Materials Included In Kit

Additional Materials Required

Safety Precautions

The ammonia solution and its vapors are irritating, especially to the eyes. It is moderately toxic by ingestion or inhalation. Dispense and perform reactions in a fume hood. The hydrochloric acid solution is toxic by ingestion or inhalation; it is severely corrosive to skin and eyes. The sodium hydroxide solution is severely corrosive to skin and eyes. When sodium hydroxide and ammonium chloride are mixed, ammonia gas is evolved. Have students work in a hood or under a funnel attached to an aspirator. Wear chemical splash goggles, chemical-resistant gloves and a chemical-resistant apron. Have students wash hands thoroughly with soap and water before leaving the laboratory. Please consult current Safety Data Sheets for additional safety 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 resulting reaction solutions and the ammonium chloride solution may be disposed of according to Flinn Suggested Disposal Method #26b. The hydrochloric acid solution may be disposed of according to Flinn Suggested Disposal Method #24b. The ammonia solution and the sodium hydroxide solution may be disposed of according to Flinn Suggested Disposal Method #10.

Lab Hints

• The experiment requires 60 minutes to complete. The graphical data analysis gives better data than just recording the highest temperature reached. Some of the temperature changes will be quite small, so a lack of precision may cause a large percent error. It may be helpful to repeat some measurements. In particular, the value of ΔH for

NH₄⁺(aq) + OH^–(aq) → NH₃(aq) + H₂O(l)

is a small value.

• The best thermometers to use are digital electronic thermometers (Flinn Scientific Catalog No. AP8716) or temperature sensors connected to a computer- or calculator-based interface system such as LabPro or CBL. 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.
• The use of computer- or calculator-based technology for data collection and analysis is tailor-made for thermochemistry experiments. The graph can easily be drawn using a graphing calculator or a graphical analysis program on a computer.
• There is often confusion surrounding the naming convention of ammonia (NH₃) solutions. Ammonia reacts with water to form an equilibrium with ammonium ions (NH₄⁺) and hydroxide ions (OH^–). At higher concentrations, this gives rise to the name ammonium hydroxide solution.
• Following is the net reaction between ammonia and hydrochloric acid. In water, ammonia forms an equilibrium with ammonium ions and hydroxide ions (reaction A). The addition of hydrochloric acid reduces the concentration of hydroxide ions to form water (reaction B). The reduction of hydroxide ions pushes the equilibrium of reaction A to the products. Therefore, the overall reaction can be described by reaction C.
  {13527_Hints_Equation_5}

Teacher Tips

• Students may need help with the calorimetric calculations. It is important to keep track of the signs associated with the heat changes. A loss of heat is assigned a negative value, a gain of heat a positive value. The heat of reaction is exothermic and has a negative value; that 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.

• Bank statements provide an analogy that many teachers find helpful in explaining Hess’s Law. Consider two students, each having ending balances of $150. One student may have started with $50 in the account, made three deposits of $50 each, and two withdrawals of $25 each. The other student may have started with $50 and made only one deposit of $150 and one withdrawal of $50. Their beginning and ending bank balances were both the same and did not depend on how they got there.
• What makes Hess’s Law a law? This may be a good time to 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.
• It is convenient to use a magnetic stirrer and stirring bar, but it is also possible to get reasonable data when stirring with the thermometer.
• The supplied 6.4-oz nested Styrofoam^® cups make a good calorimeter. A cardboard square with a hole to accommodate a thermometer can be used as a cover. A cork borer can be used to make the hole in the cardboard.
• Digital thermometers with readings of 0.1 °C work best. Standard thermometers can be used, but make taking readings more difficult.
• The experiment can also be safely performed in a well-ventilated room or under a funnel attached to an aspirator.

Further Extensions

AP^® Standards
This lab fulfills the requirements for the College Board Recommended AP^® Experiment #13: Determine the Enthalpy Change Associated with a Reaction.

Answers to Prelab Questions

1. Define ΔH_rxn.

   ΔH_rxn is the change in enthalpy for a reaction, or the heat evolved or absorbed in a reaction that occurs at constant pressure.

2. Define specific heat.

   Specific heat is the amount of heat required to raise the temperature of one gram of a substance one degree Celcius.

