Calorimetry: Heat Capacities, Enthalpies (Heats) of Phase ..., Schemes and Mind Maps of Law

Download Calorimetry: Heat Capacities, Enthalpies (Heats) of Phase ... and more Schemes and Mind Maps Law in PDF only on Docsity! Calorimetry: Heat Capacities, Enthalpies (Heats) of Phase Transitions and Chemical Reactions, and Hess’s Law Goal and Overview The heat capacity of a simple constant-pressure calorimeter will be determined. The calorimeter will be used to find the heat of fusion of ice, the heat capacity of a metal, and the heats of several chemical reactions. The heat of reaction for the oxidation of Mg metal will be calculated using Hess’s Law. Objectives and Science Skills Understand, explain, and apply the concepts and uses of calorimetry. Describe heat transfer processes quantitatively and qualitatively, including those related to heat capacity (including standard and molar), heat (enthalpy) of fusion, and heats (enthalpies) of chemical reactions. Apply Hess's law using experimental data to determine an unknown heat (enthalpy) of reaction. Quantitatively and qualitatively compare experimental results with theoretical values. Identify and discuss factors or effects that may contribute to deviations between theoretical and experimental results and formulate optimization strategies. Suggested Review and External Reading Reference material and textbook sections on thermochemistry, calorimetry, heat capacity, and enthalpy Introduction It is not always convenient or straightforward to study the internal energy changes, ∆𝐸𝐸, of processes happening at constant pressure, such as those occurring in biological systems and in standard lab settings. Enthalpy, H, is a thermodynamic quantity that is defined as a system’s internal energy, E, plus the product of pressure and volume, pV. At constant pressure, enthalpy is equivalent to the total heat content of the system, 𝑞𝑞𝑝𝑝 (or q if it is known that constant pressure conditions are in effect). 𝐻𝐻 = 𝐸𝐸 + 𝑝𝑝𝑝𝑝 at constant 𝑝𝑝 �⎯⎯⎯⎯⎯⎯⎯⎯� ∆𝐻𝐻 = ∆𝐸𝐸 + 𝑝𝑝∆𝑝𝑝 = 𝑞𝑞𝑝𝑝 = 𝑞𝑞 Other important definitions include the system, the substance or substances undergoing the physical or chemical change, and the surroundings, the constituents of the thermodynamic “universe” that either provide heat to or absorb heat from the system. Calorimetry is a technique that can be used to measure heat flow, q. A calorimeter is a calibrated measuring device that allows the amount of heat transferred to or from an object and/or during a physical or chemical change to be quantified. In lab, it is often assumed that all of the heat transfers of interest remain within the calorimeter and its contents, such that the sum of the q terms equals zero. Heat transfer to or from the environment external to the calorimeter and its contents is assumed negligible. Quantifying q: change in temperature (∆𝑇𝑇 ≠ 0) 𝑞𝑞 is proportional to the magnitude of the temperature change as well as heat capacity, the amount of heat required to change the system’s temperature by 1°C. Specific heat capacity, c, is a per-gram value; molar heat capacity, per-mole. 