Chapter 4: Problem 82
Calculate \(\Delta S\) for following process: $$ \underset{\text { at } 100 \mathrm{~K}}{X(s)} \longrightarrow \underset{\text { at } 200 \mathrm{~K}}{X(l)} $$ Given : Melting point of \(X_{(s)}=100 \mathrm{~K} ; \Delta H_{\text {Fusion }}=20 \mathrm{~kJ} / \mathrm{mol} ; C_{p, m}(X, l)=10 \mathrm{~J} / \mathrm{mol} \mathrm{K}\) (a) \(26.93 \mathrm{~J} / \mathrm{K}\) (b) \(206.93 \mathrm{~J} / \mathrm{K}\) (c) \(203 \mathrm{~J} / \mathrm{K}\) (d) \(206.93 \mathrm{~kJ} / \mathrm{K}\)
Short Answer
Step by step solution
Calculate Entropy Change Due to Fusion
Calculate Entropy Change Due to Temperature Increase
Calculate Total Entropy Change
Convert Units if Necessary
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Physical Chemistry
In the exercise, we addressed entropy through a process that involves both a phase change and a temperature increase, both of which are key concepts in physical chemistry. These concepts are essential for predicting the behavior of substances in various conditions and for designing processes in both industrial and laboratory settings.
Phase Transition
During the phase transition of substance X in our exercise, energy is added to overcome the forces holding the solid together, allowing it to become a liquid at its melting point. This energy addition results in an entropy change, as the molecules in the solid structure gain freedom of movement in the liquid phase, increasing disorder.
Enthalpy of Fusion
Molar Heat Capacity
With the molar heat capacity provided (\( 10 \text{ J/mol K} \)), we can integrate over the temperature range to find the change in entropy due to the temperature increase. This concept also helps in understanding the heat flow in chemical processes, which is important for tasks like designing thermal systems or evaluating reaction conditions.
Temperature Increase
This increased molecular motion contributes to a higher degree of disorder and results in a positive change in the system's entropy. The computation of this entropy change involves integrating the molar heat capacity of the substance over the temperature range, as demonstrated in the provided solution steps. Temperature increase is a key factor in many scientific and engineering contexts, from weather patterns to the efficiency of engines and refrigerators.