# Thermochemistry Lab Report: Calorimeter Constants, Hess's Law, and Enthalpy Changes

Categories: Chemistry

## Abstract

The aim of these three experiments was to determine the heat capacity of a calorimeter, confirm Hess's Law, and observe enthalpy changes within reactions. By measuring the change in temperature resulting from the interaction of various reactants, we determined both the calorimeter constant and the change in enthalpy for the reactions. The results varied, with some values closely resembling theoretical ones, while others showed greater discrepancies.

## Introduction

The first experiment focuses on finding the calorimeter constant for a polystyrene cup.

During chemical reactions inside a calorimeter, some heat is lost to the surroundings. To ensure accurate results in subsequent experiments, it is crucial to determine the amount of heat lost. The equation used to calculate this constant is derived from the overall heat of the reaction equation:

Overall Heat = - [(Sp.Ht. hotwater * Mass of water * Change in temperature) + (Sp.Ht. coolwater * Mass of water * Change in temperature) + (Cp calorimeter * Change in temperature)]

Since experimental errors are inevitable, three calculations were performed to obtain an average calorimeter constant.

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This experiment is vital for the success of the following two thermochemistry experiments.

The second experiment, known as Hess's Law, aims to confirm this fundamental law. Three reactions are examined, where one of them is the same as the other two, and the heats of reaction for each are measured. Hess's Law states that the heat of reaction for one reaction should equal the sum of the heats of reaction for the other two reactions. The reactions used are:

1. NaOH(s) → Na⁺(aq) + OH⁻(aq)
2. NaOH(s) + H⁺(aq) + Cl⁻(aq) → H₂O(l) + Na⁺(aq) + Cl⁻(aq)
3. Na⁺(aq) + OH⁻(aq) + H⁺(aq) + Cl⁻(aq) → H₂O(l) + Na⁺(aq) + Cl⁻(aq)

To find the heat released by each reaction, a modified version of the overall heat of reaction equation is used:

q = - [Sp.

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Ht. * m * ∆t]

Additionally, changes in entropy (∆S) are calculated using theoretical values from reference tables. Finally, the overall free energy change (∆G) is determined using the equation:

∆G = ∆H - (Temperature * ∆S)

All of this is used to verify Hess's Law by calculating the percent error involved in the experiment.

The third experiment, titled "Thermochemistry: Acid + Base," combines the concepts of the previous two experiments. It observes the change in enthalpy resulting from various reactions between strong and weak acids and bases. Four reactions are investigated:

1. HCl(aq) + NaOH(aq) → NaCl(aq) + H₂O(l)
2. HCl(aq) + NH₃(aq) → NH₄Cl(aq)
3. HC₂H₃O₂(aq) + NaOH(aq) → NaC₂H₃O₂(aq) + H₂O(l)
4. HC₂H₃O₂(aq) + NH₃(aq) → NH₄C₂H₃O₂(aq)

By monitoring the change in temperature resulting from the reaction of an acid and a base, the overall energy change for each reaction (∆H rxn/mole of limiting reactant) is calculated. This experimental value is compared to the theoretical value to determine the accuracy of the experiment.

## Experimental

In order to do any calculation for energy, we first had to find the calorimeter constant. In order to do that, we first took and weighed a polystyrene cup (our calorimeter) and added approximately 100 g of warm water to it. The actual measurements are recorded in Table 1-1. The mass of the cup with the water in it were recorded to find the exact mass of the water added. Next, a cylinder was weighed, like the cup, and about 48 mL of cool water was added. The total was weighed and recorded in the same table. Afterwards, temperature sensors connected through a LabPro device were suspended in the two containers and the calculator’s DataMate program was used to record temperature over a 90 second time interval. After a few seconds of data collection from the separate liquids, they were mixed together and stirred with the sensors until there was no time left. By using Graphical Analysis, a graph of the data was printed, displaying temperature vs. time. Tangent lines were drawn on the graph in order to determine the initial and final temperatures of the two liquids. The above procedure was repeated two more times for the sake of precision. Finally, we calculated the calorimeter constant using the formula listed in the Introduction section.