𝑞𝑞 = ∆𝐻𝐻 = 𝐶𝐶�𝑇𝑇𝑓𝑓 − 𝑇𝑇𝑖𝑖𝑖𝑖� = 𝐶𝐶𝑔𝑔𝑔𝑔𝑖𝑖𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔∆𝑇𝑇 = 𝑚𝑚𝑚𝑚∆𝑇𝑇 = 𝑛𝑛𝐶𝐶∆𝑇𝑇 Common heat capacity units 𝐶𝐶𝑔𝑔𝑔𝑔𝑖𝑖𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔 J/℃ c J/g ∙ ℃ C J/mol ∙ ℃ Quantifying q: constant temperature (∆𝑇𝑇 = 0) The enthalpy change associated with the phase change or chemical reaction, ∆ℎ or ∆𝐻𝐻, is given in units of J g⁄ (nonstandard) or kJ mol⁄ (standard). Phase changes and chemical reactions that absorb heat energy are endothermic; those that release heat, exothermic. 𝑞𝑞 = 𝑚𝑚∆ℎ = 𝑛𝑛∆𝐻𝐻 There are four parts to this experiment. First, you will calibrate your calorimeter to determine its heat capacity, 𝐶𝐶𝑐𝑐𝑔𝑔𝑔𝑔 , in J/℃, making sure that the value is within an acceptable range before proceeding. Second, you will determine the heat of fusion of ice, ∆𝐻𝐻𝑓𝑓𝑓𝑓𝑓𝑓, in kJ mol⁄ . Third, the heat capacity of a metal, either Al or Cu, will be determined, and the experimental 𝐶𝐶𝑚𝑚𝑔𝑔𝑚𝑚𝑔𝑔𝑔𝑔 will be compared to that predicted by the Law of Dulong and Petit. Fourth, ∆𝐻𝐻 values for the reactions of Mg with calorimeter very quickly so that the warm water does not have time to cool down appreciably. 7. Record the final temperature reached by the mixture to one decimal place. 8. Remove the thermometer and record the final mass of the calorimeter, lid, and both volumes of water to two decimal places. You cannot complete the rest of the experiment before obtaining satisfactory results for part 1. 9. Calculate the masses of the room temperature water and of the warm water by difference. 10. Calculate 𝐶𝐶𝑐𝑐𝑔𝑔𝑔𝑔 to three significant figures. 𝑞𝑞𝑐𝑐𝑔𝑔𝑔𝑔#1 𝑜𝑜𝑔𝑔 #2 + 𝑞𝑞𝑔𝑔𝑜𝑜𝑜𝑜𝑚𝑚 𝑚𝑚𝑔𝑔𝑚𝑚𝑝𝑝𝑔𝑔𝑔𝑔𝑔𝑔𝑚𝑚𝑓𝑓𝑔𝑔𝑔𝑔 𝑤𝑤𝑔𝑔𝑚𝑚𝑔𝑔𝑔𝑔 + 𝑞𝑞𝑤𝑤𝑔𝑔𝑔𝑔𝑚𝑚 𝑤𝑤𝑔𝑔𝑚𝑚𝑔𝑔𝑔𝑔 = 0 𝑪𝑪𝒄𝒄𝒄𝒄𝒄𝒄#𝟏𝟏 𝒐𝒐𝒐𝒐 #𝟐𝟐�𝑇𝑇𝑓𝑓 − 𝑇𝑇𝑅𝑅𝑅𝑅� + 𝑚𝑚𝑅𝑅𝑅𝑅𝑤𝑤𝑚𝑚𝑤𝑤�𝑇𝑇𝑓𝑓 − 𝑇𝑇𝑅𝑅𝑅𝑅� + 𝑚𝑚𝑤𝑤𝑤𝑤𝑚𝑚𝑤𝑤�𝑇𝑇𝑓𝑓 − 𝑇𝑇𝑤𝑤𝑤𝑤� = 0 Note that this value is either 𝐶𝐶𝑐𝑐𝑔𝑔𝑔𝑔#1 or 𝐶𝐶𝑐𝑐𝑔𝑔𝑔𝑔#2, depending on which parts of the experiment you are assigned (parts 2 and 4a or parts 3 and 4b). Do not go on to parts 2 – 4 before calculating the heat capacity of your calorimeter, which must be between 5.00 and 200. J/℃. Your TA must also check your calculation before you proceed. If the heat capacity is not within the allowed range, repeat part 1 until it is (see your TA for further instructions). You must also get data and calculate 𝐶𝐶𝑐𝑐𝑔𝑔𝑔𝑔 for the calorimeter used by the pair of students with whom you are working. Part 2. ∆𝐻𝐻𝑓𝑓𝑓𝑓𝑓𝑓 of ice Calorimeter #1, 𝐶𝐶𝑐𝑐𝑔𝑔𝑔𝑔#1 11. Record the mass of the calorimeter and lid to two decimal places. 