Thermodynamics

Introduction

The College Board lists the following principles and concepts for thermodynamics in the course description for AP^® Chemistry: state functions, change in enthalpy, heat of formation, Hess’s law, calorimetry, entropy, free energy, dependence of free energy on enthalpy and entropy changes and relationship of free energy to equilibrium constants and electrode potentials. Use this set of integrated, interactive demonstrations to help students review the major principles of thermodynamics and help them prepare for the AP Chemistry exam.

Set of three review activities includes:

1. Entropy and Free Energy—Exothermic crystallization of sodium acetate trihydrate sparks a lively debate on spontaneity, free energy, enthalpy, and entropy.
2. Hess’s Law—Two-part calorimetry demonstration provides data for reviewing the properties of state functions and performing ΔH°, ΔS° and ΔG° calculations.
3. Free Energy and Redox Reactions—Nothing challenges understanding of free energy and the Nernst equation like the concentration cell.

The series of demonstrations may be presented in a variety of ways. Each demonstration may be used to review a specific AP test topic, or all the demonstrations can be performed together to assess student understanding and grasp of thermodynamics concepts normally covered in the AP exam. Student worksheets are included as an optional assessment tool for the instructor.

Experiment Overview

Entropy and Free Energy
A supersaturated solution of sodium acetate trihydrate becomes an ordered crystalline structure when it solidifies. Use this physical change to review your students’ understanding of the Gibbs free energy expression, ΔG = ΔH – TΔS. 

Hess’s Law
Use the temperature data from calorimetry experiments and standard entropy values, along with Hess’s law, to determine the values of ΔH° and ΔG° for the decomposition of sodium bicarbonate. Students will then calculate the temperature at which the reaction would be expected to switch from product-favored to reactant-favored. 

Free Energy and Redox Reactions 
Concentration cells are a special type of voltaic cell that have the same components in each half-cell. They differ only in the concentration of the solutions. Relate the concept of free energy and use the Nernst equation to determine the direction of current and calculate the voltage for a copper concentration cell.

Materials

Safety Precautions

Sodium acetate is slightly toxic by ingestion, inhalation and skin absorption. Wear heat-resistant gloves or use tongs when handling the hot flask. Hydrochloric acid is toxic by ingestion or inhalation and severely corrosive to skin and eyes. The copper sulfate solutions are slightly toxic by ingestion. Potassium nitrate is a strong oxidant; fire and explosive risk when heated or in contact with organic materials; it is a skin irritant. Wear chemical splash goggles, chemical-resistant gloves and a chemical-resistant apron. Please review current Safety Data Sheets for additional safety, handling and disposal information.

Disposal

Please consult your current Flinn Scientific Catalog/Reference Manual for general guidelines and specific procedures, and review all federal, state and local regulations that may apply, before proceeding. The sodium acetate solution from Entropy and Free Energy may be stored in the Florence flask for repeated use. To obtain the supersaturated liquid solution, simply reheat the solid mixture. The waste solutions in Hess’s Law may be neutralized and rinsed down the drain with excess water according to Flinn Suggested Disposal Method #24b. The salt bridge gel in Free Energy and Redox Reactions may be disposed of according to Flinn Suggested Disposal Method #26a. The copper sulfate solutions may be disposed of according to Flinn Suggested disposal Method #26b.

Prelab Preparation

Entropy and Free Energy

Sodium Acetate Solution 

1. Add 250 g of sodium acetate trihydrate to a 500-mL Florence flask. Save a small amount of the solid to use as seed crystals.
2. Use a wash bottle to add approximately 15 mL of distilled or deionized water to the Florence flask. Do this by rinsing the sides of the flask. Set the flask on a hot plate. Turn the setting to medium heat.
3. Once the solid sodium acetate has completely melted and the solution is homogeneous, carefully set the flask on a ceramic pad to cool. Turn off the hot plate.
4. When the flask is cool, cover with Parafilm. Allow the flask and solution to cool to room temperature.

