# Explorations in Thermodynamics: Calorimetry, Enthalpy & Heats of Reaction

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1 Explorations in Thermodynamics: Calorimetry, Enthalpy & Heats of Reaction Dena K. Leggett, Ph.D. and Jon H. Hardesty, Ph.D. Collin County Community College Dept. of Chemistry 1. Introduction: One of the earliest scientific observations made by humans must have been the warmth provided by fire, and since that time the extraordinary utility of heat as a tool has contributed to many of the most profound technological advances in humanity s history. The science of heat flow, or more generally energy flow, is called thermodynamics. Many of the fundamental foundations of thermodynamics have been discussed in our lectures on gas laws and the kinetic molecular theory of gases where we learned that heat and kinetic energy (the energy of motion) of gaseous atoms/molecules are equivalent. Now we are ready to turn our attention to more subtle aspects of thermodynamics relating to thermal energy being extracted from or stored within a wider array of chemical compounds than gases. In this set of experiments we will focus our attention upon one particular area of thermodynamics, namely calorimetry, a technique used to measure heat flow into and out of matter. The basic idea of the technique is quite simple. The matter we are interested in studying is placed into a container called a calorimeter that segregates the thermal process we are interested in studying from the rest of the universe. As changes occur to that matter, we can follow the movement of heat from one portion of the matter to another by observing temperature changes. The container we use as a calorimeter should thermally insulate the matter we re interested in studying, it should prevent matter from entering or exiting once our measurement has begun, and it should allow for easy measurement of temperature changes. A reasonable calorimeter can be constructed from a pair of nested (i.e. one stacked inside the other) Styrofoam cups with a loose fitting cap on top to limit heat/material transfers into and out of the device (see Figure 1). 2. Specific Heat Capacity: Experimentally, measuring heat flows is somewhat difficult. We do not have a heat meter that we can use to directly measure the amount of heat released/absorbed by matter when a thermodynamic process occurs. Thermometers, however, can be used to measure changes in temperature that can be utilized as indirect measures of

2 heat flow. In order to precisely correlate measured temperature changes to the flow of particular amounts of thermal energy, a proportionality constant that relates these two quantities called the heat capacity of a material is used. It indicates the amount of heat required to raise the temperature of a sample of that material by 1 C. Heat capacity is an extensive property of matter, meaning that it varies with sample size. To account for this fact, experimentally measured heat capacities are routinely corrected to account for a measurement on a 1 g sample, giving rise to a slight variation called the specific heat capacity (c) that indicates the amount of heat required to raise the temperature of 1 g of the substance by 1 C. Mathematically, the proportionality can be expressed as shown in equation 2.1: q released/absorbed m c T (Eqn 2.1) where c is the specific heat capacity (in J/(g C)), q is the quantity of thermal energy released/absorbed (in J), m is the mass of the sample (in g), and T is the change in temperature (in C), which is taken as T final -T initial for the sample. Since specific heat capacities are positive constants for a given material, heat flow is directly proportional to changes in temperature. Thus if the change in temperature ( T) is positive, then q is also positive indicating the absorption of heat by the sample (an endothermic process). Alternatively, if T is negative then q is also negative indicating the loss of heat by the sample (an exothermic process). The fascinating feature of specific heat capacities is that they adopt a wide array of values depending upon material as shown in the Table 1. Table 1-Specific Heat Capacities of Common Substances Material Specific Heat Capacity (J/g C) at 25 C i Aluminum Graphite Gold Wood 1.76 Cement 0.88 Granite 0.79 H 2 O(l) Determining a Calorimeter Constant: When a measurement is made in a calorimeter, we must account for the fact that the calorimeter itself can release heat into or absorb heat out of the process we are investigating while our measurement is being recorded. The calorimeter is in thermal contact with the matter we are interested in studying (the system of interest), so heat can be transferred between the system and the calorimeter (a portion of the surroundings). While we may not be particularly interested in studying the heat flow into or out of the calorimeter, it is essential that we account for it to prevent errors in the measurement of the heat flow pertaining to the system of interest. Since our calorimeter (the nested

