Thermodynamics of Potassium Nitrate Dissolution in Water
Objectives:
Objectives of this experiment are:
 To learn about the relationship between K and G^{o}.
 To learn how the van’t Hoff equation can be used to determine thermodynamic values
 To gain a better understanding of G^{o}, H^{o} and S^{o} and their relationship.
Introduction:
The following equation – GibbsHelmholtz equation describes the relationship among three thermodynamic properties.
G^{o} = ΔH^{o} – TΔS^{o} eqn. 1
In the above equation, G^{o} is the Gibbs free energy. H^{o} is the change in enthalpy. When H^{o} is positive, the process is endothermic and when H^{o} is negative, the process is exothermic. Units of G^{o} and H^{o} are kJ/mol. The third parameter S^{o} is the change in entropy, which is the number of degrees of freedom. For a positive value of S^{o}, the disorder or degrees of freedom increase and for a negative S^{o}, disorder decreases. Units of S^{o} are J/mol.K.
Under any set of conditions, the free energy change is given by the expression
ΔG = G^{o} + RT ln Q eqn. 2
Where G^{o} is the free energy under standard conditions of T = 25^{o}C and 1 M concentration and 1 atm pressure for gases; ΔG is the free energy change under nonstandard conditions and Q is the reaction quotient. R is the universal gas constant and has a value of 8.314 J/L•mol and T is temperature in Kelvin. G^{o} is related to the equilibrium constant K. A positive G^{o} implies that more reactants are present at equilibrium and a negative G^{o} means that more products are present at equilibrium. G on the other hand gives information about spontaneity of a reaction; a negative value of G means that the reaction is spontaneous in the forward direction; a positive value of G means that the reaction is spontaneous in the reverse direction. At equilibrium G = 0
In this experiment, we will determine the three thermodynamic parameters ΔG^{o}, ΔH^{o} and ΔS^{o} to understand the solution process of potassium nitrate, KNO_{3} in water. The equilibrium equation of solid KNO_{3} in water is represented as follows:
KNO_{3} _{(s)} ⇌ K^{+} (_{aq}) + NO_{3}^{–} _{(aq)} eqn. 3
The solubility product constant K_{sp} is given as follows:
K_{sp} = [K^{+}] [NO_{3}^{–}] eqn. 4
where [K^{+}] is the molar concentration of potassium ion and [NO_{3}^{–}] is the molar concentration of NO_{3}^{–} for a saturated solution of KNO_{3}. At equilibrium Ghence
ΔG^{o} = RTlnK_{sp }eqn. 5
R is the gas constant, 8.314 J/mol.K. K_{sp} is a function of temperature because the solubility of KNO_{3} changes as a function of temperature (T). In a saturated solution, equilibrium exists between the solid and the ions in solution. G^{o} determines the spontaneity of dissolution of KNO_{3}; a negative ΔG^{o} means the process is spontaneous while positive ΔG^{o} means the process is nonspontaneous.
Combining eqn. 1 and eqn. 5 gives the following equation: 
 
RTlnK_{sp} = ΔH^{o} – TΔS^{o} Dividing eqn. 6 throughout by RT, gives a relationship between lnK_{sp} and T

