AMHS AP Chemistry Lab: The Thermodynamics of Solubility
In this experiment several thermodynamic variables (ΔΗ, ΔS, and ΔG) will be calculated for the simple dissolution
reaction and then compared to the literature values:
KNO3(s) + H2O → K+(aq) + NO-3 (aq)
The solubility in moles/liter of the compound will be measured for six or seven temperatures over a range of about 20 –
70 ° C. These values will then be used to calculate the thermodynamic variables using the method outlined in the
procedure. There are two simplifying assumptions made in the calculations: 1) the activities of the ions and the ionic
strength of the solutions are not considered, and 2) the temperature at which the crystals become visible is probably
lower than the equilibrium temperature.
Materials:
Solid KNO3; Boiling water bath; Graduated cylinders; Thermometer
- one 50 mL graduated cylinder with the plastic base removed (or a large test tube) and one 25 mL graduated cylinder
Procedure:
(Caution: Potassium nitrate is a strong oxidizer and skin irritant. Avoid contact with skin, eyes, and mucous
membranes. Avoid shock, heat, and contact with combustible materials. )
1. Weigh out 20.0 g of potassium nitrate and transfer it to a graduated cylinder or test tube.
2. Add 15 mL of water and heat the cylinder in a boiling water bath, stirring until all of the KNO3 has
dissolved.
3. Remove the cylinder with the potassium nitrate in it from the water bath and allow it to cool while
slowly stirring the solution with a thermometer. [Attention: stirring with a thermometer is usually not allowed in a
laboratory procedure for obvious reasons…be careful!!!]
4. Record the temperature when crystals first appear and the volume of the solution. It is assumed at this
temperature that the system is at equilibrium, and it is possible to calculate the concentration of the
ions.
(Determine and record the volume of the potassium nitrate solution. If using test tubes, this can be done by filling an
identical test tube with water until the volumes in both tubes are the same, then measuring the volume in the test tube
filled with water using a larger graduated cylinder.)
5. Now, add 5 mL of water to the test tube and warm the mixture in the water bath again until the solid
has all dissolved.
6. Cool the solution slowly, and then record the temperature and volume at which crystals first appear.
7. Repeat the cycle (steps 5 and 6) adding 5 mL of water, heating and cooling until crystals appear near
room temperature. This should take 5 to 7 determinations. If you do not reach room temperature and
get at least 5 data points, you may need to cool using an ice bath. Caution: this will require attention
to stirring and sighting the crystal formation as the solution must cool evenly until crystallization
occurs!
DATA TABLE 1: (Use an appropriate title)
Trial
1
2
3
4
5
6
7
Volume
Temperature
DATA ANALYSIS:
Because the potassium nitrate is a strong electrolyte, its solution reaction will be:
KNO3(s) + H2O → K+(aq) + NO-3 (aq)
The reaction may be considered to be at equilibrium when the solid is in contact with a saturated solution – the condition we
have when crystallization begins. The solubility, s, of the salt in moles per liter may be calculated from the amount of salt
weighed out and the volume of the solution.
The equilibrium constant, K, for the reaction will be:
-
K = [K+][NO-3 ] = (s)(s) = s2 (eqn. 1)
The equilibrium constant K may be used to calculate the ΔG for the reaction at each temperature using the thermodynamic
relationship below, where T is the Kelvin temperature and R is the gas constant (8.314 J/mol·K).
ΔG = -RTlnK

(eqn. 2)
Using equation 1, calculate the K for each temperature and using equation 2, calculate ΔG for each temperature.
The variation of K with temperature is such that if a plot of ln K (on the y axis) vs. 1/T is made, the result is a straight line with
the slope -ΔH/R.
 Show the manipulation of this equation to generate the equation of a straight line.
 Using a full page of your lab notebook, construct this graph and plot your data points...line of best fit.
 Measure the slope of the line and determine and report the value of ΔH for the reaction.
 Determine the y-intercept for this line and note the significance of this value.
At this point, K and ΔG for each temperature and a single value of ΔH have been calculated. (ΔH is nearly
constant over a small range of temperatures...thus the slope of the line!) Use the value of ΔG and ΔH to
calculate ΔS at each temperature from the Gibbs relationship ΔG = ΔH - TΔS.
DATA ANALYSIS TABLE (USE AN APPROPRIATE TITLE)
Trial
AVE.
s (mol/L)
K
ln K
Temp. (Kelvin)
--------------------
ΔG
1/T
--------------
ΔS
DATA ANALYSIS QUESTIONS:
1. Describe the chemistry involved in this experiment (in your own words) and the significance of your results.
2. Plot a small graph of the solubility of potassium nitrate vs. temperature. What does this graph suggest about the sign
of ΔH for this process? Explain.
3. Two assumptions are made in carrying out this experiment and subsequent calculations. What are they and how does
each assumption affect your results?
4. You determined the ΔH value for the following process by plotting the data. The accepted ΔHfº, ΔGfº and ΔSº values
for the process are given below. Calculate the ΔHrxn, ΔGrxn and ΔSrxn from these values (show all work). Compare to
your empirical (laboratory) values and explain any disagreement.
KNO3(s) 
ΔHfº (kJ/mol) -492.7
ΔGfº (kJ/mol) -393.1
ΔSrxn(J/mol·K) +132.9
K+(aq) +
-251.2
-282.3
+102.5
NO-3 (aq)
-206.6
-110.6
+146.4
5. How does the sign on ΔS “fit” this process? Is this process entropy or enthalpy driven – or both? Explain.
6. Describe any difficulty in carrying out each measurement. Which is most accurate? Least accurate?
7. For the least accurate measurement, are errors likely to be random or systematic? Identify two of these errors and
discuss their affect on your results.
Now the "truth"
You already know that we choose to assume gases behave ideally because it greatly simplifies ordinary work in the lab
and some of the mathematics that goes along with it. The same is true about solutions. What you have learned about
the equilibrium in saturated solutions is true enough, but what you have not been told is that ions, even in rather dilute
solutions, can clump together in groups, or establish quite large hydration spheres with water, etc. In other words,
sometimes the actual concentration of "ions" in a solution is difficult to determine by simple experimental means. The
most accurate determinations of Ksp are done by examining successively more dilute solutions in light of a mathematical
model of "real" solutions. When this is done and the ion concentration is extrapolated to zero, the "official" Ksp or what
is sometimes call the thermodynamic Ksp is found. This value should come close to the value you would get if you found
ΔGº for the process and then used the expression ΔGº= -RTlnK to determine the Ksp. This often results in disagreements
between ordinary experimental values and calculated values related by factors of 10 or 100!!!!
MORAL: Basic solubility and Ksp concepts are deceptively simple and not meant to be strictly mathematical.