12. Add ~100 mL of room temperature deionized water. 13. Record the mass of the calorimeter, lid, and water to two decimal places. Record room temperature to 1 decimal place. 14. Quickly add ~25 g fully-frozen ice to the calorimeter and water. Immediately cover with the lid and insert the thermometer (with stopper in place). 15. Record the lowest temperature attained by the mixture to one decimal place. 16. Remove the thermometer and record the final mass of the calorimeter, lid, and water to two decimal places. Calculate the masses of room temperature water and of ice by difference. 17. Calculate the heat of fusion of ice in J/g to three significant figures. Assume ice melts at 0.0°C. 𝑞𝑞𝑐𝑐𝑔𝑔𝑔𝑔#1 + 𝑞𝑞𝑔𝑔𝑜𝑜𝑜𝑜𝑚𝑚 𝑚𝑚𝑔𝑔𝑚𝑚𝑝𝑝𝑔𝑔𝑔𝑔𝑔𝑔𝑚𝑚𝑓𝑓𝑔𝑔𝑔𝑔 𝑤𝑤𝑔𝑔𝑚𝑚𝑔𝑔𝑔𝑔 + 𝑞𝑞𝑖𝑖𝑐𝑐𝑔𝑔 𝑚𝑚𝑔𝑔𝑔𝑔𝑚𝑚 + 𝑞𝑞𝑖𝑖𝑐𝑐𝑔𝑔 𝑤𝑤𝑔𝑔𝑚𝑚𝑔𝑔𝑔𝑔 = 0 𝐶𝐶𝑐𝑐𝑔𝑔𝑔𝑔#1(𝑇𝑇𝑓𝑓 − 𝑇𝑇𝑅𝑅𝑅𝑅) + 𝑚𝑚𝑅𝑅𝑅𝑅𝑤𝑤𝑚𝑚𝑤𝑤(𝑇𝑇𝑓𝑓 − 𝑇𝑇𝑅𝑅𝑅𝑅) + 𝑚𝑚𝑖𝑖𝑐𝑐𝑔𝑔∆𝒉𝒉𝒇𝒇𝒇𝒇𝒇𝒇 + 𝑚𝑚𝑖𝑖𝑐𝑐𝑔𝑔𝑚𝑚𝑤𝑤(𝑇𝑇𝑓𝑓 − 0.0℃) = 0 18. Convert to kJ/mol and calculate the percent error in your experimental result relative to a literature value of +6.01 kJ/mol. ∆ℎ𝑓𝑓𝑓𝑓𝑓𝑓 in J g × 18.02 g (water) 1 mol ice (water) × 1 kJ 1000 J = ∆𝐻𝐻𝑓𝑓𝑓𝑓𝑓𝑓 in kJ mol % error = �literature value−experimental value literature value � × 100% Part 3. Specific heat capacity of a metal and the Law of Dulong and Petit Calorimeter #2, 𝐶𝐶𝑐𝑐𝑔𝑔𝑔𝑔#2 Begin the temperature equilibration of the metal before calibrating the calorimeter (part1). Caution Steam, boiling water, hot glassware, hot metal, and hot plates surfaces can cause severe burns. Please be very careful. Do not leave the hot plate and boiling water bath completely unattended. Keep other equipment at a safe distance. Autoclave gloves are not heat-proof and are suitable for only short exposures to heat. 19. Obtain ~30 g Al or Cu metal and record which type of metal you have chosen. 20. Record the mass of metal to two decimal places. 21. Carefully slide the metal pieces into a large labeled test tube. Place the test tube in a water bath made in a 400-mL beaker. The level of the water in the bath should be higher than the level of the metal in the test tube. 22. Place the bath (containing the test tube holding the metal) on a hot plate and heat to gentle boiling for at least 20 – 30 minutes so that the metal can equilibrate to the temperature of the boiling water. 23. Record the temperature of the boiling water to one decimal place. After you have completed part 1 successfully and calculated 𝐶𝐶𝑐𝑐𝑔𝑔𝑔𝑔#2: 24. Record the mass of the calorimeter and lid to two decimal places. 25. Add ~100 mL of room temperature deionized water. 26. Record the mass of the calorimeter, lid, and water to two decimal places. Record room temperature to 1 decimal place. 