Calculate the change in entropy that occurs in the system when 1.00 mole of isopropyl alcohol (C 3 H 8 O) melts at its melting point (-89.5 °C). See Table 11.9 for heats of fusion.

Hello everyone today. We are being asked to consider a system with 1.26 moles of acetone and asked to calculate the change in entropy that occurs in the system when it melts. If its melting point is negative, 94.8°C. And it's heat of fusion is 5. kg per mall. And so the first thing I want to do is we want to consider the equation for our total entropy which is dealt to us is equal to the infill p of a reversible reaction over temperature. So what we're gonna do is we're gonna plug in our values and so for Q We're gonna have our 5.69 kill jules per mole. And since the answer has to be in terms of Jules, we must convert kill jewels, two jewels and we're going to use the conversion factor that one killer jewel is equal to 10 to the third jewels. We are then going to divide this by the total temperature. And as it's seen in the question, since it is in C, we must convert to Kelvin and we simply do that by adding to 73.15 Kelvin. This gives us an answer of 31. jewels per mole kelvin But we're not done yet because we have this 1.26 moles to take care of. And so what we're gonna do is we're gonna take our 31. jewels per mole Kelvin. And to get rid of the units in the denominator, we're going to simply multiply this number by 1. moles. Our units of moles are going to cancel out. We're gonna be left with a final answer of 40 . Jewels Per Kelvin. I hope this helped, and until next time.

Ch.18 - Free Energy and Thermodynamics

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Tro 4th Edition

Ch.18 - Free Energy and Thermodynamics

Problem 31

Chapter 18, Problem 31

Calculate the change in entropy that occurs in the system when 1.00 mole of isopropyl alcohol (C₃H₈O) melts at its melting point (-89.5 °C). See Table 11.9 for heats of fusion.

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Identify the formula for calculating the change in entropy (\( \Delta S \)) during a phase change: \( \Delta S = \frac{q_{\text{rev}}}{T} \), where \( q_{\text{rev}} \) is the heat absorbed or released during the process and \( T \) is the temperature in Kelvin.

Determine the heat of fusion (\( \Delta H_{\text{fus}} \)) for isopropyl alcohol from Table 11.9. This value represents the amount of heat required to melt one mole of the substance at its melting point.

Convert the melting point from Celsius to Kelvin by adding 273.15 to the given temperature: \( T = -89.5 + 273.15 \).

Substitute the values into the entropy change formula: \( \Delta S = \frac{\Delta H_{\text{fus}}}{T} \). Ensure that \( \Delta H_{\text{fus}} \) is in joules if it is initially given in kilojoules.

Calculate \( \Delta S \) using the values obtained in the previous steps to find the change in entropy for the melting of 1.00 mole of isopropyl alcohol.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Entropy

Entropy is a measure of the disorder or randomness in a system. In thermodynamics, it quantifies the number of ways a system can be arranged, with higher entropy indicating greater disorder. When a substance changes state, such as melting, the entropy typically increases because the molecules have more freedom to move in the liquid state compared to the solid state.

Heats of Fusion

The heat of fusion is the amount of energy required to change a substance from solid to liquid at its melting point without changing its temperature. This value is crucial for calculating the change in entropy during phase transitions, as it provides the necessary energy input for the melting process. It is typically expressed in joules per mole (J/mol).

Gibbs Free Energy and Phase Changes

Gibbs free energy is a thermodynamic potential that helps predict the direction of chemical reactions and phase changes. At equilibrium, the change in Gibbs free energy (ΔG) is zero, and the relationship between entropy (ΔS) and enthalpy (ΔH) is given by the equation ΔG = ΔH - TΔS. Understanding this relationship is essential for calculating changes in entropy during phase transitions like melting.