3 Styrofoam cups) is a fixed mass, we can rearrange the expression for the specific heat capacity of the calorimeter and take the product of the specific heat capacity of the calorimeter (c cal ) and the mass of the calorimeter as a new constant called the calorimeter constant (orimeter ) as shown below: m cal c cal (Eqn 3.1) (where Calorimeter Constant m cal c cal ) To measure the magnitude of the calorimeter constant we will carry out a measurement in which hot water is mixed with cold water in the calorimeter. Common experience tells us that the temperature of the water after mixing should lie between the initial hot and cold values. The First Law of Thermodynamics tells us that the sum of all of the thermal energy present in the calorimeter and in the two samples of water must stay constant throughout our measurement. (Remember, energy cannot be created or destroyed.) However, it will redistribute itself among all three components (the hot water, the cold water, and the calorimeter). Mathematically, the First Law for this mixing process can be written as: 0 q hot q cold (Eqn3.2) We know from our everyday experience that heat will exit the hot water and enter the cold water and the calorimeter, so we can rearrange Eqn. 3.2 to give: q hot q cold (Eqn3.3) Notice that this expression can be interpreted as an exothermic process from the perspective of the hot water ( q, heat lost) and an endothermic process from the perspective of the cold water and the calorimeter (+q s, heat gained). Since we know the heat capacity of liquid water (4.184 J/g C), and we can easily measure the masses of the hot water and the cold water that we pour into the calorimeter as well as the initial and final temperatures for each component, we can make the following substitutions into Eqn 3.3: q hot m hot c hot T hot q cold m cold c cold T cold (from Eqn 3.1) (We assume that = T cold because the cold water is in contact with the calorimeter at all times during the experiment, allowing these two components to maintain thermal equilibrium throughout the experiment.) The resulting mathematical equation (that you should derive) contains only one unknown, the calorimeter constant,. The value we determine for this constant is true for your calorimeter, and it will be incorporated into the next two portions of the experiment.

4 4. Determining the Specific Heat Capacity of a Metal: The specific heat capacity of a metal can be readily measured using a very similar technique. A sample of hot metal of known mass and temperature can be placed into a calorimeter containing a sample of cold water of known mass and temperature. Practical experience tells us that heat should exit the metal sample and enter the cold water and the calorimeter, resulting in an increase in the temperature of the water above its initial value. Assuming that no additional thermal energy will be generated or destroyed once the hot metal is added to the cold water we can utilize the First Law to write the following equation: 0 q metal q water (Eqn4.1) Rearranging this expression to solve for q metal results in equation 4.2: q metal q water (Eqn4.2) Equation 4.2 can be interpreted in terms of an exothermic process from the perspective of the metal (-q, heat lost by the metal) and an endothermic process from the perspective of the water and the calorimeter (+q, heat gained by the cold water and the calorimeter). We can write heat flow expressions for each component in Eqn 4.2 as shown below: q metal m metal c metal T metal q water m water c water T water These expressions can be substituted into Eqn 4.2 to arrive at an equation (that you should derive) that allows us to calculate the specific heat capacity of the metal (c metal ). Once this expression is obtained, we can turn our attention to the following facts. The masses of the water (m water ) and the metal (m metal ) can be easily measured along with the changes in temperatures of the water ( T water ) and the metal ( T metal ). We also know the specific heat of water (c water ), the calorimeter constant, ( ), and we can assume T water = (because the water and the calorimeter remain in contact with one another throughout the experiment). Plugging all of these known values into the expression results in an equation containing only one unknown, c metal. 5. Determining the Heat of Reaction ( H rxn ) for an Acid/Base Neutralization Reaction: Most chemical reactions occur with a net absorption or liberation of energy in the form of heat. These heat flows largely originate from two primary sources: A. In the case of matter undergoing changes in composition in the gas phase where reactants and products do not interact with solvent particles (such as H 2 (g) + Cl 2 (g) 2HCl(g)) these heat flows result from changes in the potential