27. Take the calorimeter containing the room temperature water, lid, and thermometer (with split stopper in place) to your boiling water bath. 28. Quickly and carefully, using the autoclave glove (or hot mitt), gently pour the hot metal into the calorimeter. Immediately cover with the lid, insert the thermometer, and gently swirl. You must transfer the hot metal to the calorimeter very quickly so that the metal does not have time to cool down appreciably. 29. Record the final temperature reached by the mixture to one decimal place. 30. Calculate the mass of room temperature water by difference. 31. Calculate the specific heat capacity of the metal in J/g ∙ ℃. 𝑞𝑞𝑐𝑐𝑔𝑔𝑔𝑔#2 + 𝑞𝑞𝑔𝑔𝑜𝑜𝑜𝑜𝑚𝑚 𝑚𝑚𝑔𝑔𝑚𝑚𝑝𝑝𝑔𝑔𝑔𝑔𝑔𝑔𝑚𝑚𝑓𝑓𝑔𝑔𝑔𝑔 𝑤𝑤𝑔𝑔𝑚𝑚𝑔𝑔𝑔𝑔 + 𝑞𝑞𝑚𝑚𝑔𝑔𝑚𝑚𝑔𝑔𝑔𝑔 = 0 𝐶𝐶𝑐𝑐𝑔𝑔𝑔𝑔#2(𝑇𝑇𝑓𝑓 − 𝑇𝑇𝑅𝑅𝑅𝑅) + 𝑚𝑚𝑅𝑅𝑅𝑅𝑤𝑤𝑚𝑚𝑤𝑤(𝑇𝑇𝑓𝑓 − 𝑇𝑇𝑅𝑅𝑅𝑅) + 𝑚𝑚𝑚𝑚𝑔𝑔𝑚𝑚𝑔𝑔𝑔𝑔𝒄𝒄𝒎𝒎𝒎𝒎𝒎𝒎𝒄𝒄𝒄𝒄(𝑇𝑇𝑓𝑓 − 𝑇𝑇𝑏𝑏𝑜𝑜𝑖𝑖𝑔𝑔) = 0 32. Convert 𝑚𝑚𝑚𝑚𝑔𝑔𝑚𝑚𝑔𝑔𝑔𝑔 in J/g ∙ ℃ to 𝐶𝐶𝑚𝑚𝑔𝑔𝑚𝑚𝑔𝑔𝑔𝑔 in J/mol ∙ ℃ using the molar mass of the metal (26.98 g/mol Al or 63.55 g/mol Cu). 𝐶𝐶𝑐𝑐𝑔𝑔𝑔𝑔#2(𝑇𝑇𝑓𝑓 − 𝑇𝑇𝑅𝑅𝑅𝑅) + 𝑚𝑚𝑓𝑓𝑜𝑜𝑔𝑔𝑓𝑓𝑚𝑚𝑖𝑖𝑜𝑜𝑖𝑖𝑚𝑚𝑤𝑤(𝑇𝑇𝑓𝑓 − 𝑇𝑇𝑅𝑅𝑅𝑅) + 𝑚𝑚𝑀𝑀𝑔𝑔𝑀𝑀∆𝒉𝒉𝟒𝟒𝟒𝟒 = 0 ∆ℎ4𝑏𝑏 in J g MgO × 40.31 g MgO 1 mol MgO × 1 kJ 1000 J = ∆𝐻𝐻4𝑏𝑏 in kJ mol ; ∆𝐻𝐻4𝑏𝑏,𝑔𝑔𝑖𝑖𝑚𝑚 = −146 kJ mol Please do not pour the solution down the drain. Use the liquid waste container. 50. In 1840, Hess stated that the heat absorbed or released by a chemical reaction is the same regardless of whether the reaction takes place in one step or in more than one, so the sum of the ∆𝐻𝐻 values for the steps equals the ∆𝐻𝐻 for the overall reaction. Hess’s Law makes it possible to determine enthalpies of reactions that would be difficult to measure experimentally. Apply Hess’s Law to calculate ∆𝐻𝐻4𝑑𝑑 to three significant figures using your experimental values for ∆𝐻𝐻4𝑔𝑔 and ∆𝐻𝐻4𝑏𝑏, along with given value for ∆𝐻𝐻4𝑐𝑐 . 4a. Mg(s) + 2HCl(aq) → MgCl2(aq) + H2(g) ∆𝐻𝐻4𝑔𝑔,𝑔𝑔𝑖𝑖𝑚𝑚 = −462 kJ mol 4b. MgO(s) + 2HCl(aq) → MgCl2(aq) + H2O(l) ∆𝐻𝐻4𝑏𝑏,𝑔𝑔𝑖𝑖𝑚𝑚 = −146 kJ mol 4c. H2(g) + 1 2 O2(g) → H2O(l) ∆𝐻𝐻4𝑐𝑐,𝑔𝑔𝑖𝑖𝑚𝑚 = −286 kJ mol⁄ 4d. ∆𝐻𝐻4𝑑𝑑 for Mg(s) + 1 2 O2(g) → MgO(s) ∆𝐻𝐻4𝑑𝑑,𝑔𝑔𝑖𝑖𝑚𝑚 = −602 kJ mol⁄ Follow your TA’s instructions regarding waste disposal. Please make sure to give your calorimeter to your TA. All equipment and glassware should be washed thoroughly using 1) soap and tap water, 2) tap water rinses, and 3) a final rinse with deionized water. Results / Sample Calculations 𝐶𝐶𝑐𝑐𝑔𝑔𝑔𝑔#1 and 𝐶𝐶𝑐𝑐𝑔𝑔𝑔𝑔#2 ∆𝐻𝐻𝑓𝑓𝑓𝑓𝑓𝑓 of ice, % error 𝑚𝑚𝑚𝑚𝑔𝑔𝑚𝑚𝑔𝑔𝑔𝑔 ,𝐶𝐶𝑚𝑚𝑔𝑔𝑚𝑚𝑔𝑔𝑔𝑔, % error relative to 3R ∆𝐻𝐻4𝑔𝑔,∆𝐻𝐻4𝑏𝑏, and ∆𝐻𝐻4𝑑𝑑, % error Complete the online inlab or write a lab report as directed by your TA. Discussion Questions and Review Topics What did you find and how did you do it? What were the primary sources of error? How valid were the assumptions made, including that all of the heat transfer remained within the calorimeter and its contents? How could the accuracy of the results be improved? What conclusions can you draw about the experimental method and your results?