Materials Included In Kit

Additional Materials Required

Safety Precautions

Lithium chloride is moderately toxic by ingestion. Calcium chloride and ammonium chloride are slightly toxic. Magnesium sulfate is a body tissue irritant. Sodium acetate is a body tissue and respiratory tract irritant. Avoid contact of all chemicals with eyes and skin. Wear chemical splash goggles, chemical-resistant gloves and a chemical-resistant apron. Remind students to wash their hands thoroughly with soap and water before leaving the laboratory. 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 solid samples may be stored for future use or placed in the trash according to Flinn Suggested Disposal Method #26a. The experimental solutions may be rinsed down the drain with plenty of excess water according to Flinn Suggested Disposal Method #26b.

Lab Hints

• The best thermometers to use are digital electronic thermometers (such as Flinn Scientific Catalog No. AP8716) or temperature sensors connected to a computer-based interface system. Flinn digital thermometers are reasonably inexpensive, update every second, and are precise to the nearest 0.1 °C. Temperature measurements may be a significant source of error in calorimetry experiments.
• Two polystyrene cups nested together provide better insulation and thermal stability than one cup. If two cups are used, students can easily run two trials without rinsing and drying the cup between trials. Simply have the students interchange the actual solution cup and the bottom cup between measurements.
• We report a calorimeter constant value of 17 J/°C for the Introductory Activity mixing hot and cold water where the mixing temperature (T_mix) was 34.8 °C. The value of C_cal depends on the average or mixing temperature of the hot and cold water. Intuitively, C_cal will depend on temperature, and indeed we found this to be the case. (You would expect the calorimeter constant to be zero if you mix room temperature water with room temperature water at 25 °C.)
• On the right is a graph of C_cal versus T_mix for four different mixing temperatures from 34 to 45 °C. For greatest accuracy, we recommend that the calorimeter constant determination be carried out by mixing room temperature water with hot water at 45–55 °C, for an expected T_mix in the 33–38 °C range. The maximum temperature in the exothermic heat of solution experiments would fall in this temperature range.
• Students may need help with the calorimetry calculations. It is important to keep track of the signs associated with the heat changes, and to understand the notion of the system versus the surroundings. A loss of heat is assigned a negative value, a gain of heat a positive value. If a reaction is exothermic, it releases or loses heat and q has a negative value. The same quantity of heat is absorbed by the solution and the heat change for the solution therefore has the same value but with a positive sign.
  {13836_Hints_Figure_1}
• A slight error is incorporated into the calorimeter constant calibration to make the calculations simpler and the data collection less time-consuming.
• Another type of hand warmer uses a pouch of supersaturated sodium acetate trihydrate. The crystallization of sodium acetate trihydrate from its supersaturated solution is a spontaneous physical process. The Gibbs free energy expressions for this process are:
  {13836_Hints_Equation_5}
  {13836_Hints_Equation_6}
  Because the process results in a more ordered state,
  {13836_Hints_Equation_7}
  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. Depressing a metal button in the solution pouch 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!” This hand warmer is available from Flinn Scientific, Catalog No. AP1933.
• There are two conceptual hurdles students must overcome in thermochemistry—the difference between heat and temperature and the definition of the system versus the surroundings. For a reaction taking place in solution, students must realize that the liquid, the solvent, is not directly involved in the reaction. It is part of the medium, the surroundings. Reactions are generally classified as exothermic or endothermic based on the temperature change in the surroundings, which is opposite in sign to that of the system. Thus, if the temperature of the surroundings increases, it is because the energy of the system has decreased. The temperature of the system itself is often inaccessible.
• One of the more stubborn student misconceptions is the idea that if the reaction mixture gets cold, it must have lost heat, therefore the reaction must be exothermic. This misconception may be traced to a lack of understanding of the system versus the surroundings. The temperature change that is measured in a typical coffee-cup calorimeter experiment is that of the surroundings. A heat of solution experiment is probably more confusing on this point than a heat of neutralization or heat of combustion experiment, because water is involved in the reaction. Also, using the combined mass of the solute and the solvent in the heat equation to calculate the heat change tends to blur the traditional distinction between the reactants and products versus the solvent.
• Enthalpy is an abstract concept that is often difficult for students to understand. Most textbooks include diagrams of enthalpy versus “reaction coordinate” (reactants and products) that help students visualize the difference in the sign of ΔH for exothermic and endothermic reactions. Qualitative laboratory activities such as “Thermodynamics in a Bag” (Flinn Catalog No. AP4779) and “Discovering Instant Cold Packs” (Flinn Catalog No. AP6375) are very helpful in teaching enthalpy because they allow students to see and feel the real effects of enthalpy changes.
• The most important element for success in an inquiry-based activity is student preparation. Sufficient time should be alotted for students to think through the measurements that must be made, how they will be made, the variables that will influence the measurements, and how the variables can be controlled, if necessary.

