Thermodynamics of Potassium Nitrate Dissolution in Water

Objectives:

Objectives of this experiment are:

1. To learn about the relationship between K and G^o.
2. To learn how the van’t Hoff equation can be used to determine thermodynamic values
3. To gain a better understanding of G^o, H^o and S^o and their relationship.

Introduction:

The following equation – Gibbs-Helmholtz 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^oC 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, KNO₃ in water. The equilibrium equation of solid KNO₃ in water is represented as follows:

KNO_{3 (s)} ⇌ K⁺ (_aq) + NO₃^– _(aq) eqn. 3

The solubility product constant K_sp is given as follows:

K_sp = [K⁺] [NO₃^–] eqn. 4

where [K⁺] is the molar concentration of potassium ion and [NO₃^–] is the molar concentration of NO₃^– for a saturated solution of KNO₃. At equilibrium Ghence

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 KNO₃ 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 KNO₃; a negative ΔG^o means the process is spontaneous while positive ΔG^o means the process is nonspontaneous.

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 y-intercept 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 KNO₃ 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 KIO₃ solution can be prepared by dissolving 46.0 g KIO₃ in water. Determine the K_sp, ΔG^o, ΔH^o, and ΔS^o of KIO₃ 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⁺] = [IO₃^–] = 0.219 mol/L

K_sp = [K⁺] [IO₃^–] = 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.

Plotting ln K_sp vs 1/T, gives the following plot and the fitted linear equation. The slope and y-intercept 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 y-intercept:

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
• X-Large test tube (2)
• KNO₃ Potassium nitrate
• Distilled water
• 100 mL graduated Cylinder

Procedure

1. Prepare a hot water bath in a 1L or 600 mL beaker on a stirrer/ hotplate as shown in figure 1.
2. Tare a weighing boat, and weigh about 20 g of KNO₃ in the boat. Record the exact mass of KNO₃ and transfer the compound to a clean dry 200 mL test tube.
3. Clamp the test tube to the ring stand.
4. Measure 25 mL of distilled water and add it to the test tube with KNO_3, insert a stir bar and stir gently.
5. 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.
6. 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!!!!!!

1. Heat the test tube in the hot water bath while magnetically stirring until the mixture dissolves completely.
2. 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.
3. 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 KNO₃ solution cool naturally while stirring the solution on a second stir plate.
4. Observe the KNO₃ solution while it cools, record the temperature when the first white crystal appears. This will be the temperature for the equilibrium in Equation 1.
5. 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 KNO₃ dissolves. Repeat step 8, 9 and 10 to mark the solution level as 2 and record the equilibrium temperature.
6. Repeat step 11 two more times and collect the data for the 3rd and 4th trials.
7. 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

14.

15. Determination of solution volumes at each mark:

1. Add tap water to another identical test tube up to the first mark.
2. Pour this water into a 100 mL graduated cylinder containing the stir bar you used to stir your mixture and record the volume.
3. Repeat the procedure for each of the remaining marks on the tube and measure the remaining volumes.

16.

Thermodynamics of Potassium Nitrate Dissolution in Water

Data sheet:

NAME: __________________________ Date: ______________

NAME: _______________________________ Date: ___________

Post-Lab Questions

1. Is the dissolving process of KNO₃ spontaneous or nonspontaneous? Please explain based on your data.

1. Is the KNO₃ dissolving process exothermic or endothermic? Please explain based on your data.

1. Is the calculated ΔS for KNO₃ positive or negative? What does it mean?

1. During the lab, each time when you add more water to the test tube, you have to wait longer time to get precipitation of KNO₃. Why is this?

1. How does the magnitude of K_sp influence the spontaneity of a reaction?
2. 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) + NO₃^– _(aq

H^o_f -492.7 -251.2 -206.6 kJ/mol

S^o_f   J/mol.

NAME: _________________________________ Date: ____________

Pre-Lab Questions

1. How do you determine whether a solution is saturated or not?

1. 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.

1. Calculate the molar concentration of LiCl.

1. Calculate the molar concentration of Li⁺ and Cl^-.

1. Calculate the K_sp for LiCl at 20°C.

1. 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.

Calculations:

1. Plot ln K_sp vs. 1/T and attach the graph with the Pre-Lab. Calculate H from the slope of the graph.

1. Calculate S from the intercept of the straight line obtained above.

1. When does ln K_sp become = 0

1. When is ln K_sp negative?

1. When is ln K_sp positive?