Free Emergy and Redox Reactions

Salt Bridge

1. Add 150 mL of distilled or deionized water to a 400-mL beaker and place it on a hot plate.
2. Heat the water to boiling, and then add 3 g of agar. Stir the mixture until it forms a uniform suspension.
3. Use beaker tongs to remove the beaker from the hot plate. Add 15 g of potassium nitrate to the agar solution and stir until the KNO₃ dissolves.
4. Carefully fill the U-tube with the KNO₃/agar mixture. Use a clamp to hold the U-tube vertically and let the agar mixture set up overnight.

Procedure

Entropy and Free Energy

1. Show the students the flask of supersaturated sodium acetate trihydrate solution. Have them write on the worksheet the chemical equation for the reversible crystallization of sodium acetate trihydrate from this solution. Answer the questions for Part 1 to predict the signs of ΔH, ΔG and ΔS.
2. Fill the 1000-mL beaker with approximately 500 mL of tap water.
3. Use a ringstand, clamp, and string to suspend the digital thermometer sensor in the tap water (see Figure 1).
   {12818_Procedure_Figure_1}
4. Record the initial temperature of the tap water. Before lowering the Florence flask into the beaker, ask the class to predict whether the temperature of the water will increase, decrease or remain the same when the sodium acetate crystallizes.
5. Carefully and gently submerge the Florence flask into the beaker so that all the liquid in the flask is below the water level.
6. While holding the flask in one hand, sprinkle a few crystals of sodium acetate trihydrate into the flask.
7. Monitor the temperature of water in the beaker. Record the maximum temperature change.

Hess’s Law

1. Set up a calorimeter consisting of two nested Styrofoam cups. Cover the cups using cardboard of Styrofoam with a hole in it to accept a thermometer (see Figure 1 in the Entropy and Free Energy Procedure section).
2. Weigh out 3.00 g of sodium bicarbonate. Transfer the solid to the calorimeter.
3. Measure 60.0 mL of 3 M hydrochloric acid solution into a 100-mL graduated cylinder.
4. Measure the initial temperature of the 3 M HCl solution and record the data in the data table on the Hess’s Law Worksheet.
5. Place the calorimeter assembly on a magnetic stirrer and add a magnetic stirring bar.
6. Start the magnetic bar spinning slowly and quickly add the 60.0 mL of 3 M HCl solution to the calorimeter. Place the cover on the calorimeter, and insert the thermometer.
7. Measure and record the maximum or final temperature of the solution.
8. Repeat steps 1–7, using 3.00 g of sodium carbonate instead of sodium bicarbonate in step 2.

Free Energy and Redox Reactions

1. Set up a concentration cell as shown in Figure 2.
   {12818_Procedure_Figure_2}
2. Add 200 mL of 0.01 M copper sulfate solution one clean 400-mL beaker and 200 mL of 1 M copper sulfate to another clean 400-mL beaker.
3. Invert the salt bridge and plact it in both beakers (see Figure 1 in the Entropy and Free Energy Procedure section).
4. Connect one copper metal strip to one end of an alligator clip; do the same with the other copper strip and another alligator clip.
5. Before connecting the voltmeter, ask the students to write the Nernst equation for this concentration product cell and predict which electrode should be the cathode and which should be the anode. Calculate the expected voltage when the voltmeter is connected to the concentration cell.
6. Connect the copper strip in the less concentrated copper sulfate solution to the negative lead (anode) of the voltmeter and the other copper strip to the positive lead (cathode). Record the voltage.

Student Worksheet PDF

12818_Student1.pdf

Lab Hints

• When measuring the heat transfers for exothermic reactions using a calorimeter in Hess’s Law, most of the heat released by the reactants will be absorbed by the solution. A small amount of heat, however, will be absorbed by the calorimeter itself. The heat change for the reaction becomes

  q_rxn = –(q_sol + q_cal)

  Typically, the specific heat (J/°C) of the calorimeter is determined experimentally. This value is then multiplied by the change in temperature of the solution to calculate q_cal for the reaction. q_cal = ΔT (°C) x heat capacity (J/°C). We have neglected this value for the demonstration.
• The best thermometers to use are digital electronic thermometers or temperature sensors connected to a computer- or calculator- based interface system such as LabPro or CBL. Digital thermometers are economical, update every second, and are precise to the nearest 0.1 °C. Temperature measurements may be a significant source of error in calorimetry experiments.
• The use of computer- or calculator-based technology for data collection and analysis is tailor-made for thermochemistry determinations. The graph showing temperature change can easily be drawn using a graphing calculator or a graphical analysis program on a computer.