Further Extensions

Opportunities for Undergraduate Research
Instant cold packs are used to treat sports and other injuries when ice is unavailable. Research the properties of commercial cold packs and select a “cold pack solid” from among the solids provided in this activity. Propose and test a design (quantity of solid and volume of water) for an effective instant cold pack.

Answers to Prelab Questions

1. When chromium chloride, CrCl₂, is dissolved in water, the temperature of the water decreases.
   1. Is the heat of solution exothermic or endothermic?

      The heat of solution is endothermic—the system absorbs heat from the surroundings

   2. Which is stronger—the attractive forces between water molecules and chromium and chloride ions, or the combined ionic bond strength of CrCl₂ and intermolecular forces between water molecules? Explain.

      The energy released in the formation of hydrated ions is less than the energy required to break the ionic crystal lattice and intermolecular forces between water molecules.

2. A solution was formed by combining 25.0 g of solid A with 60.0 mL of distilled water, with the water initially at 21.4 °C. The final temperature of the solution was 25.3 °C. Calculate the heat released as the solid dissolved, q_soln, assuming no heat loss to the calorimeter (see Equation 1).

   q_soln = –(m•s•ΔT) = –(25.0 + 60.0)g x 4.18 J/g•°C x (25.3 – 21.4)°C

   = –(85.0 g x 4.18 J/g•°C x 3.9 °C)
   = –1390 J

3. In Question 2 the calorimeter was found to have a heat capacity of 8.20 J/°C. If a correction is included to account for the heat absorbed by the calorimeter, what is the heat of solution, q_soln?

   q_soln = –(m•s•T + C_cal ΔT) = 1390 J + [8.20 J/°C x (25.3 – 21.4)°C]
   q_soln = –(1390 J + 32 J) = –1420 J

4. The solid in Question 2 was aluminum sulfate, Al₂(SO₄)₃. Calculate the molar heat of solution, ΔH_soln, for aluminum sulfate. Hint: The units for molar heat of solution are kilojoules per mole (kJ/mole). First determine the heat released per gram of solid.

   ΔH_soln = –(1420 J/25.0 g ) x 342.15 g/mol = –19400 J/mol = –19.4 kJ/mol

Sample Data

Heat Capacity of the Calorimeter

Calorimeter Constant Calculation Magnesium Sulfate Calorimetry Procedure Molar Heat of Solution of Magnesium Sulfate: Hand Warmer Design
Sample data to determine the heat of solution for each solid were determined using 5 g of solid and 45 mL of water. Sample calculations to determine the heat of solutions (assume 1.000 g/mL as H₂O density): Extrapolate from the information collected and estimate the temperature change for each solid when 10 g combine with 40 mL of water. The ratio of 50/45 is used to predict the expected temperature change (ΔT ) with 40 mL of water because the total mass of water and solid is used in the heat energy equation (see the sample calculation). The observed ΔT was measured with approximately 50 g total mass (45 g water plus 5 g solid). The predicted ΔT corresponds to 45 g total mass (40 g water plus 5 g solid).

• ΔT, °C (45 mL) is the observed temperature change with 45 mL of water and experimental mass of solid.
• ΔT, °C (40 mL) is the estimated temperature change with 40 mL of water and experimental mass of solid.

  = 50/45 x [ΔT, °C (45 mL)]; for CaCl₂ = (50/45) x 14.2 °C = 16.0 °C

• 10 g/40 mL ΔT is the predicted temperature increase for a hand warmer containing 10 g of solid and 40 mL of water.

  = (10 g/experimental mass of solid) x [(ΔT, °C (40 mL)]
  for CaCl₂ = (10/5.075) x 16.0 °C = 31.5 °C

Conclusion
The best all-around hand warmer would contain calcium chloride. It produces the required temperature change of at least 20 °C and is less expensive and less toxic than lithium chloride.

Answers to Questions

Guided-Inquiry Design and Procedure Questions

1. Review the calorimetry procedure and answer the following questions:
   1. What data are needed to calculate the enthalpy change for a reaction?

      Data for the three terms involved in the heat energy equation (q = m x s x ΔT) must be known or measured. The mass (m) is the mass of the solution after the solid has dissolved. The specific heat capacity (s) is assumed to be the same as the specific heat capacity of water (4.18 J/g•°C). The temperature change (ΔT) is equal to the difference between the final and initial temperatures (T_final – T_initial). Note: Assuming the specific heat capacity of the solution is the same as that of water may be a major source of error in the heat calculations.

