## The Thermodynamics of Potassium Nitrate Dissolving in Water

CONCEPTS

A mole of potassium nitrate, a strong electrolyte, dissolves in water easily to form one mole each of potassium ions (K+) and nitrate ions (NO3) ions as shown in the equation below.  A saturation point is reached when additional amount of solid KNO3 is no longer dissolving in water. This means a saturated solution is formed, when there is sufficient quantities of the ions present that recombine to form the solid KNO3.   At this condition, the dissolution of solid KNO3 into its component ions is happening at the same rate as K+ and NO3 ions recombine to form back the solid KNO3.  As a result the ion concentrations remain constant, and the reaction has reached equilibrium.

KNO3(s)   +  H2O(l)              K+(aq) +  NO3(aq)                           (Equation 1)

When the system is at equilibrium, one mole of the dissolved KNO3 will produce a mole each of K+ and NO3 ions.  This condition can be mathematically described with an equilibrium constant expression, Ksp, for KNO3 dissolving in water as shown below.

Ksp = [K+] [NO3]                                                        (Equation 2)

The Ksp expression is the solubility product constant for the dissociation reaction of KNO3 in water, which is equal to the square of the solubility (in moles/liter) of KNO3 at that temperature (equation 2).  In general, the higher the Ksp, the more soluble the solid compound is.  However, the equilibrium constant does not only tell us the solubility of the compound in water, but also show the dependency of the expression on the ions’ concentrations in molarities (moles/L).  Furthermore, because the solubility of KNO3 changes with the temperature (T in Kelvins) changes, its Ksp is a function of the temperature.  Hence, a mathematical relationship between the Ksp and absolute temperature can be determined and relate it to the thermodynamic parameters that can further explain the solubility of KNO3 in water.

The three important thermodynamic parameters ΔG (free energy change), ΔH (enthalpy change) and ΔS (entropy change) that describes why and KNO3 dissolves in water are summarized below:

• The enthalpy change (ΔH) for KNO3 dissolving in water provides the difference in energy between solid KNO3 and its dissolves ions. ΔH is positive (+) if heat is needed to dissolve KNO3 (endothermic process), and negative (-) if heat is given off when KNO3 is dissolving in water (exothermic process).
• The entropy change (ΔS) for KNO3 dissolving in water indicates the relative disorder of the dissolved ions with respect to solid KNO3. ΔS is always positive since the randomness of the system increases by the formation of the ions.  The two ions in the product side possess more disorder than the solid KNO3 as a reactant.
• The free energy change (ΔG) for KNO3 dissolving in water indicates whether the process occurs spontaneously or not.  Negative ΔG means the process is spontaneous while positive ΔG means the process is nonspontaneous.

The equilibrium constant, Ksp, and the absolute temperature (T) can be used to determine the DG of the reaction as shown in equation 3,

DG = – RT lnKsp                                                     (Equation 3)

where R is the gas constant, 8.314 J/K. mol, T is the temperature in Kelvins, and ln Ksp is the natural log of the equilibrium constant.   Since

DG = DH -TDS                                                              (Equation 4)

where DH is the enthalpy change and DS is the entropy change for the reaction, the two expressions for DG found in equations 3 and 4 can be set equal as shown in equation 5.

-RT lnKsp = DH -TDS                                                                        (Equation 5)

Using algebra, rearranging equation 5 following the equation of a straight line gives

lnKsp = – (  )(  ) +                                                                 (Equation 6)

In this experiment, you will gather temperature readings at various saturation points of KNO3 solution at varying ions’ concentrations.   The solubility product constants, Ksp, at various temperatures can then be calculated experimentally for various temperatures (T).  Using Equation 3, the free energy change, DG, can also be determine at various temperatures.  By plotting lnKsp versus 1/T,  and obtaining the linear-fit equation, the enthalpy change, DH, can then be calculated.  Using Equation 4, the entropy change, DS, for the reaction can be determined (or equation 6 using linear-fit equation).

MATERIALS

Computer
Vernier LabQuest 2

Vernier Temperature Probe

Iron Stand

400 mL beaker (for hot water bath)

2-3 pieces of boiling chips
Two 25 × 150 mm test tubes

Utility clamp

Iron ring

Hot plate

4 g of KNO3

DI water
marker

PROCEDURE

1. Wear a departmentally approved pair of safety goggles while doing this experiment.

1. Connect a Temperature Probe to Channel 1 of the Vernier LabQuest 2. Connect the LabQuest 2 to the computer with the proper cable. Start the Logger Pro program on your computer. Open the file “13 Enthalpy” from the Advanced Chemistry with Vernier.
2. Assemble a hot-water bath as shown in Figure Place a 400-mL beaker with tap water (about 250mL) and 2-3 pieces of boiling chips on a hot plate. Place an iron ring around the beaker to minimize the possibility of upsetting the water bath or to avoid it from falling off the hot plate.   Turn on the heat to about 125 oC, and adjust the temperature to about 100 oC when water starts to boil.

