Calculate the change in entropy that occurs in the system when 1.00 mole of diethyl ether (C 4 H 10 O) condenses from a gas to a liquid at its normal boiling point (34.6 °C). See Table 11.7 for heats of vaporization.

Hello everyone. Today we are being asked to consider a system with 3.62 moles of acetone. Were then asked to calculate the change in entropy that occurs in a system when it condenses at its boiling point of 56.1°C. And the heat of vaporization is 29.1 kg per mole. So the first thing I wanna do is you want to recall our equation for entropy which is entropy or delta S. Is equal to Q rev. And rev is just the heat that's transferred in a reversible reaction. And then our tea is going to of course stand for temperature. And so we're gonna just plug in our variables that we have and see what we get. So four hour Q rev or the heat transferred at a reversible process is going to be this 29.1 kg jewels per mole. And we also have to consider that our answer has to be in units of jewels per mall kelvin. So this killer jewels must be converted into regular jewels. And to do that we can just use the conversion factor That there's 10 to the third jewels per one killer jewel. And lastly we must divide by our temperature. And we said as before we need to end units of Kelvin. So we must take that 56.1°. Associates and add to 73.15 to it. And we calculate that we get a final answer of 88. jewels per mole kelvin. We must then take into account the molds that we have and so we have to take this value this 88. jewels per mole kelvin. We must multiply by that 3.62 moles of acetone that we have. Our units are gonna cancel that. We're gonna be left with the final value of about roughly 320 jewels per kelvin overall. 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 32

Chapter 18, Problem 32

Calculate the change in entropy that occurs in the system when 1.00 mole of diethyl ether (C₄H₁₀O) condenses from a gas to a liquid at its normal boiling point (34.6 °C). See Table 11.7 for heats of vaporization.

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Identify the process: The problem involves the condensation of diethyl ether from gas to liquid at its boiling point.

Recall that the change in entropy (\( \Delta S \)) for a phase change can be calculated using the formula \( \Delta S = \frac{\Delta H_{\text{vap}}}{T} \), where \( \Delta H_{\text{vap}} \) is the heat of vaporization and \( T \) is the temperature in Kelvin.

Convert the given temperature from Celsius to Kelvin by adding 273.15 to the Celsius temperature: \( T = 34.6 + 273.15 \).

Look up the heat of vaporization (\( \Delta H_{\text{vap}} \)) for diethyl ether from Table 11.7. Ensure the units are consistent, typically in Joules per mole (J/mol).

Substitute the values of \( \Delta H_{\text{vap}} \) and \( T \) into the formula \( \Delta S = \frac{\Delta H_{\text{vap}}}{T} \) to find the change in entropy.

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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 transitions from gas to liquid, such as diethyl ether condensing, the entropy typically decreases because the molecules become more ordered in the liquid state.

Heat of Vaporization

The heat of vaporization is the amount of energy required to convert a unit mass of a substance from liquid to gas at its boiling point. This value is crucial for calculating changes in entropy during phase transitions. For diethyl ether, the heat of vaporization will provide the necessary energy value to determine the entropy change when it condenses.

Phase Change and Temperature

Phase changes, such as condensation, occur at specific temperatures known as boiling or melting points. The normal boiling point of diethyl ether is 34.6 °C, which is the temperature at which it transitions from gas to liquid under standard atmospheric pressure. Understanding the relationship between temperature and phase changes is essential for calculating thermodynamic properties like entropy.