Calculating Mass Of Copper Released During Freezing Using Enthalpy Of Fusion
Understanding the thermodynamics of phase transitions is crucial in chemistry and materials science. One such transition is freezing, an exothermic process where a substance changes from a liquid to a solid state, releasing heat in the process. This article delves into calculating the mass of copper that releases a specific amount of heat during freezing, employing the concept of enthalpy of fusion and the formula q = nΔH, where:
- q represents the heat released or absorbed,
- n is the number of moles,
- ΔH signifies the enthalpy change.
In this article, we will solve a problem involving copper's heat release during freezing, step by step, and explain the concepts behind it to clarify the relationship between heat released, moles, and mass. We'll start by stating the problem, then go through each step of the solution, explaining the chemistry and physics involved. This detailed approach will enhance understanding and retention of the concepts, making them applicable to other scenarios. We'll also discuss why each step is necessary and how it contributes to the final answer. Moreover, we will explore practical applications of these calculations in metallurgy and materials science, where precise control of temperature and phase transitions is crucial.
Copper has a $\Delta H_{\text {fus }} = 13.0 \text{ kJ/mol}$. What mass of copper releases 112.4 kJ of heat as it freezes? Use $q=n \Delta H$.
A. 9.42 g B. 6.75 g C. 549 g D. 1590 g
Before diving into the calculations, it’s essential to understand the enthalpy of fusion (ΔHfus). The enthalpy of fusion is the amount of heat required to change one mole of a substance from a solid to a liquid at its melting point under constant pressure. It is an endothermic process, meaning heat is absorbed by the substance. Conversely, the reverse process, freezing, is exothermic, where heat is released as the substance transitions from a liquid to a solid. For copper, the given ΔHfus is 13.0 kJ/mol, indicating that 13.0 kJ of heat is absorbed when one mole of copper melts. When copper freezes, the same amount of heat is released. Understanding this concept is crucial because it forms the basis for calculating the heat released or absorbed during phase transitions. Additionally, the enthalpy of fusion is a specific property of a substance, and its value is critical in various industrial applications, such as casting, welding, and heat treatment processes, where maintaining precise temperature control is necessary. The sign of ΔH is positive for melting (endothermic) and negative for freezing (exothermic).
To solve this problem, we will use the formula q = nΔH, where q is the heat released, n is the number of moles, and ΔH is the enthalpy of fusion. Since freezing is the reverse process of melting, the heat released (q) will have a negative sign, but we will use the magnitude for calculations and consider the sign at the end. Here’s the step-by-step solution:
1. Identify the Given Values
- Heat released, q = 112.4 kJ
- Enthalpy of fusion for copper, ΔHfus = 13.0 kJ/mol
2. Use the Formula q = nΔH to Find the Number of Moles (n)
Since heat is released during freezing, we consider the process exothermic, and the change in enthalpy (ΔH) for freezing is the negative of the enthalpy of fusion. Therefore, ΔH = -13.0 kJ/mol. However, for calculation purposes, we can use the magnitude and adjust the sign later if needed. The formula q = nΔH can be rearranged to solve for n:
Plugging in the values:
Thus, approximately 8.65 moles of copper release 112.4 kJ of heat when freezing. This step is crucial because it bridges the heat released to the amount of substance involved. Understanding how to manipulate this equation is fundamental in thermochemistry. It allows us to quantitatively relate energy changes with the amount of material undergoing a phase transition. Moreover, this calculation demonstrates the principle of conservation of energy, where the energy released during freezing is directly proportional to the amount of substance solidifying.
3. Convert Moles to Grams
To find the mass of copper, we need to convert moles to grams using the molar mass of copper. The molar mass of copper (Cu) is approximately 63.55 g/mol. The formula to convert moles to grams is:
Substituting the values:
Therefore, the mass of copper that releases 112.4 kJ of heat as it freezes is approximately 549.6 grams. This conversion is a standard procedure in chemistry, allowing us to express amounts of substances in practical units. The molar mass acts as a conversion factor, linking the microscopic world of moles to the macroscopic world of grams, which can be measured in a laboratory or industrial setting. This calculation step is vital in various chemical and engineering applications where precise mass measurements are necessary for controlling reactions and processes.
4. Choose the Correct Answer
Comparing our calculated mass (549.6 g) with the given options, the closest answer is:
C. 549 g
Therefore, the correct answer is C. This final step validates our calculations and demonstrates the practical application of thermochemical principles in solving real-world problems. Selecting the correct answer reinforces the understanding of the entire process, from identifying the given values to performing the calculations and interpreting the results. This skill is invaluable in both academic and professional settings, where accurate problem-solving is critical.
The mass of copper that releases 112.4 kJ of heat as it freezes is approximately 549 grams. Thus, the correct answer is:
C. 549 g
The principles demonstrated in this calculation are crucial in various fields, including metallurgy and materials science. Enthalpy of fusion plays a vital role in processes such as casting, welding, and heat treatment, where controlling the heat released or absorbed during phase transitions is essential for achieving the desired material properties. For example, in casting processes, the amount of heat that needs to be removed to solidify a metal determines the cooling rate, which in turn affects the microstructure and mechanical properties of the final product. Similarly, in welding, understanding the heat released during solidification helps in controlling the weld quality and preventing defects. Moreover, these calculations are fundamental in designing heat exchangers and thermal management systems, where the efficient transfer of heat is critical. In research and development, enthalpy of fusion data is used to characterize new materials and predict their behavior under different thermal conditions. Thus, a solid understanding of these concepts is indispensable for engineers and scientists working with materials at high temperatures or in processes involving phase changes.
In summary, we calculated the mass of copper that releases 112.4 kJ of heat as it freezes by using the formula q = nΔH and converting moles to grams using the molar mass of copper. This problem underscores the importance of understanding thermochemical principles and their application in practical scenarios. Mastering these calculations is essential for students and professionals in chemistry, materials science, and engineering. The ability to relate heat released or absorbed to the mass of a substance undergoing a phase transition is a critical skill in various industrial and research applications. By understanding the fundamental concepts and applying them systematically, we can solve complex problems and gain valuable insights into the behavior of materials under different conditions. The step-by-step approach outlined in this article provides a clear methodology for tackling similar problems, reinforcing the importance of methodical problem-solving in scientific and engineering disciplines.