Teacher Tips

• The addition of too much water to the solid sodium acetate trihydrate in Entropy and Free Energy will result in leftover liquid after crystallization. Only a small amount of water must be added to dissolve the solid.
• Uses for supersaturated sodium acetate solutions include hot packs and hand warmers.
• Variations of this demonstration include performing the crystallization in a 500-mL graduated cylinder or placing a single crystal in a shallow container and pouring the solution onto the crystal. A buret may also be used to release the solution onto the crystal. These two variations can produce fairly tall columns of solid sodium acetate.
• Supersaturated solutions are extremely unstable and will precipitate, or crystallize, upon addition of just one crystal of the solute. Even slight shaking or agitation may be enough to cause crystallization to begin. Handle the Florence flask gently to avoid agitation and crystallization.
• In Hess’s Law, it is important to keep track of the signs associated with the temperature and heat changes for the systems and the surroundings. A loss of heat by the system is assigned a negative value, a gain of heat by the system a positive value. A reaction (system) that is endothermic has a positive value of Δq and ΔH. The heat absorbed by the reactants in the system (+Δq and +ΔH) is released by the surroundings, which in this case is the solution. The temperature of the solution—the surroundings— decreases for an endothermic reaction, that is the value of Δq for the surroundings is negative—equal but opposite in sign to the value of Δq for the reactants in the system.
• Review with students the definition of a natural law. A law is not engraved in stone in nature—it is an expression of the results of many experiments repeated for many different systems. The “law” is a generalization that has been widely tested and has been found to be true for every reaction that has been tested. Hess’s Law is also known as the Law of Additivity of Reaction Heats.

Sample Data

Hess’s Law

Answers to Questions

Entropy and Free Energy

1. Write the expression for the crystallization of sodium acetate trihydrate from its supersaturated solution.
   {12818_Answers_Equation_1}
2. What is the sign of ΔS for this change? Explain.

   ΔS is negative. Change is to a more ordered state.

3. Write the expression the change in free energy, ΔG, in terms of ΔH and ΔS. For the process to be spontaneous, does the crystallization need to be endothermic or exothermic and why?

   ΔG = ΔH – TΔS

   For spontaneous processes ΔG must be negative. If ΔS is negative, the expression –TΔS has a positive value. ΔH must be negative and |ΔH| must be greater than –TΔS for ΔG to be negative.

4. What was the initial and final temperature of the water in the beaker? What was the sign of the temperature change? Explain in terms of the heat released and/or absorbed by the system and the surroundings.

   The final temperature of the water bath was about 8 °C. The sign of the temperature change is positive, indicating heat absorbed by the surroundings. Heat was released by the system (the supersaturated solution of sodium acetate) when it crystallized.

Hess’s Law

1. Calculate the change in heat, q_rxn, for each reaction.
   {12818_Answers_Equation_3}
2. Calculate ΔH° for reactions 1 and 2.
   {12818_Answers_Equation_8}
3. Calculate ΔH_rxn for the reaction
   {12818_Answers_Equation_10}
4. The following data comes from the CRC Handbook of Chemistry and Physics.
   {12818_Answers_Table_2}
5. Calculate the temperature at which the decomposition reaction of sodium bicarbonate will become reactant-favored.

   2NaHCO₃(s) → Na₂CO₃(s) + CO₂(g) + H₂O(l)
   ΔG =ΔH – TΔS

   For a reaction to be reactant-favored, the change in free energy, ΔG, must be greater than zero.

   ΔG > 0

   Substituting ΔH – TΔS for ΔG

   ΔH – TΔS > 0

   Rearranging the expression yields

   {12818_Answers_Equation_11}

   For the reaction 2NaHCO₃(s) → Na₂CO₃(s) + CO₂(g) + H₂O(l)

   ΔS = [135.0 + 213.8 + 70.0 – 2(101.7)]J/K
   ΔS = 215.4 J/K

   The reaction becomes reactant-favored when

   {12818_Answers_Equation_12}

Free Energy and Redox Reactions

1. Write the expression relating free energy (ΔG) and a redox cell potential (ε).

   ΔG = –nεF.

