Determining Heats of Formation Lab Report - Google Docs

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Unformatted text preview: Abstract This lab used calorimetry and Hess’s law to determine the ΔH f for MgO (s) . The ΔH rxn of the reaction between Mg (s) and HCl as well as the reaction between MgO (s) and HCl was determined by taking the average ΔH rxn of four trials. The mean ΔH rxn of the reaction between Mg (s) and HCl was calculated to be ­428.3182 kJ/mol with a standard deviation of ± 1.2884 kJ/mol while the mean ΔH rxn of the reaction between MgO (s) and HCl was calculated to be ­121.4829 kJ/mol with a standard deviation of ± 3.8361 kJ/mol. Using this information, the ΔH f for MgO (s) was calculated to be 592.6353 kJ/mol with a standard deviation of ± 5.1245 kJ/mol with a relative error of ­1.49%. Introduction In this lab, the heat of formation of MgO (s) was determined by experimental means. This was accomplished through the use of calorimetry. Calorimetry is a method using the heat exchanged between a system and its surroundings to determine the change in energy of a system. Also, the heat of formation of a substance is the change in enthalpy when a substance is created from its constituent elements. This determination was achieved through the use of Mg (s) and MgO (s) and their dissolution in HCl. The following chemical reactions were present in this experiment. M g (s) + 2HCl(aq) M gCl2 (aq) + H 2 O(l) ↔ M gCl + H ↔ 2HCl + M gO ↔H O H 2 + 1/2O2 (g) 2 (aq) 2 (l) (1) 2 (g) (s) (2) (3) Using the ∆H values of the reactions undergone as well as the chemical equations stated above, through Hess’s law, the heat of formation of MgO (s) was determined. Calorimetry is a very important topic and it has many applications in the modern world. For example, a group of researchers have been studying the hydration of hen egg lysozymes through the use of calorimetry. Depending on the temperature of the system, the lysozymes (enzymes that are part of the immune system) of the hen eggs become denatured, destroying the immune system of the embryo. Thus, these researchers used different amounts of water to determine at what temperature the egg becomes denatured. 1 This information could become invaluable to those who raise chickens, as it will allow them to keep the eggs at an ideal temperature. Also, calorimetry can be used to observe emulsion polymerization reactions. Researchers at the University of Basque Country decided to compare calorimetry and raman spectroscopy in the analysis of these reactions. Ultimately, they decided that calorimetry and raman spectroscopy were comparable in terms of the overall conversion. 2 Clearly, calorimetry is a very versatile method that has applications in many different situations. As useful the type of calorimetry used in the lab is, it is not very practical for industrial or professional use. Thus, different types of calorimetry are used in the field. For example, isothermal titration calorimetry is another type of calorimetry used. In this method, the change in heat is measured as different substances are individually added in a step by step process. This is a relatively simple type of calorimetry, making it suitable for students at a university. However, it also has uses in industry such as the pharmaceutical sciences. 3 Clearly, this type of calorimetry is much more accurate and reliable than they type used in this experiment. However, it is obviously significantly more expensive than the calorimeter used in this experiment. Materials and Methods The following were adapted from the steps provided in ‘An Introduction to Chemical Systems in the Laboratory’. 4 In this lab, a basic calorimeter was created with two styrofoam cups and a cork top. The mass of the two cups was measured and recorded. Then, 100 mL of 2 M HCl was placed in the cup and the cup­HCl combination was massed and recorded. 0.24 grams of magnesium ribbon was measured and folded into a ball and set aside for later use. The cork lid was placed on top of the calorimeter and a thermometer was inserted in the center hole and a stirring rod was inserted in the outer hole. The temperature of the HCl in the calorimeter is measured and recorded. The folded magnesium strip set aside earlier was added to the calorimeter and the temperature of the solution was recorded every 15 seconds until the temperature was constant or decreasing. Upon completion of the trial, the calorimeter is emptied and cleaned, dumping all remnants down the sink with excess water. This entire process was repeated 3 more times for a total of 4 trials. The same process was used to test MgO except instead of 0.24 grams of solid, 0.8 grams of MgO was used in the experiment. Specifically, 75 mL of 2 M HCl was placed in