Charles Law and The Value of Absolute Zero Lab Report

Thermodynamics of Potassium Nitrate Dissolution in Water

Objectives:

Objectives of this experiment are:

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

Introduction:

The following equation – Gibbs-Helmholtz equation describes the relationship among three thermodynamic properties.

Go = ΔHo – TΔSo eqn. 1

In the above equation, Go is the Gibbs free energy. Ho is the change in enthalpy. When Ho is positive, the process is endothermic and when Ho is negative, the process is exothermic. Units of Go and Ho are kJ/mol. The third parameter So is the change in entropy, which is the number of degrees of freedom. For a positive value of So, the disorder or degrees of freedom increase and for a negative So, disorder decreases. Units of So are J/mol.K.

Under any set of conditions, the free energy change is given by the expression

ΔG = Go + RT ln Q eqn. 2

Where Go is the free energy under standard conditions of T = 25oC 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. Go is related to the equilibrium constant K. A positive Go implies that more reactants are present at equilibrium and a negative Go 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 ΔGo, ΔHo and ΔSo to understand the solution process of potassium nitrate, KNO3 in water. The equilibrium equation of solid KNO3 in water is represented as follows:

KNO3 (s) ⇌ K+ (aq) + NO3 (aq) eqn. 3

The solubility product constant Ksp is given as follows:

Ksp = [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

ΔGo = -RTlnKsp eqn. 5

R is the gas constant, 8.314 J/mol.K. Ksp 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. Go determines the spontaneity of dissolution of KNO3; a negative ΔGo means the process is spontaneous while positive ΔGo means the process is nonspontaneous.

Combining eqn. 1 and eqn. 5 gives the following equation:

-RTlnKsp = ΔHo – TΔSo

Dividing eqn. 6 throughout by RT, gives a relationship between lnKsp and T

eqn. 6
lnKsp = − (ΔHo) (1) + ΔSo eqn. 7

R T R

This linear relationship is the van’t Hoff equation. A plot of lnKsp versus 1/T yields a straight line with a slope of –ΔHo/R and a y-intercept of ΔSo/R. This. Both ΔHo and ΔSo can be obtained graphically from the slope and intercept of the fitted linear equation. Thus, from the Ksp values at various temperatures, ΔHo and ΔSo can be determined. The S for dissolution of KNO3 in water is always positive since the randomness of the system increases. The ΔHo would be positive if heat is required to dissolve the solid. Knowing Ksp at a particular temperature, ΔGo 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 Ksp, ΔGo, ΔHo, and ΔSo of KIO3 at 19°C.

KIO3 (s) ⇌ K+ (aq) + IO3 (aq) eqn. 8

Step 1. Calculate the concentration of KIO3:

Step 2. Calculate Ksp. [K+] = [IO3] = 0.219 mol/L

Ksp = [K+] [IO3] = 0.219 × 0.219 = 0.0480

Step 3. Determine the ΔGo based on the Ksp from the step 2. According to eqn. 5:

𝐽 𝐽

∆𝐺o = −8.314 (292 𝐾) 𝑙𝑛 0.0480 = 7216.9

𝑚𝑜𝑙. 𝐾 𝑚𝑜𝑙

Step 4. Determine the ΔHo and ΔSo based on the data from the following table.

Temperature (K)1/T (K-1)Kspln KspΔG (J/mol)
2920.0034250.0480-3.03667216.9
3100.0032260.1430-1.94495012.7
3350.0029852.2800-0.82422295.6

Plotting ln Ksp 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 Ho, based on Equation 7:

-5015 = -𝛥𝐻o = – 𝛥𝐻o

𝑅 8.314 𝐽/mol•K

ΔHo = 5015 K × 8.314 J/mol•K = 41695 J/mol

Step 6 ΔSo is obtained from the y-intercept:

14.413 = 𝛥𝑆o/𝑅 = 𝛥𝑆o/8.314 𝐽/𝐾•𝑚𝑜𝑙

ΔSo = 14.173 × 8.314 J/mol•K = 117.8 J/mol•K

The second method to calculate ΔSo is from eqn. 5. ΔGo and ΔHo can be obtained from steps 3 and 5 respectively. Calculated value of ΔSo at 19°C is as follows:

ΔGo = ΔHo – TΔSo

ΔSo = (Δ𝐻o− Δ𝐺o) = (41695−7216.9) J/mol = 118.1 J/K•mol

T 292

Supplies

Figure 1

word image 2496

  • 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 KNO3, 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 KNO3, 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

word image 900

word image 2497 word image 2498 word image 901

A

word image 902

B

Waste: Dispose of your KNO3 solution into the waste container provided in

Fume Hood 1

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.
Clean up:

  • Wash your test tubes with hot water and soap 3 times, rinse with Distilled water 2 times, and place the clean test tube into the “used clean test tube” bin.
  • Clean any spilled KNO3 solid around the balances and KNO3 solution on bench after you finish the lab.
  • Unplug and turn off all stirrers and stirrer hotplates

16.

Thermodynamics of Potassium Nitrate Dissolution in Water

Data sheet:

NAME: __________________________ Date: ______________

Mass of KNO3 (g)

______________________

1 2 3 4
Total Volume (mL)
Temperature (oC)
Temperature K
Calculation converting oC to K
Determining Ksp
Calculate moles of KNO3
[K+] mol/ L
Calculations of [K+]
[NO3] mol/ L
Calculations of [NO3]
Ksp
Calculations for Ksp
Determining ΔG
lnKsp
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 lnKsp vs 1/T:
ΔHo (J/mol)
Determining ΔS
ΔSo (J/mol K)
Show two calculations for ΔSo
Average ΔSo (J/mol K)

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 Ksp influence the spontaneity of a reaction?
  2. Given the following values, calculate Horxn, Gorxn and Sorxn. Explain the disagreement if any between the experimental values of So and Ho and Gorxn

KNO3 (s) ⇌ K+ (aq) + NO3 (aq

Hof -492.7 -251.2 -206.6 kJ/mol

Sof   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 Ksp 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.

Temp (°C) Ksp Temp (K) 1/T (K-1) lnKsp ΔGo (J/mol)
00.751
200.925
1001.446

Calculations:

  1. Plot ln Ksp 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 Ksp become = 0
  1. When is ln Ksp negative?
  1. When is ln Ksp positive?
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