Figure
1     Setup for heating the potassium nitrate solution

1. Weigh about 4 g of KNO3 on a tared piece of weighing paper. Record the exact mass of KNO3 (1) on your Data and Calculations section. Transfer the KNO3 to a clean 25 x 150-mm test tube.

1. Using a graduated cylinder, add 3 mL of deionized water to the test tube containing the KNO3. Heat the test tube, as shown in Figure 1, in the assembled hot-water bath. Continue heating, while stirring gently with a temperature probe, until all of the KNO3

DANGER:
Potassium nitrate solution is an irritant and oxidant. If any of the solution come in contact with your skin, thoroughly wash the area with water.

1. Carefully raise the test tube with melted KNO3 away from the hot water bath. Just lift it from beaker, suspend in air with a utility clamp, away from the steaming water bath.

NOTE:  Before raising the test tube, make sure your marker and empty 25 x
150 mm test tube is ready to perform the volume measurement in Step 5.

2. Quickly determine the volume of the KNO3 solution inside the test tube by using the same test tube size and model of 25 x 150 mm. Place the empty test tube next to the KNO3 test tube and using a marker, draw a line as accurate as you can on the empty test tube to mark the volume of KNO3 solution in the reaction test tube.  Fill up the empty test tube with tap water up to the mark you made.   Measure the volume in the test tube filled with tap water by pouring this water into a 10-mL graduated cylinder. Record this volume on your Data Sheet (2).
3. If crystals started to form, put the KNO3 test tube back to the hot water bath. Remove the test tube with the KNO3 solution from the hot-water bath and allow it to cool while slowly stirring the solution.  Just lift it from beaker, suspend in air with a utility clamp, and continue stirring (avoid splashing on walls of test tube). Record on your Data and Calculations section the temperature at which crystals first appear (3).
4. Record the temperature when crystals first appear, it is the temperature at which the solid is assumed to be in equilibrium with the solution.
5. Add 1 mL of DI water to the test tube containing the KNO3 Warm and stir the mixture in the hot-water bath until the solid has completely re-dissolved. Using the same method as in Step 6, determine and record on your Data and Calculations section the solution volume (D.2).
6. Remove the test tube containing the KNO3 solution from the hot-water bath. Allow it to cool slowly (cool at room temperature). Just lift it from beaker, suspend in air with a utility clamp, and continue stirring (avoid splashing on walls of test tube). Record on your Data and Calculations section the temperature at which crystals first appear (3).
7. Repeat Steps 9 and 10 for a total of 6 determinations. Record all volume and temperature measurements on your Data and calculations section.

Note: See sample data below which you can use to perform practice calculations for this
experiment.

EXPERIMENT VIDEO

See how the experiment is done from https://youtu.be/zvaXJzzol3M .

SAMPLE DATA

 Mass of KNO3 = 4.002 g Trial Solution Volume (mL) Temperature of Crystallization (oC) 1 7.5 2 7.8 3 8.2 4 9.1 5 9.7 6 10.3

PROCESSING THE DATA

Do the following calculations for each determination and record the results on your Data Sheet.

1. Use the mass of the KNO3 to calculate the number of moles of KNO3 present.
2. Use the number of moles of KNO3 and the volumes you determined at each temperature to calculate the molar concentration of KNO3 in the solution at each temperature. Because nearly all the KNO3 is still in solution, its molar concentration equals the molar concentrations of K+ and of NO3 in the saturated solution.
3. Use Equation 2 to calculate the equilibrium constant, Ksp, for dissolving KNO3 in water at each temperature.
4. Convert the temperatures in degrees Celsius (°C) to Kelvins (K).
5. Determine the natural logarithm of Ksp (InKsp) at each temperature.
6. Use Equation 3 to calculate ΔG at each temperature.
7. Calculate the reciprocal of each Kelvin temperature, 1/T (K-1 ).
8. Using the Vernier graphing functions or any computer spreadsheet program, construct a graph with the y-axis as InKsp and the x-axis as 1/T. Title your graph properly and save.
9. Highlight all the points on the graph and click Linear fit.  Alternatively, your laboratory instructor may ask you to use a computer spreadsheet program to perform regression analysis on your experimental data, to plot the data, and to calculate the slope of the best straight line.
10. Calculate ∆H for the reaction. Remember that the slope of the straight line in the InKsp versus 1/T plot equals –∆H/R, according to Equation 6.
11. Calculate ∆S at each temperature using Equation 4. Determine the average ∆S. Alternatively, if regression analysis is used, obtain the average ∆S from the y-intercept of the straight line.