   2. Identify the variables that will influence the experimental data.

      Some of the critical variables include: (1) the mass of the solute; (2) the volume (mass) of the solvent; (3) whether all of the solute dissolves in the solvent; (4) the heat-insulating properties of the reaction container; (5) how well the reaction mixture is stirred; (6) how stable the initial temperature reading is.

   3. What variables should be controlled (kept constant) during the procedure?

      The following variables should be held constant during the procedure: the volume (mass) of the solvent; the type of reaction container that is used (two insulating foam cups nestled one inside the other will provide better insulation than one cup); continuous stirring of the reaction mixture.

   4. The independent variable in an experiment is the variable that is changed by the experimenter, while the dependent variable responds to or depends on the changes in the independent variable. Name the independent and dependent variables in the calorimetry procedure.

      In a calorimetry experiment, the mass of the solute in grams is the independent variable and will be varied in different trials. The temperature change that is produced depends on the mass of the solute and is thus the dependent variable in a calorimetry experiment.

   5. Discuss the factors that will affect the precision of the experimental results.

      Many factors will influence the precision of the results:

      • The precision of the balance used to measure the mass of solute.
      • The precision of the graduated cylinder used to measure the volume of solvent.
      • The precision of the thermometer used to measure the temperature of the reaction mixture.
      • The number of times the experiment is repeated to average the effects of random errors.
      • The type of vessel that is used as the calorimeter—how much heat is gained or lost by the calorimeter itself.

      The first three measurements should be made with the most precise glassware and equipment available in the lab—centigram balances (at least), appropriate size graduated cylinders, and digital thermometers, if possible. One important way to improve the precision of the experimental results is to average data obtained over several runs or trials. A minimum of 2–3 trials is recommended. Alternatively, section data may be averaged to eliminate outlying results.

Post-Laboratory Review Questions
Review the following data from a calorimetry experiment to determine the heat of fusion of ice. After shaking off any excess water, several ice cubes were added to 99 g of warm water contained in a calorimeter. The initial temperature of the warm water was 46.8 °C. The ice−water mixture was stirred until the temperature reached a stable, minimum value, which was 1.1 °C. Any unmelted ice remaining at this point was immediately and carefully removed using tongs and the mass of the water in the calorimeter was measured—154 g.

1. Use the heat energy equation to calculate the amount of heat in joules released by the warm water as it cooled.

   ΔT = T_final – T_initial = 1.1 – 46.8 °C = –45.7 °C
   q(warm water) = (4.18 J/g•°C) x 99 g x (–45.7 °C) = –18,900 J

2. Based on the law of conservation of energy, what amount of heat was absorbed by the ice as it melted?

   q(ice) = –q(warm water) = +18,900 J

3. Determine the amount of energy absorbed per gram of ice as it melted.

   Mass of ice melted = 154 g – 99 g = 55 g
   Amount of energy absorbed per gram of ice as it melted = q(ice)/mass of ice = 18,900 J/55 g = 340 J/g

4. Calculate the heat of fusion (the heat required to melt ice) in units of kilojoules/mole.

   Heat of fusion (kJ/mole) = 340 J/g x 18 g/mole x 1 kJ/1000 J = 6.1 kJ/mole

5. The literature value for the heat of fusion of ice is 6.02 kJ/mole. What is the percent error for the experimentally determined heat of fusion?
   {13836_Answers_Equation_1}
6. When a mixture of ice and water originally at 0 °C is heated, the temperature remains constant (within experimental error) until all of the ice melts. Explain what happens to the heat energy that is absorbed during this time while the temperature does not change.

   The energy absorbed breaks down the attractive forces that hold the water molecules in the rigid structure of ice.

Introduction

Put your chemistry skills to commercial use! From instant cold packs to flameless ration heaters and hand warmers, the energy changes accompanying physical and chemical transformations have many consumer applications. The backbone of these applications is calorimetry—measuring heat transfer. Investigate the energy changes accompanying the formation of solutions for common laboratory salts, and then apply the results to design a hand warmer that is reliable, safe and inexpensive.

Concepts

• Enthalpy change
• Heat of solution
• Exothermic versus endothermic
• Calorimetry
• Specific heat
• System and surroundings

Background

Hand warmers are familiar cold weather gear used to quickly provide warmth to frigid fingers. Many commercial hand warmers consist of a plastic package containing a solid and an inner pouch filled with water. When the pack is activated, the solid dissolves in water and produces a large temperature change.