2. Write an equation for the overall reaction in a copper concentration cell.

   Cu²⁺(aq) (cathode) + Cu(s) (anode) → Cu(s) (cathode) + Cu²⁺(aq) (anode)
   The ions in the Cu²⁺ solution at the cathode will be reduced to copper metal, which will plate out on the copper metal electrode in that solution. Copper atoms from the copper metal electrode at the anode will be oxidized to Cu²⁺ ions.

3. Write the Nernst equation for a copper concentration cell. a) What is the value of ε° for a concentration cell? b) Under what conditions will a concentration cell be spontaneous?
   {12818_Answers_Equation_13}

   At room temperature using the value for R and converting the natural logarithm (ln) to base 10 logarithm (log), the Nernst equation reduces to the following simplified form,

   {12818_Answers_Equation_14}
   1. ε° is zero for a concentration cell (same reaction in both cells).
   2. For a spontaneous reaction ΔG < 0, therefore εcell must be greater than zero. Since ε° = 0, the value of the − log ([Cu²⁺]anode/[Cu²⁺]cathode) term must be positive. This will only happen if ([Cu²⁺]anode/[Cu²⁺]cathode) is less than one, that is [Cu²⁺]anode is less than [Cu²⁺]cathode.
4. Identify the anode and the cathode in the copper concentration cell. Be specific!

   The more dilute 0.01 M copper ion solution is the anode (copper metal is oxidized) and the more concentrated 1 M copper ion solution is the cathode (copper ions are reduced).

5. Mixing two solutions of different concentrations provides an analogy for the concentration cell. Explain in terms of what is meant by a spontaneous reaction.

   Imagine two solutions C1 and C2 separated by a membrane that is permeable to copper ions. If C2 > C1, the natural tendency will be for ions to flow across the membrane from C2 to C1 in order to eventually equalize the concentration of copper ions on both sides of the membrane. Since this process or reaction would occur without outside intervention, it must also be spontaneous inside a voltaic cell. Therefore copper metal in the more dilute solution is oxidized to produce more copper ions, and copper ions in the more concentrated solution are reduced to decrease the copper ion concentration on that side. Eventually the concentration of copper ions in the two half-cells will be identical and the cell potential reduce to zero. No further reaction takes place.

Discussion

Entropy and Free Energy
The crystallization of sodium acetate trihydrate from its supersaturated solution is a spontaneous physical process. The Gibbs free energy expressions for this process are:

Because the process results in a more ordered state, the change in entropy, ΔS, is negative. This makes the value of –TΔS positive. Since ΔG is negative, ΔH must also be negative and its absolute value must be greater than the value of –TΔS. The crystallization reaction is highly exothermic.

Adding a seed crystal to a solution of sodium acetate essentially starts a chain reaction that causes the entire solution to crystallize. The liquid becomes a solid and releases so much heat that it “freezes!” 

The unactivated sodium acetate solution is both supersaturated and supercooled, since it contains more dissolved sodium acetate than a saturated solution and has been cooled to below its freezing point without crystallization occurring. In a sealed container, the solution may be cooled to as low as –10 °C without freezing. When the crystallization is activated, the temperature of the solution increases to the freezing (melting) point of sodium acetate trihydrate, which is about 58 °C. At this temperature, the sodium acetate solution changes from a liquid to a solid. The mixture will not exceed this temperature when it crystallizes because as additional heat is released in the crystallization process, it is used to melt the crystals that have previously formed. The temperature of the system, therefore, will not rise above the freezing (melting) point until all the solid has melted again! Since the temperature of the system is above room temperature and heat is continuously lost to the surroundings, eventually all the sodium acetate trihydrate will solidify rather than melt.

