Experiment Calorimetry Lab

Experiment 6 ∙ Calorimetry Pre‐lab questions Answer these questions and hand them to the TF before beginning work. (1) What is the purpose of this experiment? _________________________________________________________________________________________________________ _________________________________________________________________________________________________________ (2) How is heat q related to enthalpy change ΔH at constant pressure? _________________________________________________________________________________________________________ _________________________________________________________________________________________________________ (3) You will determine the calorimeter constant Ccal of your calorimeter. What property of a calorimeter does Ccal measure? _________________________________________________________________________________________________________ _________________________________________________________________________________________________________ (4) You will measure the enthalpy change ΔH at constant pressure of several processes. Will these ΔH values be positive or negative? Will heat be absorbed or released? _________________________________________________________________________________________________________ _________________________________________________________________________________________________________ (5) You will calculate several temperature changes ΔT using the formula ΔT = Tmix – Ti. How will you determine the value of Tmix? _________________________________________________________________________________________________________ _________________________________________________________________________________________________________ Experiment 6 Calorimetry Mathematical development The calorimeter constant C cal Calorimetry is the science of measuring the quantities of heat released or absorbed during a chemical reaction. The amount of heat that flows in or out of a system depends on (1) the quantity of matter that constitutes the system, (2) the identity of that matter, and (3) temperature change experienced by the system as it absorbs or releases heat. In equation form q = mCΔT where q represents heat, m is the mass of the system, C is the heat capacity of the system, and ΔT is the temperature change. The heat capacity C is a measure of how a substance responds to the absorption or release of heat; substances that have a low value of C such as iron (C = 0.45 J/(g·°C)) tend to be good con‐ ductors of heat whereas substances that have a high value of C such as water (C = 4.18 J/(g·°C)) tend to be good insulators. A vessel called a calorimeter is needed to hold the sub‐ stances under study. Ideally, the calorimeter is a perfect insula‐ tor, that is, it should prevent the loss of heat from the system to the surroundings and it should not allow heat from the sur‐ roundings to enter the system. In practice, this state of affairs is extremely difficult to achieve: heat is inevitably exchanged between the system and the surroundings. Consider what happens when a quantity of hot water is poured into a quantity of cold water inside a calorimeter. The following relationship accounts for the heat exchanged: heat lost by the hot water = heat gained by the cold water + heat gained by the calorimeter This relationship is expressed symbolically as –qhw = qcw + qcal –mhwChwΔThw = mcwCcw∆Tcw + Ccal∆Tcw (Eqn. 6‐1) where mhw is the mass of the hot water, mcw is the mass of the cold water, Chw is the heat capacity of the hot water, Ccw is the heat capacity of the cold water, ΔThw is the temperature change experienced by the hot water as a result of mixing with the cold water, ∆Tcw is the temperature change experienced by the cold water as a result of mixing with the hot water, and Ccal denotes the calorimeter constant, which is a measure of the calorimeter’s ability to act as an insulator. We now