3. The specific heat of a solution is 4.18 J/(g•°C) and its density is 1.02 g/mL. The solution is formed by combining 25.0 mL of solution A with 25.0 mL of solution B, with each solution initially at 21.4 °C. The final temperature of the combined solutions is 25.3 °C. Calculate the heat of reaction, q, assuming no heat loss to the colorimeter. Use correct significant figures.

   q_solution = –q_rxn
   q_solution = (grams of solution) x (specific heat, solution) x ΔT

   = (50.0 mL x 1.02 g/mL) x 4.18 J/(g•°C) x (25.3 – 21.4)°C
   = 830 J

   q_rxn = –q_solution
   q_rxn = –830 J

4. In Question 3, the calorimeter has a heat capacity of 8.20 J/°C. If a correction is included for the heat absorbed by the calorimeter, what is the heat of reaction, q

   q_rxn = –(q_cal + q_solution)

   = –[8.20 J/°C x (25.3 – 21.4)°C + 830 J]
   = –32 J – 830 J

   q_rxn = –862 J

5. If the reaction in Question 3 is

   A(aq) + B(aq) → AB(aq)

   the molarity of A in solution A is 0.60 M and the molarity of B in solution B is 0.60 M, calculate the enthalpy of reaction, ΔH_rxn, for the formation of 1 mole of AB in solution.

   moles_A = moles_B = moles_AB
   moles_AB = 0.60 moles_A/L x 0.025 L = 0.015 moles_AB
   ΔH_rxn = q_rxn/moles_AB

   = –862 J/0.015 moles
   = –57000 J/mole
   = –57 kJ/mole

Sample Data

Part 1 Data Table. Determination of the Heat Capacity of the Calorimeter

Initial temperature (°C)

50.0 mL H₂O—room temperature ___22.9 °C___
50.0 mL H₂O—heated ___61.1 °C___

Mixing Data

T_mix, °C ___41.5 °C___
T_avg, °C ___42.0 °C___ 
q_cal, J ___+200 J___
C_cal, J/°C ___11 J/°C___

Part 2 Data Table. Determination of Heats of Reaction

Reaction 1: HCl(aq) + NaOH(aq) → NaCl(aq) + H₂O(l)

Initial temperature (°C)

50.0 mL 2.0 M HCl ___22.9___ °C
50.0 mL 2.0 M NaOH ___22.9___ °C

Mixing Data

T_mix, °C ___35.5 °C___ 
q_rxn, J ___–5560 J___
ΔH, kJ/mol ___–55.6 kJ/mole___

Reaction 2: NH₄Cl(aq) + NaOH(aq) → NH₃(aq) + NaCl(aq) + H₂O(l)

Initial temperature (°C)

50.0 mL 2.0 M NH₄Cl ___22.9___ °C
50.0 mL 2.0 M NaOH ___22.9___ °C

Mixing Data

T_mix, °C ___24.1 °C___ 
q_rxn, J ___–570 J___
ΔH, kJ/mol ___–5.7 kJ/mole___

Reaction 3: NH₃(aq) + HCl(aq) → NH₄Cl(aq)

Initial temperature (°C)

50.0 mL 2.0 M NH₃ ___22.9___ °C
50.0 mL 2.0 M HCl ___22.9___ °C

Mixing Data  T_mix, °C ___33.0 °C___ 
q_rxn, J ___–4460 J___
ΔH, kJ/mol ___–44.6 kJ/mole___

Calculations

Part 1. Calculate the Heat Capacity of the Calorimeter

1. Plot the Mixing Data with temperature on the vertical axis and the time on the horizontal axis.
   {13527_Data_Figure_2}
2. The first few data points may be erratic due to incomplete mixing and lack of equilibration with the thermometer. Draw a straight line through the subsequent points and extend the line back to the maximum temperature at time zero. Record this temperature as T_mix in the Part 1 Data Table.
3. Calculate the average initial temperature, T_avg, of the hot and cold water. Record this temperature as T_ave in the Part 1 Data Table.
   {13527_Data_Equation_6}
4. The difference between T_avg and T_mix is due to the heat lost by the hot water and absorbed by the calorimeter. The heat lost by the water, q_water, is:

   q_water = (grams of water) x (specific heat of water x (T_mix – T_avg)

   where specific heat of water is 4.18 J/(g•°C).

   The heat gained by the calorimeter, q_cal, is equal to that lost by the water, but opposite in sign.
   