 eqn. 6 
lnK_{sp} = − (ΔH^{o}) (1) + ΔS^{o} 
 eqn. 7 
R T R
This linear relationship is the van’t Hoff equation. A plot of lnK_{sp} versus 1/T yields a straight line with a slope of –ΔH^{o}/R and a yintercept of ΔS^{o}/R. This. Both ΔH^{o} and ΔS^{o} can be obtained graphically from the slope and intercept of the fitted linear equation. Thus, from the K_{sp} values at various temperatures, ΔH^{o} and ΔS^{o} can be determined. The S for dissolution of KNO_{3} in water is always positive since the randomness of the system increases. The ΔH^{o} would be positive if heat is required to dissolve the solid. Knowing K_{sp} at a particular temperature, ΔG^{o} can be calculated by using eqn. 5.
Example:
At 0°C, one liter of saturated KIO_{3} solution can be prepared by dissolving 46.0 g KIO_{3} in water. Determine the K_{sp}, ΔG^{o}, ΔH^{o}, and ΔS^{o} of KIO_{3} at 19°C.
KIO3 (s) ⇌ K^{+} (aq) + IO3^{–} (aq) eqn. 8
Step 1. Calculate the concentration of KIO_{3: }
Step 2. Calculate K_{sp. }[K^{+}] = [IO_{3}^{–}] = 0.219 mol/L
K_{sp} = [K^{+}] [IO_{3}^{–}] = 0.219 × 0.219 = 0.0480
Step 3. Determine the ΔG^{o} based on the K_{sp} from the step 2. According to eqn. 5:
𝐽 𝐽
∆𝐺^{o} = −8.314 (292 𝐾) 𝑙𝑛 0.0480 = 7216.9
𝑚𝑜𝑙. 𝐾 𝑚𝑜𝑙
Step 4. Determine the ΔH^{o} and ΔS^{o }based on the data from the following table.
Temperature (K)  1/T (K^{1})  Ksp  ln K_{sp}  ΔG (J/mol) 
292  0.003425  0.0480  3.0366  7216.9 
310  0.003226  0.1430  1.9449  5012.7 
335  0.002985  2.2800  0.8242  2295.6 
Plotting ln K_{sp} vs 1/T, gives the following plot and the fitted linear equation. The slope and yintercept are 5015 K and 14.173, respectively.
Step 5 Calculate H^{o}, based on Equation 7:
5015 = 𝛥𝐻^{o} = – 𝛥𝐻^{o}
𝑅 8.314 𝐽/mol•K
ΔH^{o} = 5015 K × 8.314 J/mol•K = 41695 J/mol
Step 6 ΔS^{o} is obtained from the yintercept:
14.413 = 𝛥𝑆^{o}/𝑅 = 𝛥𝑆^{o}/8.314 𝐽/𝐾•𝑚𝑜𝑙
ΔS^{o} = 14.173 × 8.314 J/mol•K = 117.8 J/mol•K
The second method to calculate ΔS^{o} is from eqn. 5. ΔG^{o} and ΔH^{o} can be obtained from steps 3 and 5 respectively. Calculated value of ΔS^{o} at 19°C is as follows:
ΔG^{o} = ΔH^{o} – TΔS^{o}
ΔS^{o} = (Δ𝐻^{o}− Δ𝐺^{o}) = (41695−7216.9) J/mol = 118.1 J/K•mol
T 292
Supplies
Figure 1
 1 L or 600 mL Beaker
 Vernier temperature probe
 Labquest workstation
 Ring stand (2)
 Utility clamp (3)
 Stir bar
 Rubber stopper with large hole
 Stirrer/ hotplate
 Stir plate
 XLarge test tube (2)
 KNO_{3} Potassium nitrate
 Distilled water
 100 mL graduated Cylinder
Procedure
 Prepare a hot water bath in a 1L or 600 mL beaker on a stirrer/ hotplate as shown in figure 1.
 Tare a weighing boat, and weigh about 20 g of KNO_{3} in the boat. Record the exact mass of KNO_{3} and transfer the compound to a clean dry 200 mL test tube.
 Clamp the test tube to the ring stand.
 Measure 25 mL of distilled water and add it to the test tube with KNO_{3, }insert a stir bar and stir gently.
 Insert the Vernier thermometer connected to a stopper with large hole into the 200 mL test tube with KNO_{3, }make sure the thermometer is in the solution.
 Lower the test tube into the water bath and initiate stirring, position the test tube so that it is centered on the stirrer/ hotplate.
NOTE: position the Vernier thermometer cord away from the hotplate to prevent melting the plastic cord!!!!!!
 Heat the test tube in the hot water bath while magnetically stirring until the mixture dissolves completely.
 Remove the test tube from the hot water bath and use a paper towel to dry the test tube. Quickly lift the stopper with the thermometer out of the liquid.
 Mark the solution level on the test tube with a sharpie and label it as 1 (see Figure 2). Replace the stopper with the thermometer and let the test tube with the KNO_{3} solution cool naturally while stirring the solution on a second stir plate.
 Observe the KNO_{3} solution while it cools, record the temperature when the first white crystal appears. This will be the temperature for the equilibrium in Equation 1.
 Add 5 mL of distilled water to the test tube after you record the temperature. Put the test tube back to hot water bath and heat it until all KNO_{3 }dissolves. Repeat step 8, 9 and 10 to mark the solution level as 2 and record the equilibrium temperature.
 Repeat step 11 two more times and collect the data for the 3rd and 4th trials.
 After you finish all four trials, there should be four marks on the 200 mL test tube labeled as 1, 2, 3 and 4.see Figure 2 B
Figure 2
A
B
Waste: Dispose of your KNO_{3} solution into the waste container provided in Fume Hood 1 
14.
15. Determination of solution volumes at each mark:
 Add tap water to another identical test tube up to the first mark.
 Pour this water into a 100 mL graduated cylinder containing the stir bar you used to stir your mixture and record the volume.
 Repeat the procedure for each of the remaining marks on the tube and measure the remaining volumes.
Clean up:

