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 (NO_{3}^{–}) ions as shown in the equation below. A saturation point is reached when additional amount of solid KNO_{3} 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 KNO_{3}. At this condition, the dissolution of solid KNO_{3} into its component ions is happening at the same rate as K^{+} and NO_{3}^{–} ions recombine to form back the solid KNO_{3}. As a result the ion concentrations remain constant, and the reaction has reached equilibrium.
KNO_{3}_{(s) }+ H_{2}O_{(l)} K^{+}_{(aq)} + NO_{3}^{–}_{(aq)} (Equation 1)
When the system is at equilibrium, one mole of the dissolved KNO_{3} will produce a mole each of K^{+ }and NO_{3}^{–} ions. This condition can be mathematically described with an equilibrium constant expression, K_{sp}, for KNO_{3} dissolving in water as shown below.
K_{sp} = [K^{+}] [NO_{3}^{–}] (Equation 2)
The K_{sp} expression is the solubility product constant for the dissociation reaction of KNO_{3} in water, which is equal to the square of the solubility (in moles/liter) of KNO_{3} at that temperature (equation 2). In general, the higher the K_{sp}, 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 KNO_{3 }changes with the temperature (T in Kelvins) changes, its K_{sp} is a function of the temperature. Hence, a mathematical relationship between the K_{sp} and absolute temperature can be determined and relate it to the thermodynamic parameters that can further explain the solubility of KNO_{3} in water.
The three important thermodynamic parameters ΔG (free energy change), ΔH (enthalpy change) and ΔS (entropy change) that describes why and KNO_{3} dissolves in water are summarized below:
 The enthalpy change (ΔH) for KNO_{3} dissolving in water provides the difference in energy between solid KNO_{3} and its dissolves ions. ΔH is positive (+) if heat is needed to dissolve KNO_{3} (endothermic process), and negative () if heat is given off when KNO_{3} is dissolving in water (exothermic process).
 The entropy change (ΔS) for KNO_{3} dissolving in water indicates the relative disorder of the dissolved ions with respect to solid KNO_{3}. 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 KNO_{3} as a reactant.
 The free energy change (ΔG) for KNO_{3} 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, K_{sp,} and the absolute temperature (T) can be used to determine the DG of the reaction as shown in equation 3,
DG = – RT lnK_{sp} (Equation 3)
where R is the gas constant, 8.314 J/K. mol, T is the temperature in Kelvins, and ln K_{sp }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 lnK_{sp} = DH TDS (Equation 5)
Using algebra, rearranging equation 5 following the equation of a straight line gives
lnK_{sp} = – ( )( ) + (Equation 6)
In this experiment, you will gather temperature readings at various saturation points of KNO_{3} solution at varying ions’ concentrations. The solubility product constants, K_{sp,} 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 lnK_{sp} versus 1/T, and obtaining the linearfit 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 linearfit equation).
MATERIALS
Computer
Vernier LabQuest 2
Vernier Temperature Probe
Iron Stand
400 mL beaker (for hot water bath)
23 pieces of boiling chips
Two 25 × 150 mm test tubes
Utility clamp
Iron ring
Hot plate
4 g of KNO_{3}
DI water
10 mL graduated cylinder
marker
PROCEDURE
 Wear a departmentally approved pair of safety goggles while doing this experiment.
 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.
 Assemble a hotwater bath as shown in Figure Place a 400mL beaker with tap water (about 250mL) and 23 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 ^{o}C, and adjust the temperature to about 100 ^{o}C when water starts to boil.
Figure 1 Setup for heating the potassium nitrate solution
 Weigh about 4 g of KNO_{3} on a tared piece of weighing paper. Record the exact mass of KNO_{3} (1) on your Data and Calculations section. Transfer the KNO_{3} to a clean 25 x 150mm test tube.
 Using a graduated cylinder, add 3 mL of deionized water to the test tube containing the KNO_{3}. Heat the test tube, as shown in Figure 1, in the assembled hotwater bath. Continue heating, while stirring gently with a temperature probe, until all of the KNO_{3}
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.
 Carefully raise the test tube with melted KNO_{3} 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.  Quickly determine the volume of the KNO_{3} 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 KNO_{3} test tube and using a marker, draw a line as accurate as you can on the empty test tube to mark the volume of KNO_{3} 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 10mL graduated cylinder. Record this volume on your Data Sheet (2).