SAMPLE DATA AND CALCULATIONS

Determine the Ksp for KNO3 and the three thermodynamics parameters, ΔG, ΔH, and ΔS, using the example problems below.

Example 1.

Dissolving 10.1 g of KNO3 in enough water to make 25.0 mL of solution results in a saturated solution of KNO3. Determine the Ksp for KNO3 and the thermodynamics parameters ΔG, ΔH, and ΔS with additional measured values.
Firstly, calculate the number of moles of KNO3 that dissolve,

Equation 1 in the Concepts section shows that when 0.100 mol KNO3 dissolves, 0.100 mol K+ and 0.100 mol NO3form.  Calculate the concentration of each of these ions in the saturated solution,

According to Equation 2,
Ksp = [K+] [NO3) = (4.00) (4.00) = 16.0

Example 2.

Suppose the equilibrium constant, Ksp, for KNO3 dissolving in water at 25°C is 2.4. Determine the ∆G for this process at 25°C.

Apply Equation 3, making sure that the temperature is in the proper units,

∆G = – (8.314 J / K·mol) (25 + 273 K) (In 2.4)

= – (8.314 J / K·mol) (298 K) (0.88)
= -2200 J / mol

Because ∆G is negative, this compound spontaneously dissolves in water at 25°C.

Example 3.

Suppose you measure the equilibrium constant, Ksp, for a compound dissolving in water at several temperatures, as shown in the following table:

 Temperature (˚C) Ksp 25 2.4 35 3.0 45 3.7

Determine ∆H for this process.  In order to use Equation 6 to determine ∆H, we need to calculate Inksp and 1/T from the data;

We plot InKsp as a function of 1/T and draw the best straight line through the three points:

We determine the slope of the line graphically or by regression analysis on a computer spreadsheet:

Slope = -2.0 x103 K

Finally, we relate the slope of this line to ∆H as shown in Equation 6,

Slope =  , or upon rearrangement,

∆H = -R (slope)

∆H = – (8.314 J/K·mol) (-2.0 x 103 K)

=  + 17000 J/mol

Because AH is positive, this compound absorbs heat from its surroundings to dissolve in water.

Example 4.

The data in Examples 2 and 3 represent the same ionic compound dissolving in water. Determine ∆S for this process at 25°C.

Since ∆G= -2200 J/mol at 25°C (Example 2) and that ∆H = 17000 J/mol (Example 3).  Equation 4 relates these three thermodynamic quantities,

∆G = ∆H-T∆S             upon rearrangement,

Because ∆S is positive, the products (ions) of the reaction have more disorder than the reactant (the undissolved compound). In this case, the entropy change represents the driving force for the spontaneous dissolution of the compound in water.

LAB SAFETY AND WASTE DISPOSAL

Waste Disposal
:

Carefully bring the test tube containing the KNO3 solution (in liquid state) to the Satellite Hazardous Waste Accumulation area.  Remove the red plastic funnel from the waste bottle labelled “Inorganic Waste” and pour the contents of your test tube into it.  Record total waste as 12g in your folder.  No need to collect waste in the small plastic waste bottle and weigh.
Lab Safety

Wear the appropriate Personal Protected Equipment (PPE). Read all Safety Data Sheets (SDSs) provided by instructor.  Pay attention to the safety precautions mentioned in the procedure and by the instructor. Wash your hands thoroughly with soap or detergent before leaving the laboratory.

References

Silberman, R. (1999).  The thermodynamics of potassium nitrate dissolving in water. In CHEM 1106 General Chemistry II for NJCU Chemistry Department.  Mason, OH:  Cengage Learning.

DATA AND CALCULATIONS

Temperature and Volume Data

Mass KNO3 (g) (D.1)  ______________________

 Trials —-> 1 2 3 4 5 6 Volume, mL (D.2) Temperature of Crystallization, °C ( D.3)

Determining Ksp

Moles of KNO3 _____________________

 Concentration, M Ksp

Determining ΔG

 T, °K lnKsp ΔG, J/mol

Determining ΔH

Slope of the line defined by lnKsp versus 1/T (attach your graph) ________________________

ΔH, J/mol  ___________________________

Determining ΔS

 ΔS, J/K * mol

Average ΔS =
CALCULATIONS

DATA ANALYSIS

1. Using your calculated values of Ksp, is KNO3 highly soluble in water?

2.  Using the three thermodynamics parameters, ΔG, ΔH, and ΔS, answer the following questions why and how KNO3 dissolves in water:

– Is the process spontaneous or non-spontaneous?
– Is the process exothermic or endothermic?
– Has the process resulted in increase or decrease in disorder?

2. What is the driving force for the spontaneous dissolution of KNO3 in water?