employ the substitutions mhw = ρhwVhw and mcw = ρcwVcw where ρ represents density and V represents volume. For the sake of simplicity we ignore the fact that the density and the heat capacity of water vary with temperature; thus, ρcw = ρhw = ρw and Ccw = Chw = Cw Plugging these substitutions into Eqn. 6‐1 and solving for Ccal gives ⎡ ⎤ ⎛ ΔT ⎞ Ccal = −ρw Cw ⎢Vhw ⎜ hw ⎟ +Vcw ⎥ ⎝ ΔTcw ⎠ ⎣ ⎦ Inserting the numerical values ρw = 1.00 g/mL and Cw = 4.18 J/(g·°C) gives ⎛ 4.18 J ⎞ Ccal = − ⎜ ⎟ ⎝ mL⋅°C⎠ ⎡ ⎤ ⎛ ΔThw ⎞ ⎢Vhw ⎜ ⎟ +Vcw ⎥ ⎝ ΔTcw ⎠ ⎣ ⎦ (Eqn. 6‐2a) You use a slightly modified version of Eqn. 6‐2a to compute Ccal of your calorimeter. The molar enthalpy change of reaction ΔH At constant pressure, the heat in or out of a system is equal to the enthalpy change ΔH. No special arrangement is needed to guarantee that the experiment takes place at constant pres‐ sure: the atmosphere automatically provides a constant pres‐ sure of 1 atm. Suppose that the system consists of a salt MB(s) that ab‐ sorbs heat when it dissolves in water in a calorimeter: MB(s) + heat → MB(aq) The following relationship accounts for the heat exchanged: heat gained by = the system (i.e., by the salt) heat lost by the solution + heat lost by the calorimeter At constant pressure, this heat equation can be expressed as qsys = –qsoln – qcal ΔHsys = –msolnCsolnΔT – CcalΔT (Eqn. 6‐3a) where ΔHsys is the enthalpy change of the system (i.e., the salt), msoln is the mass of the solution, Csoln is the heat capacity of the solution, ΔT is the temperature change experienced by the so‐ lution as a result of the dissolution of the salt, and Ccal is the calorimeter constant. To make the measurement of ΔHsys more meaningful, it is customary to report its value on a per‐mole basis. Thus, we are really interested in ΔHsys/nsys, where nsys is the number of moles of salt that dissolve. We will give the quantity ΔHsys/nsys the symbol ΔH . Because the number of moles n of a substance is related to the mass m of that substance and to its molar mass M by n =m/M dividing both sides of Eqn. 6‐3a by nsys and making the substi‐ tutions ΔHsys/nsys = ΔH and nsys =msys/Msys gives ΔH = − msolnCsolnΔT +Ccal ΔT msys /M sys (Eqn. 6‐4) As before, the mass msoln of the salt solution can be related to its density and its volume: msoln = ρsolnVsoln 19.6 Figure 6‐1 A see‐through view of the calorimeter. An insulated inner cup holds the solutions being studied. The lid of the vessel is equipped with a cap (which should remain in place at all times), a thermometer, and a stir‐ ring ring. For simplicity, we assume that the aqueous salt solution is so dilute that its density ρsoln and heat capacity Csoln are the same as those of pure water, that is, ρsoln = ρw = 1.00 g/mL and Csoln = Cw = 4.18 J/(g·°C). Substituting these values into Eqn. 6‐ 4 gives ⎛ M sys ΔT ⎞ ΔH = − ⎜ ⎟ ⎝ msys ⎠ ⎡⎛ 4.18 J ⎞ ⎤ V +C ⎢⎜ ⎟ soln cal ⎥ ⎣⎝ mL⋅°C⎠ ⎦ (Eqn. 6‐5) You use Eq. 6‐5 to compute the value of the molar enthalpy change ΔH of a variety of reactions. Procedure Determination of C cal The first part of the lab session is devoted to evaluating Ccal of your calorimeter. You use an aluminum vessel as a calorimeter. The solutions that you are studying should be placed in the in‐ sulated inner cup of the calorimeter. The lid of the calorimeter is equipped with a cap (which should remain in place at all times), a thermometer, and a stirring ring (see Figure 6‐1). It is essential that you use the same calorimeter for all your work. Measure out about 50 mL of deionized water using a graduated cylinder. This volume corresponds to Vcw in Eqn. 6‐ Do not boil the water too far ahead of the time that you will be ready to mix it with the cold water in the calorimeter. If you add significantly less than 100 mL of boiling water, you will arrive at a value of Ccal that is negative, which is impossible. Careful! The calorimeter may be quite hot. Put on heavy gloves before attempting to remove the inner cup of the calorimeter. 