   Calculate q_cal for the determination and enter this value in the Part 1 Data Table.

   q_water = 100.0 g x 4.18 J/(g•°C) x (41.5 – 42.0) °C

   = –200 J

   q_cal = q_water

   = 200 J

5. Calculate the heat capacity of the calorimeter, C_cal. This is equal to the heat the calorimeter absorbs when 100 mL of solution changes 1 °C in temperature.
   {13527_Data_Equation_7}

   where T_initial is the initial temperature of the cool water. Record the heat capacity, C_cal, in the Part 1 Data Table.

   C_cal = 200 J/(41.5 – 22.9) °C

   = 11 J/°C

Part 2. Calculate the Enthalpy of Reaction, ΔH

1. Graph the temperature versus time on a separate sheet of graph paper for each of the three reactions tested. Extrapolate the line back to find the instantaneous mixing temperature, T_mix for each reaction. Record this value for each reaction in the Part 2 Data Table.
2. Calculate the amount of heat evolved in each reaction, q_rxn. If it is assumed that all the heat of reaction is absorbed by the solution and calorimeter, then:

   q_rxn = –[heat absorbed by solution + heat absorbed by colorimeter]
   q_rxn = –[(grams of solution x specific heat of solution x ΔT_solution) + (C_cal x ΔT_solution)]
   
   where ΔT_solution = (T_mix – T_initial) for each reaction mixture. Assume the density of the final solutions is 1.03 g/mL and the specific heat of all the solutions is 4.18 J/g•°C.
   
   Record the q_rxn for each reaction in the Part 2 Data Table.

   (1) NaOH(aq) + HCl(aq) → NaCl(aq) + H₂O(l)

   ΔT_solution = (35.5 – 22.9) °C = 12.6 °C
   q_rxn = –[(103 g x 4.18 J/(g•°C) x 12.6 °C) + (11 J/°C x 12.6 °C)] = 5560 J = –5.56 kJ

   (2) NH₄Cl(aq) + NaOH(aq) → NH₃(aq) + NaCl(aq) + H₂O(l)

   ΔT_solution = (24.1 – 22.9) °C = 1.2 °C
   q_rxn = –[(103 g x 4.18 J/(g•°C) x 1.2 °C) + (11 J/°C x 1.2 °C)] = –530 J = –0.53 kJ

   (3) NH₃(aq) + HCl(aq) → NH₄Cl(aq)

   ΔT_solution = (33.0 – 22.9) °C = 10.1 °C
   q_rxn = –[(103 g x 4.18 J/(g•°C) x 10.1 °C) + (11 J/°C x 10.1 °C)] = –4460 J = –4.46 kJ

3. Calculate the enthalpy change, ΔH_rxn, in terms of kJ/mole, for each of the reactions. Record the values in the Part 2 Data Table.

   All reactions use 0.050 L x 2.0 mol/L = 0.10 moles of each reactant

   (1) NaOH(aq) + HCl(aq) → NaCl(aq) + H₂O(l)

   ΔH_rxn = –5.56 kJ/0.10 moles = –55.6 kJ/mole

   (2) NH₄Cl(aq) + NaOH(aq) → NH₃(aq) + NaCl(aq) + H₂O(l)

   ΔH_rxn = –0.53 kJ/0.10 moles = –5.3 kJ/mole

   (3) NH₃(aq) + HCl(aq) → NH₄Cl(aq)

   ΔH_rxn = –4.46 kJ/0.10 moles = –44.6 kJ/mole

Part 3. Verify Hess’s Law

1. Write the net ionic equations for the three reactions involved in the experiment. Show how the first two reactions are arranged algebraically to determine the third.

   (1) OH^–(aq) + H₃O⁺(aq) → 2H₂O(l)
   (2) NH₄⁺(aq) + OH^–(aq) → NH₃(aq) + H₂O(l)
   (3) NH₃(aq) + H₃O⁺(aq) → NH₄⁺(aq) + H₂O(l)
   Equation (1) – Equation (2) = Equation (3)

2. Calculate the value of ΔH for the third reaction from the values of ΔH determined for the first two reactions using Hess’s Law.

   ΔH_rxn(3) = ΔH_rxn(1) – ΔH_rxn(2) = [–55.6 kJ/moles – (–5.3 kJ/mol)] = –50.3 kJ/mole

3. Find the percent difference between the calculated and measured values of ΔH for the third reaction.

   Measured ΔH_rxn = –44.6 kJ/mole

   {13527_Data_Equation_8}

Answers to Questions

1. What is meant by calorimetry?

   Calorimetry is the experimental determination of heat changes in a chemical process.