5 energies of the electrons as reactant particles are converted into product particles. When the electrons are less stable in the products than they are in the reactants, energy is absorbed by the reacting particles and transferred into the surrounding environment as heat (Figure 2a). If this condition occurs the reaction is said to be an endothermic reaction. Alternatively, when electrons are more stable in the products than they are in the reactants, energy is released from the reacting particles in the form of heat extracted from the surrounding environment (Figure 2b). If this condition occurs the reaction is said to be an exothermic reaction. Effectively, the heat flow that is observed in these reactions equates to the changes in the relative stabilities of the electrons within the atoms/molecules/ions as reactants are converted to products. Products Products Reactants a q final > q q initial final< q initial +q -q reaction reaction Reactants b Figure 2. Potential Energy Diagrams for Endothermic (I) and Exothermic (II) Reactions B. In the case of matter undergoing changes in composition in solution where reactants and products do interact with solvent particles (such as the reaction HCl(aq) + NaOH(aq) H 2 O(l) + NaCl(aq)) these heat flows result from a combination of a) changes in the potential energies of the electrons in reactant particles versus product particles as described above, and b) changes in the strengths of the interactions between solvent particles and reactant particles versus the strengths of the interactions between solvent particles and product particles as the reaction proceeds from start to finish. Since most reactions that we study in the laboratory are carried out in solution, the values that are typically measured and tabulated incorporate these combined effects unless otherwise indicated. To properly measure the heat flows into/out of a chemical reaction in solution using a calorimeter, it is essential that the system be carefully defined as only the chemical reaction of interest. In this context, the system is precisely defined as the point of location of bond breakage and/or bond formation in the reactant atoms/molecules/ions along with those few solvent molecules directly interacting with the reactant particles. The surroundings are taken as the calorimeter and the bulk solution that in practice means those solvent molecules not directly interacting with the reactant particles. The overwhelming majority of solvent molecules in a reasonably dilute solution fall into this bulk solution category, and as a result it must be remembered that when a thermometer is placed into the solution to measure the temperature of the solution, it is measuring the temperature of this bulk solvent (i.e. the surroundings).

6 In this portion of the experiment we will mix a measured volume of 1.00 M aqueous NaOH solution with an equivalent measured volume of 1.00 M aqueous HCl solution to provide a stoichiometric ratio of reactants for the neutralization reaction shown below. HCl(aq) + NaOH(aq) H 2 O(l) + NaCl(aq) Thermodynamically, we can follow the same line of reasoning adopted in the prior two sections. According to the First Law of Thermodynamics, energy cannot be created or destroyed as the reaction occurs within the calorimeter, it can only be transferred from one component to another. Thus, we can write the following expression: 0 q rxn q solution (Eqn5.1) where q rxn is the heat released/absorbed by the reaction (system), q solution is the heat absorbed/released by the bulk solution and is the heat absorbed/released by the calorimeter. Since we are attempting to measure the heat released or absorbed by the reaction, we can solve for q rxn to generate equation 5.2. q rxn q solution (Eqn 5.2) At this point, we can take advantage of our understanding of the specific heat capacity of the solution and the previously measured calorimeter constant to write the following expressions. q solution m solution c solution T solution (fromeqn 3.1) In order to use the expression for the heat absorbed/released by the solution, we need to make an important assumption. In a dilute solution, the overwhelming majority of all the particles in solution are solvent molecules; therefore, it is reasonable to assume that the specific heat capacity of the solution will be very close to the specific heat capacity of the solvent, and in fact, we will set c solution = c water to simplify our problem. Moreover, since the solution and the calorimeter are in contact with one another throughout the measurement period, we can take T solution =. Finally, the mass of the solution can be approximated as the sum of the masses of the HCl and NaOH solutions combined in the calorimeter. When these approximations are made our expressions for q solution and become: q solution m solution c water T solution T solution When these two expressions are substituted into Eqn 5.2 we arrive at an equation (that you should derive) that will allow us to calculate the amount of heat released or absorbed by the acid/base neutralization reaction. When a reaction is carried out in an open container, under a constant pressure (such as atmospheric pressure) this observable heat flow (q rxn ) is equal to the change in Enthalpy for a Reaction ( H rxn ) (also called the heat of reaction). Enthalpy (H) is a