2a; record the volume in your notebook. Pour the water into the inner cup of the calorimeter. Replace the lid and record the temperature of the water at 30‐sec intervals until it stabilizes. Be sure that the thermometer is suspended near, but not touching, the bottom or sides of the inner cup. Call the tem‐ perature at which the water stabilizes the initial temperature of the cold water Tcw,i; be sure to record it. Using a Bunsen burner, bring about 100 mL of deionized water to a full boil in a beaker. Assume that the temperature of the boiling water is 100 °C; call this the initial temperature of the hot water Thw,i. Do not attempt to measure the tempera‐ ture of the boiling water because you may destroy the tem‐ perature sensor in the thermometer in the process. Put on heavy‐duty gloves, extinguish the burner, pour the boiling wa‐ ter into the calorimeter, replace the lid, and vigorously agitate the contents of the calorimeter by moving the stirring ring up and down. Record the temperature 30 sec after the hot water is added to the calorimeter and at 30‐sec intervals thereafter for at least 5 min; agitate the contents of the calorimeter through‐ out the data acquisition period. You want to observe a tem‐ perature decrease: if you don’t, continue taking data past the recommended 5 min time period. At the end of the data acquisition period, measure the total volume of water Vtot in the calorimeter using a graduated cyl‐ inder. The volume of hot water Vhw in Eqn. 6‐2a equals the to‐ tal volume of water in the calorimeter minus Vcw, that is, Vhw = Vtot – Vcw. Working up the C cal data In your notebook prepare a plot of your Ccal data, plotting time along the x axis and temperature along the y axis. Call the time when you added the hot water to the cold water t = 0. The plot should look like Figure 6‐2. For maximum accuracy the plot should take up a full page in your notebook. Do not wait to prepare this plot and to calculate C cal at home after lab! If your Ccal data is no good, you must know so immediately so that you can take remedial action. The value of Ccal is computed from Eq. 6‐2a: ⎛ 4.18 J ⎞ Ccal = − ⎜ ⎟ ⎝ mL⋅°C⎠ ⎡ ⎤ ⎛ ΔThw ⎞ ⎢Vhw ⎜ ⎟ +Vcw ⎥ ⎝ ΔTcw ⎠ ⎣ ⎦ (Eqn. 6‐2a) You already measured Vcw and Vhw. We now explain how the quantities ΔTcw and ΔThw are determined. Let’s define ΔTcw = Tcw,f – Tcw,i and ΔThw = Thw,f – Thw,i Tcw,i and Thw,i are the initial temperatures of the cold water and of the hot water, respectively; you already measured Tcw,i and you are assuming that Thw,i = 100 °C. Tcw,f and Thw,f are the final temperatures reached by the cold water and the hot wa‐ ter, respectively. It’s clear that Tcw,f = Thw,f because the two bodies of water will have been mixed. Let’s call this common final temperature of the mixture Tmix. Thus, the quantities we are looking for are ΔTcw = Tmix – Tcw,i and ΔThw = Tmix – Thw,i Use a ruler to draw a straight line through the data points lying on the downward sloping portion of the plot. Make sure that the line intercepts the vertical temperature axis erected at t = 0 (see Figure 6‐2). The temperature Tmix corresponds to the y‐intercept of the line and represents the temperature that the Figure 6‐2 Hypothetical data collected during the measurement of Ccal. The hot water is added to the cold water in the calorimeter at t = 0. The line drawn through the data points intercepts the vertical temperature axis at Tmix. mixture would have exhibited if mixing and heat exchange were instantaneous. We are at last ready to calculate Ccal using Eqn. 6‐2b, which is a more detailed version of Eqn. 6‐2a: ⎤ ⎛T ⎞ ⎛ 4.18 J ⎞ ⎡ mix − 100°C + V ⎥ (Eqn. 6‐2b) ⎟ ⎢Vhw ⎜ ⎟ cw ⎝ mL⋅° C ⎠ ⎢ ⎥ ⎝ Tmix − Tcw,i ⎠ ⎦ ⎣ Ccal = − ⎜ Ccal must be a positive number. If you arrive at a negative number, you did something wrong. A common mistake is boil‐ ing the water too far ahead of the time, leading