Determining the Heat of Reaction
Anthony Pahl, with partners Eva Carlson, Johanna Christner, and Samantha Johnson
1075H, Department of Chemistry, University of Minnesota with T. A. Anatolii Purchel

Abstract
	Heats of reaction measured in a lab tend to be inaccurate due to the heat lost in the surroundings.  By constructing a calorimeter to quantify this heat lost, an accurate heat of reaction can be determined for an acid-base reaction.  After constructing a calorimeter, it's constant of calorimetry was found using a mixture of two amounts of distilled H2O at different temperatures within the calorimeter.  An acid-base reaction was then performed within between aqueous NaOH and aqueous HNO3.  The heat of the reaction between these two was determined to be 68.5kJ/mol, at 20.3% error between the accepted value found using similar methods of 57kJ/mol.  The calorimeter constants were 104.6J/K and 85.5J/K for the two calorimeters constructed.  The inaccuracies were discussed to be attributed to different methods of the water and the acid-base experiments and the low heat conductivity of polystyrene.
Introduction
	Heats of reaction are difficult to obtain in a lab setting.  After starting a reaction, simply measuring the temperature change will be wildly inaccurate as the heat can be transferred through the air and through the container into the surroundings, skewing the heat of reaction downward significantly.  The purpose of this lab was to construct a simple calorimeter, determine it's calorimeter constant, and then determine the heat of reaction of the reaction between aqueous NaOH and aqueous HNO3 to form aqueous NaNO3 and H2O.  This can be compared to known values to verify the accuracy of the calorimeter.  Once a calorimeter has been constructed, the amount of heat lost during any thermodynamic exchange can be quantified.  Further measurements using this calorimeter can use the calculated calorimeter constant to make accurate change in heat calculations, most used in chemical reactions to find the heat of reaction.  This solves the issue of inconsistent temperature changes when conducting chemical reaction experiments.  Calorimeters such as these are used often in the lab setting, and have been used to determine many different heats of reaction using procedures similar to ours. These heats of reaction have been used to formulate heats of formation for many compounds. These values can be easily obtained through looking online1.
	During this report, the procedure for constructing the calorimeter, determining the calorimeter constant, and finding the heat of reaction for a simple acid-base reaction will be outlined.  The findings of the experimentation will be examined, and sources of error in the data will be discussed.
Experimental
	The required glassware for this lab were multiple beakers to hold water and chemicals and a graduated cylinder.  Other materials include two polystyrene cups, a square of cardboard, and a rubber band.  The apparatuses used to perform the tests were a temperature probe connected to a computer with LoggerPro software, a hot plate, an ice bath, and a magnetic spinning rod.
	Two chemical compounds in solution form were required to conduct the heat of reaction portion of the experiment.  A 6M solution of NaOH and a 3M solution of NaOH were both obtained to vary the test for the heat of reaction.  6M solutions of HNO3 and 3M solutions of HNO3 were also obtained.  These compounds are all corrosive and should be handled with care2,3.  Distilled H2O was also required to determine the constant of calorimetry.
Determining the Constant of Calorimetry
	A calorimeter was constructed out of the polystyrene cups and the cardboard square.  The two cups were placed in one another and the cardboard was placed on top to fully cover the opening of the upper polystyrene cup.  A small hole was poked in the cardboard to allow the temperature probe to fit inside.  A rubber band was around the calorimeter vertically to keep the cardboard in place and to ensure the opening stays covered.  A second calorimeter was also constructed using the same method.
	Two separate amounts of 70mL of distilled H2O were added to two beakers.  One beaker was placed upon a hot plate and the temperature setting was set to 3, a heat close to but not reaching the boiling point for water.  The other beaker was placed in an ice bath.  A stirring rod was placed in the calorimeter.  After five to ten minutes, the water from the ice bath was poured into the calorimeter and the top was replaced.  After another five to ten minutes, allowing the temperature of the calorimeter to lower to the temperature of the cold water, the hot plate was turned off.  The temperature probe was placed in the hot water and the temperature was recorded.  With much haste, the temperature probe was then placed in the cold water and the data collection was started.  The hot water was carefully poured into the calorimeter and the top was replaced.  The calorimeter was placed upon a different hot plate and the spin setting was turned on, agitating the water and fully mixing the two different-temperature amounts of water.  After the data had finished collecting, the temperature right before the hot water was added was recorded and the final temperature of the mixed water was recorded.  This method was repeated twice for each each calorimeter.
Determining the Heat of Reaction
	The procedure for making the temperature measurements is similar to the one used in determining the calorimeter constant, but no heating or cooling was required.  70mL of 6M NaOH was placed in the calorimeter and 70mL of 6M HNO3 was placed in a beaker.  The temperature probe was placed in the calorimeter and the data collection was started.  The HNO3 was then poured into the calorimeter and the cardboard top was replaced and secured.  The spinning mode of the hot plate was turned on to agitate the reaction.  After the data collection had finished, the initial and final temperatures of the reaction were recorded.  This procedure was repeated twice with 70mL of 6M NaOH and 6M HNO3 and once with as 70mL of 3M NaOH and 35mL of 6M HNO3 in calorimeter 1.  This procedure was repeated twice for 70mL 3M NaOH and 70mL of 3M HNO3 in calorimeter two and once for 60mL of 3M of each.
	After the reaction had completed and all data was collected, the product was reacted with baking soda fully.  This disposes of any extra acid or base in the solution for proper disposal down the drain.
Results
Determining the Constant of Calorimetry
	Three temperature times were collected for each trial: the initial temperature of the hot water, the initial temperature of the cold water, and the final temperature after both had been combined fully.  The hot water temperature was measured independently through a temperature probe beforehand.  The initial cold water and final temperatures were taken from the data collection software.  As seen on an graph of trial 1 for calorimeter 2 in Figure 1, the first section of the data collected was the temperature of the cold water as it sits in the calorimeter.  It is labeled as 1.  The very last data point of section 1 was recorded as the initial cold water temperature.  The hot water was then added, and section 2 is the process of the two mixing.  Section 3 is when they are fully mixed, and the very first data point of section 3 was taken for the final temperature of the water.