The supersaturated solution may be regenerated for repeat use by heating the solidified crystals above 58 °C, whereupon the sodium acetate trihydrate crystals will melt. (Alternatively, the sodium acetate trihydrate crystals may be said to dissolve in their own water of hydration.) The reversible crystallization–dissolving process for sodium acetate trihydrate may also be represented by means of the following equation. The forward reaction represents crystallization (freezing). Notice that heat is released in this reaction—the reaction is exothermic, as evidenced by the fact that the temperature of the water bath increases. The reverse reaction represents the dissolving or melting process. Notice that heat must be added to the system in this direction.

Hess’s Law
Enthalpy, entropy and free energy are state functions. Any changes in these quantities arising from a chemical or physical change depend only on the final and initial states of the products and reactants and not on the overall pathway for the transformation. The heat or enthalpy change for a chemical reaction is called the enthalpy of reaction, ΔH_rxn. This energy change is equal to the amount of heat transferred, at constant pressure, by the reaction system.

According to Hess’s Law, if a reaction can be carried out in a series of steps, the sum of the enthalpies for each step equals the enthalpy change for the overall reaction. Another way of stating Hess’s Law is that if a reaction is the sum of two or more other reactions, the ΔH_rxn for the overall reaction must be the sum of the ΔH_rxn values of the constituent reactions. In this two-part demonstration the synthesis of zinc oxide and the decomposition of sodium bicarbonate will be examined to determine both ΔH_rxn and ΔG_rxn using calorimetric data and entropy tables.

The balanced chemical equations for the reactions of sodium bicarbonate and sodium carbonate with hydrochloric acid are shown below (Equations 5 and 6). Sodium bicarbonate decomposes to produce sodium carbonate, carbon dioxide and water according to the following balanced chemical equation (Equation 7). Equation (3) may be obtained by the following algebraic combination of reactions (1) and (2):
Reaction (3) = 2 x (Reaction 1) – Reaction (2). According to Hess’s law, ΔH_rxn (3) = 2ΔH_rxn (1) – ΔH_rxn (2). Note that the same algebraic combination may be applied to any state function, such as ΔS or ΔG.

The heat of reaction for the reaction of either sodium bicarbonate or sodium carbonate with water is calculated from the calorimetry data using the heat energy equation (Equation 8). where q = heat energy gain or loss and ΔT is the temperature change in °C. Since ΔT equals the final temperature of the solution minus the initial temperature of solution, an increase in solution temperature results in a positive value for both ΔT and q. A positive value for q means the solution gains heat, while a negative value means the solution loses heat.

For a reaction to be reactant-favored, ΔG_rxn must be positive.

ΔG_rxn > 0

Substituting ΔH_rxn and ΔS_rxn The decomposition reaction of sodium bicarbonate yields ΔH_rxn and ΔS_rxn values that are both positive.

ΔH_rxn = 90.4 kJ
ΔS_rxn = 215.4 J/K

The temperature at which this reaction is reactant-favored is Free Energy and Redox Reactions
A concentration cell is a voltaic cell that is spontaneous due to the difference in concentrations of two equivalent half-cells having the same reactants.

This demonstration uses the copper(II) ion solution with a copper metal electrode. In one beaker the copper(II) ion concentration is 0.01 M, while in the second beaker, the concentration of the copper(II) ion is 1.00 M.

For a spontaneous electrochemical reaction the change in free energy, ΔG, must be negative. Since free energy is related to the cell potential by the following equation, the cell potential ε must be positive for a voltaic cell.

For this voltaic cell the oxidation and reduction half cell reactions are The cell potential ε is equal to

E = E° – (RT/nF)•ln([Cu²⁺]_a/[Cu²⁺]_c)

Where [Cu²⁺]_a is the molar concentration of copper(II) ions at the anode and [Cu²⁺]_c is the molar concentration of copper(II) ions at the cathode. Since E° is zero for a concentration cell, the cell potential reduces to

E = – (RT/nF)•ln([Cu²⁺]_a/[Cu²⁺]_c)

For E to be positive, ln([Cu²⁺]_a/[Cu²⁺]_c) must be less than zero. This is only true if the ratio of ln([Cu²⁺]_a/[Cu²⁺]_c) is less than one. Therefore, the 0.01 M copper(II) solution is the anode solution and the 1.00 M copper(II) solution is the cathode.