2. How does graphical analysis improve the accuracy of the data?

   Use of a graphical temperature analysis allows the determination of the instantaneous theoretical temperature of mixing of the solutions.

3. The equation for calculating the heat evolved in each reaction is:

   q_rxn = –[(grams of solution  x specific heat of solution x ΔT_solution) + (C_cal x ΔT_solution)]
   
   What is the meaning of the negative sign in front of the brackets?

   The values included in the brackets allow the calculation of the heat absorbed by the solution and calorimeter. This is a positive value. The heat of reaction, q_rxn, is the heat evolved by the chemical process and is the same quantity of heat as that absorbed by the solution and calorimeter but opposite in sign.

4. Do the lab results support Hess’s Law?

   The values are close to that predicted by Hess’s Law.

5. How could the procedure be modified to achieve greater accuracy?

   The most difficult measurement is the small temperature change associated with reaction (2). Repeating this determination, perhaps with a more sensitive thermometer, would improve the data.

6. Find a table in a reference that lists standard heats of formation for the species included in your net ionic equations. Use them to calculate ΔH_rxn for each of the three net ionic equations. Do these values support Hess’s Law?
   {13527_Answers_Table_5}

   (1) H⁺(aq) + OH^–(aq) → H₂O(l)

   ΔH_rxn(1) = –285.9 kJ/mol – [0 + (–230.0)] kJ/mol = –55.9 kJ/mol

   (2) NH₄⁺(aq) + OH^–(aq) → NH₃(aq) + H₂O(l)

   ΔH_rxn(2) = [–80.3 + (–285.9)] kJ/mol – (– 32.5) kJ/mol + (–230.0)] kJ/mol = –3.7 kJ/mol

   (3) NH₃(aq) + H⁺(aq) → NH₄⁺(aq)

   ΔH_rxn(3) = –132.5 kJ/mol – [(0) + (–80.3)] kJ/mol = –52.2 kJ/mol
   ΔH_rxn(1) –ΔH_rxn(2) = –55.9 kJ/mol – (–3.7 kJ/mol) = –52.2 kJ/mol

   These data exactly support Hess’s Law.

Introduction

The release or absorption of heat energy is a unique value for every reaction. Were all these values experimentally determined? This lab demonstrates the principle of Hess’s Law—if several reactions add up to produce an overall reaction, then the heat transfers of the reactions will add up to the value of the heat transfer for the overall reaction.

Concepts

• Enthalpy of reaction
• Heat of formation
• Hess’s law
• Calorimetry

Background

In this experiment, the enthalpy changes for the reaction of ammonia and hydrochloric acid will be determined using Hess’s law. If the enthalpy change for the reaction between sodium hydroxide and hydrochloric acid and the reaction between sodium hydroxide and ammonium chloride are determined, the enthalpy change for the reaction between ammonia and hydrochloric acid can be calculated. The balanced equations for these reactions are as follows:

When Equation 2 is reversed and added to Equation 1, the result is Equation 3.

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, in the reaction. This change represents the difference in enthalpy of the products and the reactants and is independent of the steps in going from reactants to products.

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: If a reaction is the sum of two or more other reactions, the ΔHrxn for the overall reaction must be the sum of the ΔH_rxn values of the constituent reactions. In this laboratory experiment, the value of ΔH_rxn for Equation 1 minus the value of ΔH_rxn for Equation 2 will equal the value of ΔH_rxn for Equation 3. Unfortunately, there is no single instrument that can directly measure heat or enthalpy in the way a balance measures mass or a thermometer measures temperature. It is possible, however, to measure heat change when a chemical reaction occurs. If the reaction occurs in solution, the heat change is calculated from the mass, temperature change, and specific heat of the solution, according to Equation 4, 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.

The three reactions in this experiment are all acid–base neutralizations. Acid–base neutralizations are exothermic processes. Combining solutions containing an acid and a base results in a rise of solution temperature. The heat given off by the reaction is calculated using Equation 4. This heat quantity can be converted to the enthalpy of reaction, in terms of kJ/mol, by using the concentrations of the reactants.

When measuring the heat transfers for exothermic reactions using a calorimeter, most of the heat released is absorbed by the solution. A small amount of this heat 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)

Experiment Overview

The purpose of this experiment is to verify Hess’s Law. Three acid–base reactions, chosen so that the third reaction equation equals the first reaction equation minus the second, are measured for temperature change by calorimetry. The values of heat change and enthalpy of reaction are calculated for each reaction. The measured value for the third reaction is then compared to the value calculated by subtracting the enthalpy of reaction for reaction two from the enthalpy of reaction of reaction one.