16.
Thermodynamics of Potassium Nitrate Dissolution in Water
Data sheet:
NAME: __________________________ Date: ______________
Mass of KNO_{3} (g)
______________________  1  2  3  4  
Total Volume (mL) 



 
Temperature (^{o}C) 



 
Temperature K 



 
Calculation converting ^{o}C to K
 
Determining K_{sp}  
Calculate moles of KNO_{3 }
 
[K^{+}] mol/ L 



 
Calculations of [K^{+}]
 
[NO_{3}^{– }] mol/ L 



 
Calculations of [NO_{3}^{– }]
 
K_{sp} 



 
Calculations for K_{sp}

Determining ΔG  
lnK_{sp} 




ΔG (J/mol) 




Calculation for ΔG
 
Determining ΔH  
1/T (K^{1})
 
Calculation for 1/T
 
Equation and Slope of the straight line from the plot of lnK_{sp} vs 1/T:
 
ΔH^{o} (J/mol) 
 
Determining ΔS  
ΔS^{o} (J/mol K) 




Show two calculations for ΔS^{o}
 
Average ΔS^{o} (J/mol K) 

NAME: _______________________________ Date: ___________
PostLab Questions
 Is the dissolving process of KNO_{3} spontaneous or nonspontaneous? Please explain based on your data.
 Is the KNO_{3} dissolving process exothermic or endothermic? Please explain based on your data.
 Is the calculated ΔS for KNO_{3 }positive or negative? What does it mean?
 During the lab, each time when you add more water to the test tube, you have to wait longer time to get precipitation of KNO_{3}. Why is this?
 How does the magnitude of K_{sp} influence the spontaneity of a reaction?
 Given the following values, calculate H^{o}_{rxn}, G^{o}_{rxn} and S^{o}_{rxn}. Explain the disagreement if any between the experimental values of S^{o} and H^{o} and G^{o}_{rxn}
KNO_{3} _{(s)} ⇌ K^{+} (_{aq}) + NO_{3}^{–} _{(aq}
H^{o}_{f} 492.7 251.2 206.6 kJ/mol
S^{o}_{f} J/mol.
NAME: _________________________________ Date: ____________
PreLab Questions
 How do you determine whether a solution is saturated or not?
 The equilibrium of a saturated LiCl aqueous solution is shown below:
LiCl (s) ⇌ Li^{+} (aq) + Cl^{–} (aq) At 20°C, the solubility of LiCl in water is 550.0 g/L.
 Calculate the molar concentration of LiCl.
 Calculate the molar concentration of Li^{+} and Cl^{. }
 Calculate the K_{sp} for LiCl at 20°C.
 The equilibrium of a saturated NaF aqueous solution is shown below:
NaF (s) ⇌ Na+ (aq) + F (aq)
The following table gives you data for the solubility of NaF at different temperatures.
Complete the following table; show complete calculations.
Temp (°C)  Ksp  Temp (K)  1/T (K^{1})  lnK_{sp}  ΔG^{o} (J/mol) 
0  0.751 




20  0.925 




100  1.446 




Calculations:
 Plot ln K_{sp} vs. 1/T and attach the graph with the PreLab. Calculate H from the slope of the graph.
 Calculate S from the intercept of the straight line obtained above.
 When does ln K_{sp} become = 0
 When is ln K_{sp} negative?
 When is ln K_{sp} positive?