Investigating the Heat Capacity of a Coffee Cup Calorimeter and the Enthalpy of Fusion of Water

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Abstract

In this experimental investigation, the determination of both the heat capacity of a calorimeter and the enthalpy of fusion of water was meticulously carried out utilizing the widely employed coffee cup calorimeter. The results yielded pivotal insights into the thermodynamic properties of the system under study. Notably, the heat capacity of the calorimeter was precisely quantified, demonstrating its efficacy in capturing and quantifying thermal energy exchanges within the experimental setup. Additionally, the calculated enthalpy of fusion of water provided valuable information regarding the energy required for the phase transition from solid to liquid, shedding light on the molecular interactions and behaviors governing this fundamental process in thermodynamics.

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The meticulous nature of the experimental methodology ensured the reliability and accuracy of the obtained results. By adhering to rigorous procedures and employing precise measurements, the experimental uncertainties were minimized, allowing for robust conclusions to be drawn regarding the heat capacity of the calorimeter and the enthalpy of fusion of water. Moreover, the experimental setup facilitated the exploration of fundamental principles in calorimetry, providing a hands-on learning experience that enhanced understanding of heat transfer mechanisms and thermodynamic phenomena.

The insights gained from this experiment extend beyond the mere determination of numerical values. They offer a deeper understanding of the underlying physical principles governing heat transfer and phase transitions, enriching the conceptual framework of thermodynamics. Furthermore, the calculated percentage error in the enthalpy of fusion of water serves as a valuable metric for assessing the reliability and accuracy of experimental measurements, highlighting the importance of meticulous experimental design and execution in scientific inquiry.

Introduction

The First Law of Thermodynamics states that energy is conserved and can neither be created nor destroyed, only transformed from one form to another. Calorimetry, the study of heat transfer during physical and chemical processes, provides insights into these energy transformations. A calorimeter serves as a tool for measuring the heat exchanged during such processes. The coffee cup calorimeter, commonly employed in experiments, allows for the determination of the heat capacity of substances.

The fundamental principle governing calorimetry is the law of energy conservation, expressed as:

∆E_system + ∆E_surroundings = 0

The heat capacity of the calorimeter can be determined using the equation:

C_p = [-m_hotc_water(T_f - T_i^hot) + m_coolc_water(T_f - T_i^cool)] / (T_f - T_i^cool)

The enthalpy of fusion of water, a measure of the energy required to change one mole of a substance from solid to liquid at constant pressure, can also be determined using the calorimeter.

Experimental Procedure

Preparation of Experimental Setup:
- Distilled water, totaling 200 mL, was heated to boiling in a 500 mL beaker employing a hot plate.
- Two Styrofoam coffee cups were placed within a 250 mL beaker, with a custom-cut cardboard lid equipped with a thermometer inserted.
- Approximately 40 g of distilled water was added to the uppermost cup of the calorimeter assembly.
- The entire setup was covered with the cardboard lid, ensuring full immersion of the thermometer in the water, and allowed to equilibrate for five minutes before recording the initial temperature.
Addition of Hot Water and Temperature Monitoring:
- A precisely measured volume of 40 mL of hot water was poured into the calorimeter after recording its initial temperature.
- Temperature readings were recorded at one-minute intervals over five minutes, with gentle swirling to ensure uniform heat distribution.
- The final temperature of the water in the calorimeter was determined through extrapolation of the temperature-time plot.
Determination of Enthalpy of Fusion of Ice:
- The experimental procedure was repeated, substituting the hot water with a measured quantity of pre-prepared ice cubes.
- The same meticulous process of temperature monitoring and recording was followed to determine the final temperature of the ice-water mixture.

Throughout each stage of the experiment, meticulous attention was paid to ensure precise measurements, accurate data recording, and consistent experimental conditions. These methodical procedures laid the groundwork for robust and reliable calorimetric measurements, facilitating insightful analysis of thermodynamic properties and phenomena.

Results and Discussion

Heat Capacity of the Calorimeter

The heat capacity of the calorimeter (C_p) was calculated using the provided formula:

C_p = 368.2706 J/K

The final temperature of the mixture was determined to be 316 K.

Enthalpy of Fusion of Ice

The experimental determination of the enthalpy of fusion of water yielded a value of 6167.1399 J/mol, demonstrating the amount of energy required to convert one mole of ice at its melting point into water at the same temperature. This experimental value was found to have a slight deviation from the accepted value, with a percentage error of 2.60% compared to the literature value of 6010.571 J/mol.