the styrofoam cups. Also, the corks used in the experiment did not have a hole for the stirring rod; they only had a hole for the thermometer. Thus, the thermometer was used to stir the solution during each trial. Also, instead of recording the temperature every 15 seconds, a computer program was used to record the temperature in much smaller intervals, creating a relatively continuous graph. Results At the very beginning of the experiment, the mass of the styrofoam cups was determined to be 3.3814 grams. This mass was used in all calculations in which the mass of the calorimeter was needed. Since the Mg (s) and the MgO (s) were dissolved in the 2 M HCl in 4 trials each, the results are best represented in a table. The following table contains the numerical values used and results obtained for the trials using Mg (s) . After the table, the graphs of the temperature change for each respective trial are present. Table 1: Mg (s) Trial Data Trial Mass of Mass with Mass of T o of HCl T f of ΔH rxn Cups (g) HCl (g) Mg (s) (g) (ºC) Solution (°C) (kJ/mol) Q exp 1 3.3814 78.0810 0.2368 21.4 36.7 ­426.9972 0.177 2 3.3814 76.9460 0.2425 21.5 37.5 ­429.4120 0.009 3 3.3814 79.7700 0.2156 21.4 35.1 ­429.4349 0.009 4 3.3814 79.6160 0.2430 21.8 37.2 ­427.4286 0.177 Figure 1: Mg (s) Trial 1 Graph Figure 2: Mg (s) Trial 2 Graph Figure 3: Mg (s) Trial 3 Graph Figure 4: Mg (s) Trial 4 Graph The reaction between the Mg (s) and the HCl is displayed by chemical equation (1). All of the ΔH rxn values stated in (Table 1) were calculated using the following formula. ΔH rxn = (mass of solution) ∙ (specif ic heat of 2 M HCl) ∙ (change in temperature) (4) Since all Q exp values determined by the Q­test were under 0.51, none of the values can be rejected with a 90% certainty of the correctness of the action. Thus, the mean ΔH rxn is ­428.3182 kJ/mol with a standard deviation of ± 1.2884 kJ/mol. The following table contains the numerical values used and results obtained forthe trials using MgO (s) . After the table, the graphs of the temperature change for each respective trial are present. Table 2: MgO (s) Trial Data Trial Mass of Mass with Cups (g) HCl (g) Mass of T o of HCl T f of ΔH rxn MgO (s) (g) (ºC) Solution (°C) (kJ/mol) 1 3.3814 79.2001 0.8324 21.7 29.8 ­108.2405 0.594 2 3.3814 80.3079 0.7891 21.8 30.6 ­125.8598 0.339 3 3.3814 79.9400 0.8232 22.7 31.4 ­118.7048 0.067 4 3.3814 80.7100 0.8233 22.4 31.1 ­119.8841 0.067 Figure 5: MgO (s) Trial 1 Graph Figure 6: MgO (s) Trial 2 Graph Figure 7: MgO (s) Trial 3 Graph Figure 8: MgO (s) Trial 4 Graph The reaction between the MgO (s) and the HCl is displayed by chemical equation (2). Actually, the reaction that was undergone in this experiment is the reverse of the reaction that is displayed in chemical equation (2). All of the ΔH rxn values stated in (Table 1) were calculated using formula (4). Since Q exp for trial 1 is greater than 0.51, this value can be rejected with a 90% certainty of the correctness of the action. Thus, only values obtained in trials 2, 3, and 4 are used in the statistical analysis. The mean ΔH rxn is ­121.4829 kJ/mol with a standard deviation of ± 3.8361 kJ/mol. For chemical equation (3), the ΔH rxn value was looked up and determined to be ­285.8 kJ/mol. Thus, having determined the ΔH rxn for all 3 of the reactions, through the use of Hess’s law the heat of formation of MgO (s) can be determined. The heat of formation of MgO (s) is determined to be ­592.6353 kJ/mol with a standard deviation of ± 5.1245 kJ/mol. According to the literature, the actual heat of formation of MgO (s) is ­601.6 kJ/mol. Using the equation for relative error, the relative error of the calculated heat of formation of MgO (s) is ­1.49%. Discussion The heat of formation of MgO (s) was properly determined by experimental means through the use of calorimetry. Once again, calorimetry is the process in which the ΔH rxn for reactions (1) and (2) were determined by analyzing the change in temperature of the 2 M HCl solution when the Mg (s) or MgO (s) is added. This works because the temperature change of the water is directly proportional to the heat given off by the reaction, assuming that the calorimeter works in a perfect manner and does not allow any heat to escape to the environment. Also, the heat of formation is the amount of heat required to for MgO (s) from its constituent elements, Mg and O 2 . In the experiment, it was decided that 75 mL of 2 M HCl would work better than 100 mL of 2 M HCl because this made the dilution process very easy. The 2 M HCl was created using a 6 M HCl stock solution along with deionized water. Thus, in order to create the 2 M HCl, 25 mL of 6 M HCl and 50 mL of deionized water were combined in the calorimeter. Even though less HCl was used, the