Which state in each of the following pairs has the higher entropy per mole of substance? (a) H 2 at 25 °C in a volume of 10 L or H 2 at 25 °C in a volume of 50 L

well every once in this video are being asked to identify which one has a higher entry paper mold between equal amounts of N two at 30 degrees Celsius and 15 liters for the volume. And comparing it with N two at 30 degrees Celsius and 65 liters. So let's go ahead and recall what entropy even is. So entropy is a measure of disorder or randomness. So because we have equal amounts of end two at third degree Celsius in liters and end two at 30 degrees Celsius in 65 liters the ladder has the higher entropy. So given that the molecule amount and temperature all the same here, we can only go ahead and compare volume. So comparing volume here. So we're comparing 15 liters versus liters. We see that 65 liters is the greater volume or the larger volume. So because this has a larger volume, this means that we have more room or space for the amount of particles to bump into each other as well as bumping into the walls of the container. This means that there's more mobility and greater randomness or disorder leading to a higher or more entropy. So my answer then is the one with the higher entropy per mole is going to be my end to at 30°C. And that's 65 L. So this right here is going to be my final answer for this problem

Ch.18 - Thermodynamics: Entropy, Free Energy & Equilibrium

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McMurry 8th Edition

Ch.18 - Thermodynamics: Entropy, Free Energy & Equilibrium

Problem 56a

Chapter 18, Problem 56a

Which state in each of the following pairs has the higher entropy per mole of substance? (a) H₂ at 25 °C in a volume of 10 L or H₂ at 25 °C in a volume of 50 L

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Entropy is a measure of the disorder or randomness in a system. In general, the greater the volume a gas occupies, the greater the number of possible positions and arrangements for the gas molecules, leading to higher entropy.

Consider the two states of H₂ gas: one at 10 L and the other at 50 L, both at the same temperature of 25 °C.

Since both samples are at the same temperature, the kinetic energy of the molecules is the same in both cases. Therefore, temperature does not affect the comparison of entropy in this scenario.

The key difference between the two states is the volume. A larger volume allows for more possible microstates (ways to arrange the molecules), which increases the entropy.

Therefore, H₂ at 25 °C in a volume of 50 L has higher entropy per mole of substance compared to H₂ at 25 °C in a volume of 10 L.

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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 microscopic configurations that correspond to a thermodynamic system's macroscopic state. Higher entropy indicates greater disorder and more available microstates, which is crucial for understanding the spontaneity of processes.

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of an ideal gas through the equation PV = nRT. This law helps predict how gases behave under different conditions and is essential for understanding how changes in volume affect the entropy of a gas, as it influences the number of accessible microstates.

Volume and Entropy Relationship

For gases, an increase in volume generally leads to an increase in entropy. This is because a larger volume allows gas molecules to occupy more positions and configurations, resulting in greater disorder. Therefore, when comparing two states of the same substance at the same temperature, the state with the larger volume will typically have higher entropy.

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Textbook Question

When rolling a pair of dice, there are two ways to get a point total of 3(1+2;2+1) but only one way to get a point total of 2(1+1). How many ways are there of getting point totals of 4 to 12? What is the most probable point total?

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