The energy or enthalpy change associated with the process of a solute dissolving in a solvent is called the heat of solution (ΔH_soln). At constant pressure, this enthalpy change, ΔH_soln, is equal in magnitude to the heat loss or gain, q, to the surroundings. In the case of an ionic solid dissolving in water, the overall energy change is the net result of three processes—the energy required to break the attractive forces between ions in the crystal lattice (ΔH₁ = +C kJ/mole), the energy required to disrupt intermolecular forces between water molecules (ΔH₂ = +D kJ/mole), and the energy released when the dissociated (free) ions form ion-dipole attractive forces with the water molecules (ΔH₃ = −F kJ/mole). The overall process can be represented by the following equations.

M_aX_b(s) → aM^b+(aq) + bX^a–(aq)
ΔH_soln = ΔH₁ + ΔH₂ + ΔH₃ = (+ C + D −F) kJ/mole

If the amount of energy released in the formation of hydrated ions (ΔH₃) is greater than the amount of energy required to separate the solute and solvent particles (ΔH₁ + ΔH₂), then the sum (ΔH_soln) of the energy changes will be negative and the solution process exothermic (releases heat). If the amount of energy released in the formation of hydrated ions is less than the amount of energy required to separate the solute and solvent particles, then the sum of the energy changes will be positive and the solution process endothermic (absorbs heat).

Heats of solution and other enthalpy changes are generally measured in an insulated vessel called a calorimeter that reduces or prevents heat loss to the atmosphere outside the reaction vessel. The process of a solute dissolving in water may either release heat into the resulting aqueous solution or absorb heat from the solution, but the amount of heat exchanged between the calorimeter and the outside surroundings should be minimal. When using a calorimeter, the reagents being studied are mixed directly in the calorimeter and the temperature is recorded both before and after the reaction has occurred. The amount of heat transfer (q) may be calculated using the heat energy equation: where m is the total mass of the solution (solute plus solvent), s is the specific heat of the solution, and ΔT is the observed temperature change. The specific heat of the solution is generally assumed to be the same as that of water, namely, 4.18 J/g•°C.

When measuring the heat transfer for an exothermic heat of solution using a calorimeter, most of the heat released is absorbed by the aqueous solution (q_aq). A small amount of the heat will be absorbed by the calorimeter itself (q_cal). The overall heat transfer (q_soln) for the reaction (the system) then becomes: In order to determine the correction factor qcal for heat of solution calculations, the heat capacity of the calorimeter, also called the calorimeter constant, must be determined experimentally. The calorimeter constant has units J/ºC. This calibration experiment is done by mixing equal volumes of hot and cool water in the calorimeter and measuring the temperature after 20 seconds. The resulting value is assumed to be the instantaneous mixing temperature, T_mix. The average temperature T_avg of the initial hot (T_H) and cool water (T_C) is also calculated:

T_avg = (T_H + T_C)/2

The difference between T_avg and T_mix is due to the heat lost by the water and absorbed by the calorimeter. The heat lost by the water, q_water, is: where the mass is the total mass of hot and cool water. The heat gained by the calorimeter, q_calor, is equal to that lost by the water, but opposite in sign. The calorimeter constant, C_cal, is calculated as follows where T_initial is the initial temperature of the calorimeter containing cool water. To calculate the correction factor q_cal for use in Equation 2—to determine the heat of solution or heat of reaction for any system—the calorimeter constant is multiplied by the change in temperature of that solution:

q_cal = ΔT (°C) x C_cal (J/°C)

Experiment Overview

The purpose of this advanced inquiry lab is to design an effective hand warmer that is inexpensive, nontoxic and safe for the environment. The investigation begins with an introductory activity to become familiar with the principles of calorimetry and heat of solution calculations. The results provide a model for the guided-inquiry challenge, which is to design an optimum hand warmer for consumer applications. Each student group will be provided six different solids, along with their costs and individual Safety Data Sheets (SDS). Determine the heat of solution for each solid and analyze the cost and safety information to propose a design for the best all-around hand warmer.

Materials

Prelab Questions

1. When chromium chloride, CrCl₂, is dissolved in water, the temperature of the water decreases.
   1. Is the heat of solution exothermic or endothermic?
   2. Which is stronger—the attractive forces between water molecules and chromium and chloride ions or the combined ionic bond strength of CrCl₂ and intermolecular forces between water molecules? Explain.
2. A solution was formed by combining 25.0 g of solid A with 60.0 mL of distilled water, with the water initially at 21.4 °C. The final temperature of the solution was 25.3 °C. Calculate the heat released as the solid dissolved, q_soln, assuming no heat loss to the calorimeter (see Equation 1).
3. In Question 2, the calorimeter was found to have a heat capacity of 8.20 J/°C. If a correction is included to account for the heat absorbed by the calorimeter, what is the heat of solution, q_soln?
4. The solid in Question 2 was aluminum sulfate, Al₂(SO₄)₃. Calculate the molar heat of solution, ΔH_soln, for aluminum sulfate. Hint: The units for molar heat of solution are kilojoules per mole (kJ/mole). First determine the heat released per gram of solid.

