Which state in each of the following pairs has the higher...

Which state in each of the following pairs has the higher entropy per mole of substance? (a) $\mathrm{H}_{2}$ at $25^{\circ} \mathrm{C}$ in a volume of 10 $\mathrm{L}$ or $\mathrm{H}_{2}$ at $25^{\circ} \mathrm{C}$ in a volume of 50 $\mathrm{L}$ (b) $\mathrm{O}_{2}$ at $25^{\circ} \mathrm{C}$ and 1 $\mathrm{atm}$ or $\mathrm{O}_{2}$ at $25^{\circ} \mathrm{C}$ and 10 $\mathrm{atm}$ (c) $\mathrm{H}_{2}$ at $25^{\circ} \mathrm{C}$ and 1 $\mathrm{atm}$ or $\mathrm{H}_{2}$ at $100^{\circ} \mathrm{C}$ and 1 $\mathrm{atm}$ (d) $\mathrm{CO}_{2}$ at $\mathrm{STP}$ or $\mathrm{CO}_{2}$ at $100^{\circ} \mathrm{C}$ and 0.1 $\mathrm{atm}$

Which state in each of the following pairs has the higher entropy per mole of substance?
(a) $\mathrm{H}_{2}$ at $25^{\circ} \mathrm{C}$ in a volume of 10 $\mathrm{L}$ or $\mathrm{H}_{2}$ at $25^{\circ} \mathrm{C}$ in a volume of 50 $\mathrm{L}$
(b) $\mathrm{O}_{2}$ at $25^{\circ} \mathrm{C}$ and 1 $\mathrm{atm}$ or $\mathrm{O}_{2}$ at $25^{\circ} \mathrm{C}$ and 10 $\mathrm{atm}$
(c) $\mathrm{H}_{2}$ at $25^{\circ} \mathrm{C}$ and 1 $\mathrm{atm}$ or $\mathrm{H}_{2}$ at $100^{\circ} \mathrm{C}$ and 1 $\mathrm{atm}$
(d) $\mathrm{CO}_{2}$ at $\mathrm{STP}$ or $\mathrm{CO}_{2}$ at $100^{\circ} \mathrm{C}$ and 0.1 $\mathrm{atm}$

Key Concepts

Entropy

Entropy is a thermodynamic property that quantifies the disorder or randomness within a system. It increases with the number of accessible microstates available to a system's particles, reflecting the system's energy dispersal at a microscopic level.

Ideal Gas Law

The ideal gas law (PV = nRT) provides a relationship between pressure, volume, temperature, and the number of moles of a gas. This law is fundamental in understanding how changes in any of these variables can lead to changes in a gas's state properties, including entropy.

Dependence of Entropy on Volume and Pressure

For ideal gases, entropy increases when the volume increases or the pressure decreases, assuming constant temperature. This is because a larger volume allows more spatial distribution of the molecules, increasing the number of available microstates.

Temperature Dependence of Entropy

Temperature plays a crucial role in determining entropy. At higher temperatures, molecules have greater kinetic energy and are able to access a wider range of microstates, resulting in higher entropy per mole.

Molar Quantity and Molar Entropy

The mole is a unit for quantifying the amount of substance, and molar entropy refers to entropy per mole. This concept allows for standard comparisons of entropy across different states, independent of the total amount of substance present.

Transcript

00:01 Let's compare entropy.

00:03 So, myter entropy is a measure of the disorder or the randomness of a system or of a molecule, things like that.

00:10 So we're going to look at some different examples and try to decide which one's going to have a higher entropy.

00:15 So we're looking for the higher entropy.

00:17 So let's look at number one.

00:19 So for number one, we're looking at hydrogen gas at 25 degrees celsius in a 10 -liter container or a 5 -liter container.

00:26 So a way we can kind of compare these two is we know that delta s is equal to.

00:31 In for the moles are the standard the natural log of the final volume over the initial volume.

00:39 So if we're going to compare and see that our vf is greater than our vi, then our delta s would be greater than zero.

00:51 So if we're comparing our 10 liters to our 50, this should be a 50, to our 50 liters, then our 50 liters, 50 liters is going to have the higher entropy because that would be a greater final volume.

01:10 Looking at number two, we have oxygen gas at 25 degrees celsius at one atmosphere or at 10 atmospheres.

01:17 So let's look at an example.

01:20 If we have a gas inside a container at one atmosphere, or 10 atmospheres, as we increase the pressure or in this visual way to see it is by making the volume smaller, we now have to order those tighter and closer together...

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