Table 1-1: Calorimeter Constant Determination
Measurement Value
Mass of polystyrene cup (calorimeter) 52.8 grams
Mass of warm water added to calorimeter 100.5 grams
Mass of cylinder 23.6 grams
Volume of cool water added to cylinder 48 mL

Even though we conducted an experiment to find the heat capacity of a calorimeter, we were given a new value for the constant for experiment 2, due to inaccuracy in our results. For the lab called Hess’s Law, we first started by setting up the calculator to collect temperature data again. The procedure is the same as the one used in the last experiment, except that the time interval is set to 4 minutes. Next, we obtain a polystyrene cup to use as our calorimeter and fill it with 100 g of water. The cup is placed within a 250-mL beaker to keep it in a sustained environment. A temperature sensor is placed in the water and is stabilized. Then, we obtained solid NaOH and weighed about 2 grams to the nearest thousandth decimal point. This value is recorded, along with all other data in Table 2-1. Afterwards, data collection begins and after about 15 seconds, the NaOH is added to the water. The resulting solution is stirred for the duration of the time interval and by using Graphical Analysis a graph is produced. This procedure is repeated twice more for 0.5 M HCl in place of water for one trial, and then 1.0 M HCl and 1.0 M NaOH solution for the third trial. All of the measurements are recorded in the table mentioned above.

Table 2-1: Hess's Law Experiment Data
Trial Mass of NaOH (grams) Initial Temperature (°C) Final Temperature (°C)
1 2.03 grams 23.9°C 19.0°C
2 2.04 grams 23.8°C 19.1°C
3 2.02 grams 24.0°C 18.9°C

For the final experiment, the procedure is very similar to its predecessors. We began by initializing the LabPro and DataMate to collect temperature data over time (this time it is a 180 second interval). First, we measure as close as we can to 50 g of a base of our choice in a 100-mL graduated cylinder. A temperature sensor is placed in the cylinder. Next, we weighed 100 g of a chosen acid in the calorimeter. The calorimeter is placed in a 1000-mL beaker for stability and a temperature sensor is submerged in the acid. After the sensors have a chance to equilibrate, we started to collect data. When about 15 seconds have passed, we poured the base into the calorimeter with the acid and stirred for the duration of the time with both sensors. Then, when time was up, we used Graphical Analysis to print the resulting temperature vs. time graph. This processed is repeated three more times until every combination of strong and weak acids and bases is used.

## Analysis

Data from the first experiment seemed accurate, although determining initial and final points by drawing tangent lines introduced some inherent inaccuracy. Using the formula discussed in the introduction, we calculated the calorimeter constant:

Cp calorimeter = -66.522 J/°C

The average of the three obtained values was 169.255 J/°C, significantly higher than the default value provided for the next lab, which was 15.0 J/°C.

In the Hess's Law experiment, we first found the change in temperature, which was used to calculate the heat released by each equation. The total ∆H was calculated, and the number of moles of the limiting reactant for each reaction was determined. The experimental ∆H rxn/mol NaOH was compared to the theoretical value, resulting in a percent error of 19.24%. The entire class's data yielded a 14.47% error. Theoretical values were then used to calculate ∆H, ∆S, and ∆G for reaction 2, resulting in ∆G = -116.062 kJ/mol.

In the third experiment, calculations included finding ∆H rxn, determining the limiting reactant for each reaction, and calculating experimental values of ∆H rxn/mol of limiting reactant. The percent error for one reaction was 1.25%, while other reactions showed higher discrepancies.

## Conclusion

The results of this experiment were a mix of both very accurate and nowhere close. For the first experiment, the values for the calorimeter constant were very imprecise, ranging from negative values to ten times greater than the theoretical 15.0 J/°C. This is most likely due to a series of miscalculations and human error. In experiment two, the numbers were far more favorable, with a 19.24 % error for our data and a 14.47 % error for the entire class. This number still seems too high to justify the verification of Hess’s Law and should probably be redone with more care in consistently measuring reactants, but other than that, the experiment was completed well enough.

The results for the final experiment are also quite mixed. While some experimental values had only a 1.25 % error, others were grossly erroneous with about 65.1 % error. The most inaccurate data was the ones collected for the reaction of a weak acid and a strong base, which yielded an obviously flawed 300 % error. For the results that were inaccurate, the source of error was most likely to due a miscalculation on my part, possibly in the calculation of the theoretical values, or the experimental for that matter. Much more care must be taken when repeating this lab, for the possible errors are numerous.

The purpose of these three labs were to observe the nature of heat and reactions, which the experiments do rather nicely. The procedures described do an excellent job describing the purpose of each step, though they are easy to do incorrectly. In the end, the experiments yielded mediocre results, a mixed bag of incredibly accurate to just very wrong. Thermochemistry is indeed a rather elusive topic, but these experiments make it much more tangible.

## Recommendations

To improve the accuracy of future experiments, greater attention to detail and precision in measurements is necessary. Redoing certain experiments with a focus on minimizing errors and calibration could yield more reliable results. Additionally, further exploration of thermochemistry concepts and related experiments could enhance understanding and proficiency in this field.

Updated: Dec 29, 2023