Calorimetry and Hess's Law: An Insight into Heat Capacities and Enthalpy of Formation

Introduction

The principles underlying physical chemistry allow for the meticulous exploration of reactions and their energetic profiles. Among these, calorimetry and Hess's Law provide foundational methods for determining the heat involved in chemical processes. This report delves into an experiment aimed at comparing the heat capacities of different types of calorimeters and determining the standard enthalpy of formation (∆Hºf) of magnesium oxide (MgO) utilizing Hess's Law. According to Hess's Law, the total enthalpy change in a reaction is the sum of all changes, regardless of the reaction path.

This experiment focuses on this principle to measure the enthalpy change in forming MgO from its elemental constituents.

Objectives

• To evaluate and compare the heat capacities of a coffee cup calorimeter and a copper calorimeter.
• To accurately determine the standard enthalpy of formation for magnesium oxide by applying Hess's Law.

Methodology

Apparatus and Materials

The experiment utilized two calorimeters (a coffee cup calorimeter and a copper calorimeter), thermometers, Styrofoam cups, beakers, graduated cylinders, hydrochloric acid (HCl), magnesium oxide (MgO), and magnesium (Mg) powder.

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Procedure

Heat Capacity Determination

1. Coffee Cup Calorimeter: A clean and dry coffee cup calorimeter was filled with 50 cm³ of tap water, and its temperature was recorded at one-minute intervals for four minutes. Subsequently, 50 cm³ of hot water was added, and temperature changes were noted every 15 seconds for three minutes.
2. Copper Calorimeter: The procedure was repeated using a copper calorimeter.

Reaction Experiments

1. Magnesium and HCl Reaction: Approximately 1.0-1.1 g of magnesium powder was reacted with 50 cm³ of 2M HCl, and temperature changes were recorded.
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2. Magnesium Oxide and HCl Reaction: Between 1.6-1.8 g of MgO was reacted with 50 cm³ of 2M HCl, with temperature changes noted accordingly.

Results and Analysis

Determination of Heat Capacities

The experiment revealed distinct heat capacities for the two calorimeters. The coffee cup calorimeter demonstrated a higher heat capacity (99.75 J/ºC) compared to the copper calorimeter (27.60 J/ºC), attributed to the insulating properties of the Styrofoam material and the thermal conductivity of copper.

Enthalpy of Formation for Magnesium Oxide

By conducting reactions between magnesium and HCl, and magnesium oxide and HCl, and utilizing known enthalpy changes for the reaction of hydrogen gas with oxygen, the standard enthalpy of formation for magnesium oxide was determined. Applying Hess's Law, the experiment yielded an enthalpy change of -486.19 kJ/mol for the formation of MgO, compared to the literature value of -601.6 kJ/mol, resulting in a 19.18% error. This discrepancy may be attributed to heat loss due to imperfect insulation of the calorimeters and potential pre-reaction of magnesium powder with atmospheric oxygen.

Discussion

The experiment underscored the importance of calorimeter selection based on the specific heat capacity requirements of the reaction being studied. The higher heat capacity of the coffee cup calorimeter suggests it is more suitable for reactions with larger enthalpy changes, where more heat is absorbed or released. Conversely, the copper calorimeter, with its lower heat capacity, might be preferred for reactions with smaller enthalpy changes. The observed error in the enthalpy of formation for MgO highlights the challenges in experimental thermodynamics, including the need for precise measurement and control of external factors such as heat loss and reactant purity.

Coffee-cup calorimeter was calculated that it was higher heat capacity compared to copper calorimeter which is 99.75 J/ºC and 27.60 J/ºC by using the formula given:

q(hot) = q(cold) + q(cal)

q(hot) = m(h) x c x (T(h)- T(f)) = heat lost by hot water

q(cold) = m(c) x c x (T(f) - T(c)) = heat gained by cold water

q(cal) = C(cal) x (T(f)- T(c)) = heat gained by calorimeter

where,

c = specific heat of water = 4.18 J/ gºC

C (cal) = heat capacity of the calorimeter

T (h) = temperature of hot water

T (c) = temperature of cold water

T (f) = final temperature after mixing

m = mass of water (hot or cold)

Conclusion

This investigation into calorimetry and the application of Hess's Law provided valuable insights into the determination of heat capacities and the standard enthalpy of formation for magnesium oxide. While the experiment demonstrated the feasibility of these methods, it also highlighted the critical role of accurate calorimetry and the potential for error due to experimental limitations. Future efforts should focus on minimizing heat loss and ensuring reactant purity to enhance the accuracy of enthalpy measurements.

References

The experiment drew upon foundational principles and methodologies in physical chemistry, as outlined in academic resources and specialized literature on calorimetry and Hess's Law. These sources provide a theoretical basis for the experimental techniques and calculations employed in determining heat capacities and enthalpy changes.