	The initial temperatures of the first trial for calorimeter 1 were 73.8°C for the hot water and 11.4°C for the cold water.  The final temperature was 38.5°C.  The second trial had hot and cold temperatures of 68.2°C and 3.8°C respectively.  The final temperature for the second trial was 31.3°C.  For the second calorimeter, the temperatures recorded for initial hot water, initial cold water, and final temperature were 72.6°C, 11.4°C, and 38.5°C for trial 1.  The second trial had values of 69.3°C, 12.8°C, 37.1°C for initial temperature of hot water, initial temperature of cold water, and final temperature.  These results were compiled and can be found in Figure 2.
Determining the Heat of Reaction
	Two temperatures were measured throughout the chemical reaction.  Figure 3 displays a graph of the data collected for the third trial of calorimeter 2.  Section 1 is the temperatures collected while the base was in the calorimeter.  The last data point in section one was recorded and was assumed to be the initial temperature of both of the solutions.  Section 2 is when the reaction is occurring.  At section 3, the reaction has completed.  The first data point in section 3 was taken to be the final temperature of the reaction.
	The trials for calorimeter 1 and 70mL of 6M NaOH and  HNO3 gave initial temperature readings of 22.8°C and 22.6°C. The final temperatures were 66.6°C and 66.5°C respectively.  The third trial with calorimeter 1 with 70mL of 3M NaOH and 35mL of 6M HNO3 gave initial and final temperature readings of 22.7°C and 51.4°C.  For calorimeter 2, the first and third trials used 70mL of 3M NaOH and 70mL of 3M HNO3, while the second trial used 60mL of 3M NaOH and 60mL of 3M HNO3.  The results for trials 1, 2, an 3 were 23.2°C and 43.4°C, 22.9°C and 43.0°C, and 23.6°C and 43.2°C.  This data can be found in Figure 4.
Discussion
	To determine the constant of calorimetry, it is assumed that no heat is lost to the environment.  Therefore, the quantity of heat of the cold water, the quantity of heat of hot water, and the quantity of heat of the calorimeter will add up to zero.  We can manipulate this equation to determine the change in heat that went into the calorimeter, and therefore how much heat the calorimeter absorbs per degree kelvin increase in temperature (Equation 1, Appendix). For each trial, the change in temperature was calculated for the cold water, the hot water, and the calorimeter, then the calorimeter constant was calculated.  An average calorimeter constant was found to be 104.6J/K for calorimeter 1 and 85.5J/K for calorimeter 2.
	To determine the heat of reaction, first the total change heat of each reaction was calculated.  Using a similar equation to last time, the change in heat of the reaction and the change in heat of the water and the change in heat of the calorimeter all add up to zero.  We can manipulate this equation to solve for ΔHrxn (Equation 2, Appendix).  Because the solutions react in a 1 to 1 ration (Equation 3, Appendix), we divide the total heat released by either the amount of moles used of NaOH or HNO3. An average of 68.5kJ/mol was calculated for the heat of reaction.
	Using heats of formation found using methods and procedures similar to ours, the accepted heat of reaction for this reaction is 57kJ/mol1 (Equation 4, Appendix).  This gives a percent error for this lab of 20.3%.  There are a few sources of error that can be pinpointed to account for this difference.  While calculating the constant of calorimetry, some time is elapsed between when measuring the hot water initial temperature and when the water is finally combined.  The hot water will inevitably cool down slightly when transferring the liquid.  This error can be decreased by measuring the temperature of the hot water as close to the combination of the liquids as possible.  Any data that is measured using calorimeters is limited due to the assumption that no heat is lost to the surroundings and all is absorbed in the calorimeter.  Heat will escape while transferring liquid and through the calorimeter itself.  Our data is further limited by the fact that the polystyrene cups have such a low heat conductivity.  It is assumed that the initial temperature of the calorimeter is the same as the cold water at the beginning and it's final temperature is equal to the water at the end.  In reality, the polystyrene cup will very negligibly change it's temperature.  It may in fact be more accurate to use a calorimeter constant of zero.
	Other than errors associated with the calorimeter constant, the acid-base reaction portion also has sources of error that will skew the data we get.  While heat is lost while transferring the liquids while calculating the calorimeter constant, none is lost while transferring the room-temperature chemical solutions.  The different properties of the two uses of the calorimeter limits the accuracy at which one can use the calorimeter constant to predict the acid-base reaction absorption.  In addition to this, our solutions for NaOH and HNO3 were not perfect.  Decomposition of the base solutions meant that the molarity of the solutions was less, leading to less chemical reacting and a lower heat of reaction.  This is proved through the reaction with baking soda during the cleanup of the lab.  If each solution had the perfect amount of molar, the reaction would react completely and there final product would be neutral.  After every trial, the baking soda reacted with the product, meaning that there was leftover acid or base (Equation 5, 6, 7, Appendix).
Conclusion
	The heat of reaction of the solutions of NaOH and HNO3 has been determined to be -68.5kJ/mol.  This was determined through construction of a calorimeter and initial testing to find a calorimeter constant.  The acid-base reaction was then performed in the calorimeter, and using the calorimeter constant the heat of reaction was determined.  The value for the heat of reaction calculated using heats of formation found using similar methods is 57kJ/mol, giving a percent error of 20.3%.  The calorimeter constants for the first and second calorimeter were 104.6J/K and 85.5J/K.  Now that the calorimetry constants have been determined, the calorimeters can be used to accurately measure various change in heat reactions in different experiments.
References
(1) Standard Enthalpies of Reaction [Online]; Unknown Year. http://en.wikipedia.org/wiki/Standar d_enthalpy_of_formation (Accessed 11/8/2013)
(2) Sodium Hydroxide; SLS3127 [Online].  ScienceLabs.com: Houston, TX, 10/09/2005
(3) Nitric Acid; SLN2161 [Online].  ScienceLabs.com: Houston, TX, 10/10/2005
Appendix
Ccal=(mcΔThot+mcΔTcold)ΔTcal		(1)
ΔHrxn=(-mcΔTwater-CcalΔTcal)/nreaction	(2)
NaOH(aq)+HNO3(aq) → NaNO3(aq)+H2O(l)	(3)
H++OH- → H2O	(4)
NaHCO3 ↔Na++HCO3	(5)
HCO3-+H+↔H2CO3		(6)
HCO3+OH-↔H2O+CO2	(7)
Figure 1: Data Collection for the Combination of H2O
Figure 2: Results of the Combination of H2O to Determine the Calorimeter Constant

