CHM 152
Lab 10: The Thermodynamics of an Aqueous Salt
Last updated Jan. 2012
Introduction
When a salt is placed in water, there exist an equilibrium between the solid and the dissociated aqueous
ions, regardless of how soluble or insoluble the salt may be. The equilibrium constant for such systems is
often called the solubility product constant, Ksp. Potassium nitrate, for example, would establish the
following equilibrium when dissolved in water.
KNO3(s)  K+(aq) + NO3-(aq)
Ksp = [K+][NO3-]
The Gibbs free energy change of a system ( G) is related to its equilibrium constant by the following
reaction.
G = -RTlnKsp
For this equation, the gas constant (R) is 8.314 J/mol K and, as often the case, T is the temperature in
Kelvin.
Recall that G is also related to the changes in enthalpy ( H) and entropy ( S) by the following equation.
G= H-T S
Combining these two equations gives us
-RTlnKsp = H - T S
which we can rearrange algebraically to give us the following linear equation (y = mx + b).
ln Ksp = (- H/R)(1/T) + S/R
This means that a plot of ln Ksp over 1/T should be linear with a slope equal to - H/R and a y-intercept
equal to S/R.
For this lab, you will measure the solubility of potassium nitrate at different temperatures. From the known
concentrations of these solutions we can determine the solubility product constant at each temperature.
You will then plot of lnKsp over 1/T to determine the enthalpy and entropy changes of this system, which
can be used to determine its Gibbs free energy change as well.
Concepts to Review
Equilibrium constants
Gibbs free energy
Enthalpy change
Entropy change
Plotting with Excel
Diluting solutions
Procedure
Part I: Measuring the Solubility of Potassium Nitrate Over Different Temperatures
1. Assemble a hot bath as follows (note: this is the same set-up that was used in Lab 3: Freezing-Point
Depression).
a) Fasten a support ring to a ring stand
b) Set a wire gauge on the support ring
c) Place a 600mL beaker of water on the wire gauge. Fasten a second support ring around the
beaker to reduce the risk of knocking it over.
d) Attach a clamp to ring stand just above your beaker. This will be used to hold your sample
(step 4).
e) Add a couple of boiling chips to the water to reduce the risk of uneven boiling (“bumping”)
2. Use a Bunsen burner to pre-heat the water as you prepare your sample.
3. Weigh out 20g of potassium nitrate and transfer to a large test tube.
4. Set the apparatus in the beaker of hot water. Use the clamp from step 1d to keep the sample submerged
in the water without touching the bottom of the beaker.
5. Using a graduated cylinder, add 15mL of distilled water to the test tube. Cap the test tube with a rubber
stopper that’s threaded with a thermometer and wire stirrer (this item will be pre-assembled for you; see
instructor for its location). The stopper doesn’t have to fit in the opening of the test tube. It can simply be
set on top of it.
6. Heat the solution, with stirring, until all solid has dissolved.
7. Remove the test tube from the hot bath. Continue stirring as you slowly cool the solution.
8. Record the temperature where you first see crystals begin to form. We will assume that this temperature
is where the solid and solution are in equilibrium.
9. Add another 5mL of distilled water to your solution and repeat steps 6-8.
10. Repeat step 9 four more times to give you a total of six determinations.
Waste Disposal
Solution waste should go in the Inorganic Waste bottle.
Name: _____________________________
Section: ________
Data
1) Mass of KNO3, g
__________
2) Moles of KNO3
__________
3) Volume of KNO3, mL
(density = 2.11 g/mL)
__________
4) Solubility data
Trial
1
2
3
4
5
6
Volume of water, mL
________
________
________
________
________
________
Total volume, mL
________
________
________
________
________
________
[KNO3], M
________
________
________
________
________
________
Temperature when
crystals form, C
________
________
________
________
________
________
5) Calculate Ksp at each temperature. Use these values to find G of each trial.
Trial
1
2
3
4
5
6
Temperature, K
________
________
________
________
________
________
Ksp
________
________
________
________
________
________
G, J/mol
________
________
________
________
________
________
In the space below, show your work for the determination of K sp and G for Trial 1.
6) Using Excel, draw a plot of lnKsp over 1/T (showing the linear equation and R2). Include a copy with
your report.
Trial
1
2
3
4
5
6
ln Ksp
________
________
________
________
________
________
1/T, K-1
________
________
________
________
________
________
Slope
__________
Y-intercept
__________
7) H, J/mol
Show your work below.
__________
8) S, J/mol
Show your work below.
__________
9) Assuming H and S are fairly constant in the temperature range studied, use these values to calculate
the G of each trial.
Trial
Temperature, K
G, J/mol
1
2
3
4
5
6
________
________
________
________
________
________
________
________
________
________
________
________
In the space below, show your work for the determination of G for Trial 1.
Name: _____________________________
Section: ________
Post-lab Questions
1. For each temperature studied, does the sign of G agree with your observations? Explain.
2. Does the sign of S agree with what you would predict? Explain.
3. In CHM 151, was KNO3 predicted to be soluble or insoluble in water? Are the values of K sp consistent
with this prediction? Explain.
4. Based on your values of H and S, when is this reaction predicted to be spontaneous: all temperatures,
never, or only at a low or high enough temperature?
Does your values of K and G agree with this prediction? Explain.
5. If you failed to factor in the volume of KNO 3, how would each of the following be affected (too high,
low, or no effect)? Explain your answers.
a) Ksp
b) G (calculated from Ksp)
Name: _____________________________
Section: ________
Pre-lab Questions
1. A salt, MA, establishes the following equilibrium when dissolved in water.
MA(s)  M+(aq) + A-(aq)
a) Write the expression for the solubility product constant, K sp, of this system.
b) How would the Ksp of a soluble salt differ from one that’s insoluble?
2. A 200.0mL solution with 3.1 x 10-3 mol of MA will begin to precipitate at 19.4 C. Calculate each of
the following at this temperature.
a) Ksp
b) G
3. The solubility of MA was measured over several temperatures, giving a linear plot of lnK sp over 1/T with
a slope of 2.44 x 10-3 and a y-intercept of 10.6. Calculate each of the following.
a) H
b) S