to the addition of significantly less than 100 mL of boiling water. Check your calculations or repeat the experiment. If on the second try you once again arrive at a Ccal that is negative and you’re sure that no errors have been committed, set Ccal equal to zero joules per degree Celsius and continue with the experiment. Experiment # 1 Determination of ΔH of NH4Cl(s) → NH4+(aq) + Cl–(aq) Weigh out 3–4 g of ammonium chloride (NH4Cl(s)). In your notebook record the exact mass taken. Measure out with a graduated cylinder about 100 mL of deionized water and place it in the calorimeter; record the exact volume in your note‐ book. Cover the calorimeter with the lid and record the tem‐ perature of the water in the calorimeter at 30‐sec intervals un‐ til it stabilizes. We will call the temperature at which the water stabilizes the initial temperature Tsoln,i; be sure to record it. Once the temperature of the water in the calorimeter has stabilized, add the NH4Cl(s) to the calorimeter, replace the lid, and agitate the contents of the calorimeter by moving the stir‐ ring ring up and down. Record the temperature 30 sec after the NH4Cl(s) is added to the calorimeter and at 30‐sec intervals thereafter for at least 5 min; agitate the contents of the calo‐ rimeter throughout the data acquisition period. When you add the NH4Cl(s), the temperature of the water in the calorimeter will go down. You must take data until you observe a temperature increase of at least a few tenths of a de‐ gree; you may have to collect data past the recommended 5 min time period. At the end of the data acquisition period, dispose of the so‐ lution in a hazardous waste receptacle. Rinse out the calorime‐ ter and dispose of the rinses in a hazardous waste receptacle. Repeat the procedure in this section, but this time weigh out 4–5 g of NH4Cl(s): you want data from two runs. Experiment # 2 Determination of ΔH of KCl(s) → K+(aq) + Cl–(aq) Weigh out 3–4 g of potassium chloride (KCl(s)). Record the ex‐ act mass taken. Measure out with a graduated cylinder about 100 mL of deionized water and place it in the calorimeter; re‐ cord the exact volume in your notebook. Cover the calorimeter with the lid and record the temperature of the water in the calorimeter at 30‐sec intervals until it stabilizes. Call the tem‐ perature at which the water stabilizes the initial temperature Tsoln,i; be sure to record it. Once the temperature of the water in the calorimeter has stabilized, add the KCl(s) to the calorimeter, replace the lid, and agitate the contents of the calorimeter by moving the stir‐ ring ring up and down. Record the temperature 30 sec after the KCl(s) is added and at 30‐sec intervals thereafter for at least 5 min; agitate the contents of the calorimeter throughout the data acquisition period. When you add the KCl(s), the temperature of the water in the calorimeter will go down. You must take data until you ob‐ serve a temperature increase of at least a few tenths of a de‐ gree; you may have to collect data past the recommended 5 min time period. At the end of the data acquisition period, dispose of the so‐ lution in a hazardous waste receptacle. Rinse out the calorime‐ ter and dispose of the rinses in a hazardous waste receptacle. Repeat the procedure in this section, but this time weigh out 4–5 g of KCl(s): you want data from two runs. Experiment # 3 Determination of ΔH of NH4Cl(s) + KCl(s) → NH4+(aq) + K+(aq) + 2 Cl–(aq) Weigh out 3–4 g of NH4Cl(s) and 3–4 g of KCl(s). In your note‐ book record the exact mass of each compound taken. Measure out with a graduated cylinder about 100 mL of deionized water and place it in the calorimeter; record the exact volume in your notebook. Cover the calorimeter with the lid and record the temperature of the water in the calorimeter at 30‐sec intervals until it stabilizes. We will call the temperature at which the wa‐ ter stabilizes the initial temperature Tsoln,i; be