Materials

Prelab Questions

1. Define ΔH_rxn.
2. Define specific heat.
3. The specific heat of a solution is 4.18 J/(g∙°C) and its density is 1.02 g/mL. The solution is formed by combining 25.0 mL of solution A with 25.0 mL of solution B, with each solution initially at 21.4 °C. The final temperature of the combined solutions is 25.3 °C. Calculate the heat of reaction, q, assuming no heat loss to the colorimeter. Use correct significant figures.
4. In Question 3, the calorimeter has 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 reaction, q?
5. If the reaction in Question 3 is

   A(aq) + B(aq) → AB(aq)

   and the molarity of A in solution A is 0.60 M and the molarity of B in solution B is 0.60 M, calculate the enthalpy of reaction, ΔH_rxn, for the formation of 1 mole of AB in solution.

Safety Precautions

The ammonia solution and its vapors are irritating, especially to the eyes. It is moderately toxic by ingestion or inhalation. Dispense in a fume hood. The hydrochloric acid solution is toxic by ingestion or inhalation; it is severely corrosive to skin and eyes. The sodium hydroxide solution is severely corrosive to skin and eyes. Wear chemical splash goggles, chemical-resistant gloves and a chemical-resistant apron. Wash hands thoroughly with soap and water before leaving the laboratory.

Procedure

Part 1. Determine the Heat Capacity of the Calorimeter

1. Set up a calorimeter of two nested Styrofoam^® cups with a cover having a hole in it to accept a thermometer (see Figure 1).
   {13527_Procedure_Figure_1}
2. Measure 50.0 mL of distilled water in a 50-mL graduated cylinder and transfer the water into the calorimeter.
3. Place the calorimeter assembly on a magnetic stirrer, add a magnetic stirring bar, and set the bar spinning slowly.
4. Measure and record the temperature of the water in the Part 1 Data Table.
5. Heat approximately 75 mL of distilled water to about 70 °C in a 250-mL beaker.
6. Measure 50.0 mL of the 70 °C distilled water in a 50-mL graduated cylinder.
7. Measure and record the temperature of the hot water in the Part 1 Data Table.
8. Immediately pour the hot water into the room temperature water in the calorimeter.
9. Cover the calorimeter, insert the thermometer, and stir the water.
10. Record the temperature every 20 seconds for a total of 3 minutes in the Part 1 Data Table.
11. Empty the calorimeter and dry the inside of calorimeter when finished.

Part 2. Determine the Heats of Reaction

Reaction 1: HCl(aq) + NaOH(aq) → NaCl(aq) + H₂O(l)

1. Measure 50.0 mL of a 2.0 M HCl solution in a 50-mL graduated cylinder and transfer to the calorimeter.
2. Record the temperature of the HCl solution in the Part 2 Data Table.
3. Rinse the 50-mL graduated cylinder with distilled water.
4. Measure 50.0 mL of a 2.0 M NaOH solution in a 50-mL graduated cylinder.
5. Record the temperature of the NaOH solution in the Part 2 Data Table.
6. Put a magnetic stirring bar into the calorimeter and start the bar spinning slowly in the HCl solution.
7. Quickly add the 50.0 mL of 2.0 M NaOH solution to the calorimeter, cover, and insert the thermometer.
8. Record the temperature after 20 seconds, and then every 20 seconds for a total of 3 minutes, in the Part 2 Data Table.

Reaction 2: NH₄Cl(aq) + NaOH(aq) → NH₃(aq) + NaCl(aq) + H₂O(l)

9. Thoroughly rinse and dry the calorimeter, thermometer, stirrer bar and graduated cylinder used for reaction 1.
10. Repeat steps 1–8 of Part 2 using 2.0 M NH₄Cl solution and 2.0 M NaOH solution. Be sure to perform this procedure in the fume hood.

Reaction 3: NH₃(aq) + HCl(aq) → NH₄Cl(aq)

11. Thoroughly rinse and dry the calorimeter, thermometer, stirrer bar, and graduated cylinder used for reaction 2.
12. Repeat steps 1–8 of Part 2 using 2.0 M NH4OH solution and 2.0 M HCl solution. Be sure to perform this procedure in the fume hood.
13. Discard all solutions as directed by the instructor.

Student Worksheet PDF

13527_Student1.pdf