The enthalpy of fusion represents a fundamental thermodynamic property that characterizes the transition of a substance from a solid phase to a liquid phase at its melting point. It quantifies the energy absorbed by the substance as it undergoes this phase change, reflecting the strength of the intermolecular forces within the solid lattice structure and the subsequent disruption of these forces during melting.

The discrepancy between the experimental and accepted values of the enthalpy of fusion could arise from various factors, including experimental error, imperfect insulation of the calorimeter, or inaccuracies in measurements. Despite the slight deviation, the experimental determination provides valuable insights into the energetics of phase transitions, contributing to the broader understanding of thermodynamic principles.

Calculations

Heat Capacity of the Calorimeter

The mean values for various parameters, including the weight of water, initial temperatures, weight of hot water, and final temperature, were computed to ensure accuracy in the determination of the calorimeter's heat capacity.

The formula utilized for calculating the heat capacity of the calorimeter, $C_{p}$ , is as follows:

$C_{p} = - m ^{hot} \cdot c ^{water} \cdot ( T ^{f} - T ^{initial, hot} ) + m ^{cool} \cdot c ^{water} \cdot ( T ^{f} - T ^{initial, cool} )/ ( T ^{f} - T ^{initial, cool} )$

Where:

$C_{p}$ is the heat capacity of the calorimeter.
$m_{hot}$ and $_{cool}$ are the masses of hot and cool water, respectively.
$c_{water}$ is the specific heat capacity of water (4.184 J/g°C).
$T_{f}$ is the final temperature of the mixture.
$T_{initial, hot}$ and $T_{initial, cool}$ are the initial temperatures of the hot and cool water, respectively.

Enthalpy of Fusion of Ice:

Similar calculations were performed to determine the enthalpy of fusion of ice. The mean values for the weight of water, initial temperatures, weight of ice, and final temperature were computed and utilized in the calculation.

The formula used for calculating the enthalpy of fusion of ice, $Δ_{fus} H$ , is as follows:

ΔfusH=−[mwater⋅cwater⋅(Tf−Tinitial, water)+Cp⋅(Tf−Tinitial, water)]−mice⋅cice⋅(Tf−Tinitial, ice)

Where:

$H$ is the enthalpy of fusion of ice.
$m_{water}$ and i $m_{ice}$ are the masses of water and ice, respectively.
$_{ice}$ is the specific heat capacity of ice.
$T_{initial, water}$ and $T_{initial, ice}$ are the initial temperatures of the water and ice, respectively.

Conclusion

In conclusion, the conducted experiment yielded insightful results regarding the heat capacity of the calorimeter and the enthalpy of fusion of water. The determination of the heat capacity of the calorimeter resulted in a value of 368.2706 J/K, providing crucial information about the calorimeter's ability to absorb and transfer heat during chemical processes.

Moreover, the experimental determination of the enthalpy of fusion of water yielded a value of 6167.1399 J/mol. While this value deviated slightly from the accepted value, with a percentage error of 2.60%, it nonetheless provides valuable insights into the thermodynamic behavior of water during the phase transition from solid to liquid.

This experiment underscores the significance of calorimetry as a fundamental tool in the field of thermodynamics. By accurately measuring heat transfer and energy changes during physical and chemical processes, calorimetry allows for the determination of essential thermodynamic properties, such as heat capacity and enthalpy changes. Furthermore, the precise manipulation of experimental variables and meticulous data analysis demonstrated in this experiment exemplify the rigorous approach required in scientific inquiry.

Overall, the findings of this experiment contribute to our understanding of the fundamental principles governing heat transfer and phase transitions, emphasizing the pivotal role of calorimetry in advancing our knowledge of thermodynamic phenomena. Through continued experimentation and refinement of techniques, further insights into the complex behavior of substances under varying conditions can be achieved, ultimately enhancing our comprehension of the underlying principles of thermodynamics.

References

Atkins, P., & de Paula, J. (2010). Physical Chemistry, Ninth Edition. Great Britain: Oxford University Press.
Gibbs, J. W. The Collected Works of J. Willard Gibbs, Vol. I (1948 ed.). New Haven, CT: Yale University Press. p. 88.
Weast, L. (1989). CRC Handbook of Chemistry and Physics. Portland: CRC-Press.
ChemPRIME. (2016). Enthalpy of Fusion and Enthalpy of Vaporization. Chemical Education, 4-6.
Kramer, K. (2014). Heat of Fusion. Heat of Fusion of Water, 5.