barium nitrate is added so that
a substantial amount of precipitate is obtained rapidly. The ratio of activity in the filtrate to the
total activity can be multiplied by the total number of moles of Ba2+
present to give the amount (in mols) in solution, and thence the concentration
at equilibrium. The initial
concentration is calculated from the known concentration of the barium nitrate
and total volume of the mixture. All
counts must be adjusted to the same time by using the equation ln(A/Ao) = -kt,
so that the effects of decay during the experiment are eliminated, and you must
work fairly quickly.
II.
Titrimetric Determination of the Ksp of Ba(OH)2. In an earlier experiment, we did a
conductimetric titration of Ba(OH)2 to determine the stoichiometry
of the reaction with H2SO4. The same procedure could be adapted to a measurement of Ksp for
barium hydroxide. About 1 mL of a
saturated solution could be titrated.
Footnotes