Calculate the change in entropy that occurs in the system when 1.50 mol of isopropyl alcohol (C 3 H 8 O) melts at its melting point (-89.5 °C). See Table 12.9 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.19 - Free Energy & Thermodynamics

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Tro 6th Edition

Ch.19 - Free Energy & Thermodynamics

Problem 31

Chapter 19, Problem 31

Calculate the change in entropy that occurs in the system when 1.50 mol of isopropyl alcohol (C₃H₈O) melts at its melting point (-89.5 °C). See Table 12.9 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 12.9. This value represents the amount of heat required to melt one mole of the substance at its melting point.

Calculate the total heat absorbed (\( q_{\text{rev}} \)) by multiplying the heat of fusion by the number of moles: \( q_{\text{rev}} = n \times \Delta H_{\text{fus}} \), where \( n = 1.50 \) mol.

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

Substitute the values of \( q_{\text{rev}} \) and \( T \) into the entropy change formula to find \( \Delta S \): \( \Delta S = \frac{q_{\text{rev}}}{T} \).

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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 amount of energy in a physical system that is not available to do work. When a substance undergoes a phase change, such as melting, the entropy typically increases because the molecules move from a more ordered solid state to a less ordered liquid 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 melting, as it provides the necessary energy input needed to overcome the intermolecular forces holding the solid together.

Phase Change Calculations

Phase change calculations involve using thermodynamic principles to determine changes in energy and entropy during transitions between solid, liquid, and gas states. For melting, the change in entropy can be calculated using the formula ΔS = ΔH_fusion / T, where ΔH_fusion is the heat of fusion and T is the absolute temperature in Kelvin. This approach is essential for quantifying the thermodynamic properties of substances during phase changes.

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Calculate the change in entropy that occurs in the system when 1.50 mol of isopropyl alcohol (C3H8O) melts at its melting point (-89.5 °C). See Table 12.9 for heats of fusion.

Verified Solution

Key Concepts

Entropy

Heats of Fusion

Phase Change Calculations

Calculate the change in entropy that occurs in the system when 1.50 mol of isopropyl alcohol (C₃H₈O) melts at its melting point (-89.5 °C). See Table 12.9 for heats of fusion.