same amount of Mg (s) and MgO (s) that was suggested in the manual were used. This was appropriate since the 75 mL of 2 M HCl provided enough HCl to ensure that all of the solid was properly dissolved. Lastly, 2 M HCl was used instead of any other concentration because it was easy to create and the specific heat of 2 M HCl was already known. Through 4 trials of each reaction, the ΔH rxn values weredetermined to be ­428.3182 kJ/mol with a standard deviation of ± 1.2884 kJ/mol for reaction (1) and ­121.4829 kJ/mol with a standard deviation of ± 3.8361 kJ/mol for reaction (2). Using these values, the ΔH rxn for reaction (3) that was looked up, and Hess’s law, the heat of formation of MgO (s) was determined to be ­592.6353 kJ/mol with a standard deviation of ± 5.1245 kJ/mol. Considering that the actual heat of formation of MgO (s) is ­601.6 kJ/mol, as stated in the literature, the relative error of the calculated heat of formation is ­1.49%. This means that the calculated value is 1.49% above what it actually should have been. In terms of possible errors involved in this experiment, they seemed to be minimized, as seen in the results. The calculated heat of formation of MgO (s) was only 1.49% away from the actual value. This is a very accurate result given the sophistication of calorimeter that was used in this experiment. Also, only 1 data point was determined to be an outlier using the Q test, suggesting that the data was precise for the most part. However, one crucial element was ignored during this experiment; the net heat lost to the surroundings. While the calorimeter did a relatively good job of preventing heat loss to the atmosphere, heat was most certainly still lost to the calorimeter itself, the thermometer, and to the atmosphere. Determining the amount of heat lost is very difficult. However, if the heat capacity of the calorimeter vessel and the thermometer was known and integrated into the results, they would likely be more accurate and closer to the actual ­601.6 kJ/mol value. This would be done by measuring the temperature change of both the thermometer and the calorimeter, calculating the heat absorbed by each, and adding that value to the total amount of heat released by the reaction. Since the calorimeter is likely more effective/insulated at lower temperatures, the neat heat loss is likely slightly dependent on the initial solution temperature. However, it is impossible to know just how dependent it is without doing further tests. Chemists likely determine the specific heat of a calorimeter by completing a reaction in which they know exactly how much energy should be given off. Thus, they know exactly how much the temperature of the solution should change if no heat was lost to the calorimeter. When the reaction is actually performed, heat would obviously be lost to the calorimeter, making the solution a lower temperature, leaving the chemist with an expected value and an experimental value. Through several simple calculations, the chemist would easily be able to determine the specific heat of the calorimeter. If the specific heat of 2 M HCl was 3.46 J/g ºC instead of 3.64 J/g ºC, the relative error in the final ΔH f for MgO (s) would be significantly greater. Using this different specific heat, the ΔH rxn for reaction (1) would be ­407.1376 kJ/mol, the ΔH rxn for reaction (2) would be ­115.4755 kJ/mol. Assuming that the same ΔH rxn for reaction (3) is used, the calculated ΔH f for MgO (s) would be ­577.4921 kJ/mol. Using the equation for the relative error, the relative error would be ­4.01%, which is significantly larger than the relative error using the other specific heat. Overall, the experiment was a success. Through the use of calorimetry and Hess’s law, the ΔH f for MgO (s) was determined within 1.49% of its actual value. Other than the possibility of a calorimeter that did not properly insulate the solution, no other major sources of error could be detected. Acknowledgements References 1. Hydration of Thermally Denatured Lysozyme Studied by Sorption Calorimetry and Differential Scanning Calorimetry. Vitaly Kocherbitov and Thomas Arnebrant. The Journal of Physical Chemistry B. 2006. 110 (20), 10144­10150. 2. Monitoring Emulsion Polymerization Reactors:  Calorimetry Versus Raman Spectroscopy. Oihana Elizalde, Maider Azpeitia, Marlon M. Reis, José M. Asua, and Jose R. Leiza. Industrial & Engineering Chemistry Research. 2005. 44 (18), 7200­7207. 3. Isothermal Titration Calorimetry in the Student Laboratory. Lars Wadsö, Yujing Li, and Xi Li. Journal of Chemical Education. 2011. 88 (1), 101­105. 4. An Introduction to Chemical Systems in the Laboratory. Stipes, University of Illinois, Urbana­Champaign. 2015. ...
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