sure to record it. Once the temperature of the water in the calorimeter has stabilized, add the NH4Cl(s) and the KCl(s) to the calorimeter, replace the lid, and agitate the contents of the calorimeter by moving the stirring ring up and down. Record the temperature 30 sec after the NH4Cl(s) and the KCl(s) are added to the calo‐ rimeter and at 30‐sec intervals thereafter for at least 5 min; agitate the contents of the calorimeter throughout the data ac‐ quisition period. When you add the NH4Cl(s) and the KCl(s), the tempera‐ ture of the water in the calorimeter will go down. You must take data until you observe a temperature increase of at least a few tenths of a degree; you may have to collect data past the recommended 5 min time period. At the end of the data acquisition period, dispose of the so‐ lution in a hazardous waste receptacle. Rinse out the calorime‐ ter and dispose of the rinses in a hazardous waste receptacle. Repeat the procedure in this section, but this time weigh out 4–5 g of NH4Cl(s) and 4–5 g of KCl(s): you want data from two runs. Data analysis Experiments # 1 and # 2 You use Eq. 6‐5 to compute the molar enthalpy change ΔH of the reactions carried out in Experiment # 1 and # 2: ⎛ M sys ΔT ⎞ ΔH = − ⎜ ⎟ ⎝ msys ⎠ ⎡⎛ 4.18 J ⎞ ⎤ ⎢⎜ ⎟ Vsoln +Ccal ⎥ ⎣⎝ mL⋅°C⎠ ⎦ (Eqn. 6‐5) For Experiment # 1 the variable Msys refers to the molar mass of NH4Cl (M = 53.49 g/mol) and the variable msys refers to the mass of NH4Cl used. For Experiment # 2 the variable Msys re‐ fers to the molar mass of KCl (M = 74.55 g/mol) and the vari‐ able msys refers to the mass of KCl used. The variable Vsoln re‐ fers to the volume of solution in the calorimeter. The value of ΔT is determined by the same technique em‐ ployed in the measurement of Ccal. Time is plotted along the x axis and temperature along the y axis. Call the time when you added the NH4Cl(s) or the KCl(s) to the calorimeter t = 0. Draw a straight line through the data points lying on the upward sloping (i.e., increasing temperature) portion of the plot, mak‐ ing sure that the line intercepts the vertical temperature axis erected at t = 0. The temperature Tmix corresponds to the y‐ intercept of the line and represents the temperature that the mixture would have exhibited if mixing and heat exchange were instantaneous. In both experiments, ΔT = Tmix – Tsoln,i. Note that ΔT should be a negative number because Tmix < Tsoln,i. Experiment # 3 You use Eq. 6‐3a to compute the enthalpy change ΔH of the re‐ action carried out in Experiment # 3: ΔH = –msolnCsolnΔT – CcalΔT (Eqn. 6‐3a) Performing the substitution msoln = ρsolnVsoln and assuming that ρsoln = 1.00 g/mL and Csoln = 4.18 J/(g·°C) gives Eqn. 6‐3b, which is a more detailed version of Eqn. 6‐3a: ⎡⎛ 4.18 J ⎞ ⎤ ΔH = −ΔT ⎢⎜ ⎟ Vsoln + Ccal ⎥ ⎣⎝ mL⋅° C ⎠ ⎦ (Eqn. 6‐3b) The value of ΔT is determined by the same technique employed in the measurement of Ccal. Time is plotted along the x axis and temperature along the y axis. Call the time when you added the NH4Cl(s) and the KCl(s) to the calorimeter t = 0. Draw a straight line through the data points lying on the upward slop‐ ing (i.e., increasing temperature) portion of the plot, making sure that the line intercepts the vertical temperature axis erected at t = 0. The temperature Tmix corresponds to the y‐ intercept of the line. Note that ΔT = Tmix – Tsoln,i should be a negative number because Tmix < Tsoln,i. Lab report form In (I.A), (II.A), (III.A), and (IV.A) you are asked to submit plots similar to Figure 6‐2. Prepare a separate plot for each run. Give each plot a truly informative title (i.e., don’t just call it “Experiment 1, Run 1”), label the axes, and include appropriate units and divisions of those axes. Draw the straight line from which the value of Tmix is determined and write the value of Tmix on the plot. Do not submit small plots: use a whole sheet of paper. Scale the horizon‐ tal and vertical axes so that