Safety Precautions

Lithium chloride is moderately toxic by ingestion. Calcium chloride and ammonium chloride are slightly toxic. Magnesium sulfate is a body tissue irritant. Sodium acetate is a body tissue and respiratory tract irritant. Avoid contact of all chemicals with eyes and skin. Wear chemical splash goggles, chemical-resistant gloves, and a chemical-resistant apron. Wash hands thoroughly with soap and water before leaving the laboratory. Please follow all laboratory safety guidelines.

Procedure

Part A. Heat Capacity of the Calorimeter

1. Set up a calorimeter consisting of two nested polystyrene cups in a ring clamp attached to a support stand.
2. Place a magnetic stirrer below the calorimeter, then lower the ring clamp until the bottom of the cup just sits on the surface of the magnetic stirrer (see Figure 1).
   {13836_Procedure_Figure_1}
3. Measure 100.0 mL of distilled water in a 100-mL graduated cylinder and transfer the water to the calorimeter.
4. Add a magnetic stirring bar to the calorimeter, and set the bar spinning slowly. If a magnetic stirrer is not available, use a stirring rod. Do not remove the stirring rod from the calorimeter.
5. Measure and record the initial temperature of the water.
6. Heat approximately 125 mL of distilled water to 60–70 °C in a 250-mL beaker.
7. Using heat-resistant gloves, measure 100.0 mL of the hot water in a 100-mL graduated cylinder.
8. Measure and record the temperature of the hot water.
9. Immediately pour the hot water into the room temperature water in the calorimeter.
10. Insert the thermometer, and stir the water.
11. Record the mixing temperature T_mix after 20 seconds.
12. Empty the calorimeter and dry the inside.
13. Calculate the calorimeter constant, C_cal, using T_mix and Equations 3 and 4 from the Background section.

Part B. Calorimetry Procedure
Examine the heat energy change for the following solution.

MgSO₄(s) + H₂O(l) → Mg²⁺(aq) + SO₄^2–(aq)

1. Measure 100.0 mL of distilled or deionized water in a 100-mL graduated cylinder and transfer to the calorimeter.
2. Measure and record the initial temperature of the water.
3. Measure 5.00 g of anhydrous magnesium sulfate in a weighing dish.
4. Put a magnetic stir bar or stirring rod into the calorimeter and slowly stir the water.
5. Quickly add the 5.00 g of anhydrous magnesium sulfate to the calorimeter and insert the thermometer.
6. Monitor the temperature and record the highest or lowest temperature reading.
7. Calculate the molar heat of solution for magnesium sulfate. Include the correction due to the heat capacity of the calorimeter.

Guided-Inquiry Design and Procedure
Form a working group with other students and discuss the following questions.

1. Review the calorimetry procedure:
   1. What data is needed to calculate the enthalpy change for a reaction?
   2. Identify the variables that will influence the experimental data.
   3. What variables should be controlled (kept constant) during the procedure?
   4. The independent variable in an experiment is the variable that is changed by the experimenter, while the dependent variable responds to or depends on the changes in the independent variable. Name the independent and dependent variables in a calorimetry experiment to determine the molar heat of solution.
   5. Discuss the factors that will affect the precision of the experimental results.
2. Working collaboratively with the general procedure provided in the Introductory Activity, design and carry out experiments to determine the heat of solution for each solid in Set A and Set B. Be sure to review all safety precautions with your instructor before starting.
3. Extrapolating from the information collected, predict which solid(s) could be used in an effective hand warmer meeting the following requirements:
   • The hand warmer must contain 10 g of an ionic solid and an inner pouch filled with 40 mL of water.
   • Activating the hand warmer must increase the temperature of the resulting solution by at least 20 °C.
   • The solid should be nontoxic, safe for the environment and economical.
4. Review the cost information shown below and consult the SDS for each potential hand warmer. Propose the optimum design for the most cost-effective hand warmer that is nontoxic and least harmful to the environment.
   {13836_Procedure_Table_1}
5. With your instructor’s permission, verify the design and demonstrate the use of your hand warmer.

Student Worksheet PDF

13836_Student1.pdf