Calorimeter 1
Calorimeter 2
Trial #
1
2
1
2
Initial Temp. Hot Water (°C)
73.8
68.3
69.3
72.6
Initial Temp. Cold Water (°C)
6.4
3.8
12.8
11.4
Final Temp. (°C)
34.7
31.3
37.1
38.5
Cal. Constant (J/K)
109.7
99.3
95.2
75.7
Average Constant (J/K)
104.6
85.5



Figure 3: Data Collection for the Reaction of NaOH and HNO3
Figure 4: Results of the NaOH and HNO3 Reaction

Calorimeter 1
Calorimeter 2
Trial Info
70ml 6M NaOH
70mL 6M HNO3
70ml 6M NaOH
70mL 6M HNO3

70ml 6M NaOH
35mL 6M HNO3

70ml 3M NaOH
70mL 3M HNO3

70ml 3M NaOH
70mL 3M HNO3

70ml 3M NaOH
70mL 3M HNO3

Initial Temp (°C)
22.77
22.63
22.73
69.3
72.6
23.6
Final Temp. (°C)
66.56
66.50
51.38
37.1
38.5
43.2
Heat of Reaction (kJ/mol)
-72.208
-72.109
-74.206
-64.57
-65.61
-62.65
Average Heat of Reaction (kJ/mol)
-72.8
-64.27