the data points occupy most of the area of the plot. (I.A) Prepare a plot of the data collected in the measurement of Ccal. (I.B) Report the quantities needed for the calculation of Ccal according to Eqn. 6‐2b: ⎤ ⎛T ⎞ ⎛ 4.18 J ⎞ ⎡ mix − 100°C + V ⎥ ⎟ ⎢Vhw ⎜ ⎟ cw ⎝ mL⋅° C ⎠ ⎢ ⎥ ⎝ Tmix − Tcw,i ⎠ ⎦ ⎣ Ccal = − ⎜ Vhw [mL] Vcw [mL] Thw,i [° C] 100 °C Tcw,i [° C] Tmix [° C] Tmix – 100 °C [° C] (Eqn. 6‐2b) Tmix – Tcw,i [° C] (I.C) Show the calculation of Ccal according to Eqn. 6‐2b. (I.D) What are the units of Ccal? (II.A) Prepare plots of the data collected in the measurement of ΔH of NH4Cl(s) → NH4+(aq) + Cl–(aq). Experiment 6 ∙ Calorimetry Lab report form Page 2 (II.B) Report the quantities needed in the calculation of ΔH of NH4Cl(s) → NH4+(aq) + Cl–(aq) according to Eqn. 6‐5: ⎛ M sys ΔT ⎞ ΔH = − ⎜ ⎟ ⎝ msys ⎠ ⎡⎛ 4.18 J ⎞ ⎤ ⎢⎜ ⎟ Vsoln +Ccal ⎥ ⎣⎝ mL⋅°C⎠ ⎦ (Eqn. 6‐5) Calculate the value of ΔH of each of your two runs and the mean value of ΔH . The variable Msys refers to the molar mass of NH4Cl (M = 53.49 g/mol); the variable msys refers to the mass of NH4Cl used; Vsoln refers to the volume of solution in the calorimeter. Run msys [g] Vsoln [mL] Tsoln,i [° C] Tmix [° C] ΔT = Tmix – Tsoln,i [° C] C cal ΔH 1 2 mean (II.C) Show the calculation of ΔH for Run 1. (II.D) What are the units of ΔH ? (III.A) Prepare plots of the data collected in the measurement of ΔH of KCl(s) → K+(aq) + Cl–(aq). Experiment 6 ∙ Calorimetry Lab report form Page 3 (III.B) Report the quantities needed in the calculation of ΔH of KCl(s) → K+(aq) + Cl–(aq) according to Eqn. 6‐5. Calculate the value of ΔH of each of your two runs and the mean value of ΔH . The variable Msys refers to the molar mass of KCl (M = 74.55 g/mol); the vari‐ able msys refers to the mass of KCl used; Vsoln refers to the volume of solution in the calo‐ rimeter. Run msys [g] Vsoln [mL] Tsoln,i [° C] Tmix [° C] ΔT = Tmix – Tsoln,i [° C] C cal ΔH 1 2 mean (IV.A) Prepare plots of the data collected in the measurement of ΔH of NH4Cl(s) + KCl(s) → NH4+(aq) + K+(aq) + 2 Cl–(aq). (IV.B) Report the quantities needed in the calculation of ΔH of NH4Cl(s) + KCl(s) → NH4+(aq) + K+(aq) + 2 Cl–(aq) according to Eqn. 6‐3b. Calculate the value of ΔH of each of your two runs and the mean value of ΔH. ⎡⎛ 4.18 J ⎞ ⎤ ΔH = −ΔT ⎢⎜ ⎟ Vsoln + Ccal ⎥ ⎣⎝ mL⋅° C ⎠ ⎦ Run Vsoln [mL] Tsoln,i [° C] Tmix [° C] ΔT = Tmix – Tsoln,i [° C] C cal 1 2 mean (IV.C) What are the units of ΔH? (Eqn. 6‐3b) ΔH Lab report form Post­lab questions (1.a) Let ΔH NH4Cl represent the mean value of ΔH of NH4Cl(s) → NH4+(aq) + Cl–(aq) re‐ ported in (II.B), let ΔH KCl represent the mean value of ΔH of KCl(s) → K+(aq) + Cl–(aq) re‐ ported in (III.B), and let ΔH represent the mean value of ΔH of NH4Cl(s) + KCl(s) → NH4+(aq) + K+(aq) + 2 Cl–(aq) reported in (IV.B). Write a mathematical equation that shows how ΔH NH4Cl and ΔH KCl are related to ΔH. (1.b) Confirm whether the data you collected in Experiment # 3 fits the equation you wrote in (1.a) by completing the following table. Show the calculation of ΔH according to the equation you wrote in (1.a) using data from your two runs in Experiment # 3 and calculate the percent error using percent error = 100% × (ΔHcalc – ΔHreport)/ΔHreport mNH4Cl Run [g] mKCl [g] ΔH ΔH NH4Cl KCl ΔH calculated by eqn. in (1.a) ΔH reported in (IV.B) % error 1 2 Calculation of ΔH according to the equation in (1.a) for Run # 1 in Experiment # 3: Calculation of ΔH according to the equation in (1.a) for Run # 2 in Experiment # 3: Experiment 6 ∙ Calorimetry Lab report form Page 5 (1.c) Regardless of whether your data furnishes agreement or not, which experimental op‐ erations might contribute most to any observed discrepancy? (2) In this experiment you measure enthalpy change ΔH. You are not measuring standard enthalpy change ΔHº. Why are the enthalpy changes you measure not standard? (Consult‐ ing your lecture textbook may help in answering this question.)