 If crystals started to form, put the KNO_{3} test tube back to the hot water bath. Remove the test tube with the KNO_{3} solution from the hotwater 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).
 Record the temperature when crystals first appear, it is the temperature at which the solid is assumed to be in equilibrium with the solution.
 Add 1 mL of DI water to the test tube containing the KNO_{3} Warm and stir the mixture in the hotwater bath until the solid has completely redissolved. Using the same method as in Step 6, determine and record on your Data and Calculations section the solution volume (D.2).
 Remove the test tube containing the KNO_{3} solution from the hotwater 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).
 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 KNO_{3} = 4.002 g  
Trial  Solution Volume (mL) 
Temperature of Crystallization (^{o}C) 
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.
 Use the mass of the KNO_{3} to calculate the number of moles of KNO_{3} present.
 Use the number of moles of KNO_{3} and the volumes you determined at each temperature to calculate the molar concentration of KNO_{3} in the solution at each temperature. Because nearly all the KNO_{3} is still in solution, its molar concentration equals the molar concentrations of K^{+} and of NO_{3}^{–} in the saturated solution.
 Use Equation 2 to calculate the equilibrium constant, K_{sp}, for dissolving KNO_{3} in water at each temperature.
 Convert the temperatures in degrees Celsius (°C) to Kelvins (K).
 Determine the natural logarithm of K_{sp} (InK_{sp}) at each temperature.
 Use Equation 3 to calculate ΔG at each temperature.
 Calculate the reciprocal of each Kelvin temperature, 1/T (K^{1} ).
 Using the Vernier graphing functions or any computer spreadsheet program, construct a graph with the yaxis as InK_{sp} and the xaxis as 1/T. Title your graph properly and save.
 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.
 Calculate ∆H for the reaction. Remember that the slope of the straight line in the InK_{sp} versus 1/T plot equals –∆H/R, according to Equation 6.
 Calculate ∆S at each temperature using Equation 4. Determine the average ∆S. Alternatively, if regression analysis is used, obtain the average ∆S from the yintercept of the straight line.
SAMPLE DATA AND CALCULATIONS
Determine the K_{sp} for KNO_{3 }and the three thermodynamics parameters, ΔG, ΔH, and ΔS, using the example problems below.
Example 1.
Dissolving 10.1 g of KNO_{3} in enough water to make 25.0 mL of solution results in a saturated solution of KNO_{3}. Determine the K_{sp} for KNO_{3 }and the thermodynamics parameters ΔG, ΔH, and ΔS with additional measured values.
Firstly, calculate the number of moles of KNO_{3} that dissolve,
Equation 1 in the Concepts section shows that when 0.100 mol KNO_{3} dissolves, 0.100 mol K^{+} and 0.100 mol NO_{3}^{– }form. Calculate the concentration of each of these ions in the saturated solution,
According to Equation 2,
K_{sp} = [K^{+}] [NO_{3}^{–}) = (4.00) (4.00) = 16.0
Example 2.
Suppose the equilibrium constant, K_{sp}, for KNO_{3} 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, K_{sp}, for a compound dissolving in water at several temperatures, as shown in the following table:
Temperature (˚C)  K_{sp} 
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 Ink_{sp} and 1/T from the data;
We plot InK_{sp} 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 x10^{3} 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 10^{3} 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 = ∆HT∆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 KNO_{3 }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 KNO_{3} (g) (D.1) ______________________
Trials —>  1  2  3  4  5  6 
Volume, mL (D.2)  
Temperature of Crystallization, °C
( D.3) 
Determining K_{sp}
Moles of KNO_{3} _____________________
Concentration, M  
K_{sp} 
Determining ΔG
T, °K  
lnK_{sp}  
ΔG, J/mol 
Determining ΔH
Slope of the line defined by lnK_{sp} versus 1/T (attach your graph) ________________________
ΔH, J/mol ___________________________
Determining ΔS
ΔS, J/K * mol 
Average ΔS =
CALCULATIONS
DATA ANALYSIS

Using your calculated values of K_{sp}, is KNO_{3} highly soluble in water?
2. Using the three thermodynamics parameters, ΔG, ΔH, and ΔS, answer the following questions why and how KNO_{3} dissolves in water:
– Is the process spontaneous or nonspontaneous?
– Is the process exothermic or endothermic?
– Has the process resulted in increase or decrease in disorder?  What is the driving force for the spontaneous dissolution of KNO_{3} in water?