7 defined thermodynamic function that possesses certain specific properties that are valuable for understanding the theory of thermodynamics and for making experimental measurements. Since the amount of heat released or absorbed from a specific chemical reaction is dependent upon the size of the chemical reaction carried out (i.e. the number of moles of limiting reagent used) it is customary to correct the observed heat flow for the reaction size by dividing q rxn by the number of moles of limiting reagent. It is this value that is typically reported as H rxn. PROCEDURES: 1. DETERMINATION OF THE CALORIMETER CONSTANT ii Assemble your calorimeter as close to the picture in Figure 1 as equipment allows. Make sure the thermometer/temperature probe is not touching the bottom of the calorimeter. Determine the mass of the assembled calorimeter. Measure approximately 50 ml of water and deliver into the calorimeter. Determine the mass of the calorimeter and the water. Allow the cold water and the calorimeter to thermally equilibrate for 15 minutes. While this is occurring, accurately measure approximately 50 ml of water and deliver into a dry 250 ml beaker. Heat the water in the 250 ml beaker to approximately 40 C. Allow the temperature to stabilize. Accurately measure the temperature of the cold water in the calorimeter and the temperature of the hot water in the beaker immediately before pouring into the calorimeter. Add the hot water to the calorimeter and begin recording the temperature every 10 seconds for 3-5 minutes. (A maximum temperature should be clearly observed in this data.) Determine T for the cold water and record. This is assumed to be the same T for the calorimeter. Determine T for the hot water and record. 2. DETERMINATION OF THE SPECIFIC HEAT CAPACITY OF A METAL iii Rinse and dry the calorimeter. Place 75mL of water into the calorimeter, and complete assembly of the thermometer/stirrer apparatus as near to the picture in Figure 1 as equipment allows. Determine the mass of the water/calorimeter apparatus, and set aside temporarily. Obtain the unknown metal and accurately weigh a sample of approximately 50 g. Record the precise mass of the metal sample.

8 Set up a 600mL beaker containing approximately 400mL of water and heat the water to a boil. Once a boil is achieved record the temperature of the boiling water. Transfer the metal sample to a large, clean, dry test tube and heat the test tube in the boiling water bath for at least 15 minutes to allow the metal to reach the temperature of the boiling water. (Do not allow water to condense inside the test tube. You may find it helpful to cap the test tube with a rubber stopper containing one or more holes to prevent this from happening.) Once the 15-minute heating period of the metal is complete, make one final check of the temperature of the water in the calorimeter and record the temperature. (Do not place a hot thermometer into the cold water!) Pour the metal sample out of the hot test tube into the calorimeter. Cover the calorimeter, and carefully stir the water for 60 seconds. Using the temperature probe, record the temperature every 10 seconds during this 60 second interval. Determine the highest recorded temperature from the graph. 3. NEUTRALIZATION OF HYDROCHLORIC ACID WITH SODIUM HYDROXIDE 1 Rinse and dry the calorimeter. Record the exact concentrations of the HCl and the NaOH solutions. Accurately deliver 50 ml of HCl into the calorimeter. Determine the temperature of the acid. Accurately deliver 50 ml of NaOH into a beaker. Determine the temperature of the base. If it is not equal to the temperature of the acid, you can run cool water on the outside of the beaker to lower the temperature of the base, or you can warm the beaker in your hands to heat base until an equivalent temperature is achieved. Have a stopwatch ready to record temperature readings in the calorimeter every 10 seconds. Add the NaOH solution to the calorimeter and begin recording the temperature of the reaction mixture. Once a maximum has been reached, record the temperature every 30 seconds for 3 minutes. Determine T for the bulk solution and calorimeter (assumed to be equivalent for both). Dispose of the neutralized acid as instructed.

9 Critical Data to Include in your Lab Report: Show all calculations: o Calculate the calorimeter constant and the specific heat capacity of the calorimeter. o Calculate the specific heat capacity of the metal sample. Determine percent error for the specific heat capacity of the metal. o Calculate H rxn per mole of hydrochloric acid neutralized with sodium hydroxide. Determine the percent error for the heat of reaction for the neutralization reaction. (Use the theoretical heat of reaction calculated using heats of formation from your lecture textbook as the true value.) In the measurement of a calorimeter constant,, a negative value is occasionally found. What does a negative value for this constant indicate? If you used 100 ml of HCl solution and 100 ml of NaOH solution in your measurement, would q rxn be larger, smaller, or equal to the value you measured? Why? Would H rxn be larger, smaller, or equal to the value you observed experimentally? Why? Cite references in the format specified by your instructor Endnotes: i Silberberg, M.S. Principles of General Chemistry; McGraw-Hill:Boston, 2007; p 187. ii Adapted from Bishop, Bishop, and Whitten Standard and Microscale Experiments in General Chemistry, 5 th Ed.; Brooks-Cole, iii Adapted from Hall, J.F. Experimental Chemistry, 6 th Ed.; Houghton-Mifflin: New York, 2003

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